Various researchers have considered the case when the data is sampled from a submanifold embedded in the ambient Euclidean space.

our experiments are carried out on two real-world data sets.


Related Work: Recently there has been significant interest in distributed online learning questions (see for example [8,9,10]).

instead, they may use an arbitrary communication protocol, but make prediction using the cumulative payoff vector (using any past payoff vectors that they could have received) and some regularizer.


In practice, an active-set strategy is introduced to further reduce cost of each iteration to the active size of variables and constraints for primal-sparse and dual-sparse LP respectively, where a primal-sparse LP has most of variables being zero, and a dual-sparse LP has few binding constraints at the optimal solution.

the algorithm then conducts a projected line search to find smallest r ∈ {0, 1, 2, ...} satisfying and update x by x t,k+1 ← (x t,k + β r d * j ) + .


The two types of comparisons are edit distance computations, which take time O(rm) to check distance at most r, and q-gram distance computations, which take time linear in the signature length.

we use binary signatures as a coarse filtering step, but reserve edit distance for ambiguous merging decisions.


We therefore suspect that there is considerable room for improving our analysis of high dimensional data in the sub-exponential decay case.

the approximation property of RKHS of Gaussian kernel has been studied in Steinwart and Christmann [2008], where the margin noise exponent is defined to derive the risk gap.


For controllable generation, SGAN can generate images with high visual quality in terms of both visual comparison and inception score, thanks to the disentangled latent space modeling.

we simply set them equal without heavy tuning 1 .


We next examine the ability of the proposed method in dealing with gross outliers in motion data.

for the sake of objective comparisons we use only implementations available publicly 5 .


For more details and a comparison between FID and Inception Score see Supplement Section 1, where we show that FID is more consistent with the noise level than the Inception Score.

the likelihood heavily depends on the noise assumptions for the real data and can be dominated by single samples [45].


The interactive framework of clustering model has been studied before where the oracle is given the entire clustering and the oracle can answer whether a cluster needs to be split or two clusters must be merged [7,6].

the queries Q ⊆ V × V can be done adaptively.


In our proofs, we relied on the compactness of the set X .

using Lemma (4), we get that Using similar arguments and using Equation (10) we can show that Summarizing, we have lim sup we can conclude that a.s. lim N →∞ To show that MHA is indeed a γ-bounded strategy, we use two special experts H 0,0 , H −1,−1 whose predictions are λ n 0,0 = λ max and λ n −1,−1 = 0 for every n and to shorten the notation, we denote g(y, λ, x) λ(c(y, x) − γ).


we have a rich set of features for each variant (e.g.


Hence, the set of scale-space voxels covered is a 3D box, the width of the bounding box by its height (both discretized by a factor of 8 for efficiency) by 5, covering exactly one "octave" of scale space (i.e.

we want to find points in feature space where the density of the positive set is large, and the density of the negative set is small.


In the machine learning community different needs have led to the development of a separate set of tools.

tangent supports reverse mode and forward mode, as well as function calls, loops, and conditionals.


This results in 3,505,366 games between 206,059 unique players.

we fixed µ 0 = 1200, σ 0 = 400 and computed the log-evidence L := P (y|β, τ ) for varying values of β and τ (see Figure 2 (right)).


The truncation level K c in the MGP is not fixed, but inferred from the adaptive sampler, with threshold parameter κ set to 0.05 (it is recommended to be set small for most applications).

to motivate this model, consider the representation we may also express X = ΨΦ T , with Ψ ∈ R P ×Kc and Φ ∈ R N ×Kc ; the kth column of Ψ is defined by Lu :k and the kth column of Φ defined by Rv :k . Consequently, the low-rank assumption for H yields a low-rank model X = ΨΦ T , precisely as in [17,18].


The tangent space integration, thus, scales better.

the metric tensor at x ∈ M is defined as the inverse of a local diagonal covariance matrix with entries Here x nd is the d th dimension of the n th observation, and ρ a regularization parameter to avoid singular covariances.


We vary the maximum length of words for different tasks to cope with its longest sentence.

in the forward phase (prediction), the representation of each sentence is formed without knowledge of each other.


Isomap (Figure 1(e)) performs poorly on this data set due to the low sampling rate on the manifold and the fact that the true mapping f is not isometric.

if the true p Y follows the change of variable model (1), the recovered g converges to the true f −1 0 in the sense that they both describe a change of variable from the prior distribution p X to the distribution p Y .


A more complete description of Cobot's abilities, and his early experiences as a social agent in LambdaMOO, can be found in (Isbell et al.2000).

we can determine that a feature is relevant for a user if that feature's weight vector is far from that user's bias feature weight vector, and from the all-zero vector.


The first can be bounded by the sum of the expected widths of the confidence intervals corresponding to each context x t i that might be chosen at each round t, where the expectation is over the randomness of the algorithm's distribution π t . A theorem of ?

there are many settings in which the notion of merit we wish to predict may be different or even at odds with the notion of fairness we would like to enforce.


As we see, decreases sharply to less than 5 after all nonzero components have been identified.

(3.9) the dictionary and its corresponding solution x B = x ⇤ B + xB and x N = 0 is optimal for the value of 2 [ ⇤ , max ], where Note that although initially the perturbations are nonnegative, as the dictionary gets updated, the perturbation does not necessarily maintain nonnegativity.


As an example of that, we here consider discriminative factor modeling, in which the factor scores are employed within a nonlinear SVM.

in the E-step, we approximate the posterior of A, {Φ k }, ψ, f , λ and γ by a factorized distribution q(A) k q(Φ k )q(ψ)q(f )q(λ)q(γ) and in the M-step we optimize W and θ, using L-BFGS [23].


There are a number of possible sign-function approximations, including hyperbolic and arc tangent, and shifted sigmoid function, the latter of which is the most flexible because of its free parameter β.

under assumption B, an expression for the resulting α ij can be derived using the weak law of large numbers yielding: where x ∈ C i and x ∈ C j correspond to the samples as they are classified in a previous recognition pass; N i and N j are number of samples from model c i and c j respectively.


The bulk of an ERFNet is made up of standard residual blocks where each full convolution has been replaced by a pair of 1D alternatives: a 3 × 1 convolution followed by a 1 × 3 convolution.

for example, in a Residual Network (ResNet) (He et al., 2016a) this standard block is a pair of sequential 3×3 convolutions.


For a directed graph, the PageRank algorithm [19] aims to measure the nodes' importance by solving the linear problem , where d = 0.15 is called the "teleport" probability, N is the number of nodes and A is the column-normalized adjacency matrix.

our strategy degrades gracefully as the number of stragglers increases, or as the deadline is pulled earlier.


It consists of building a strong classifier as a linear combination of weaklearners, by adding them one after another in a greedy manner.

we dub it as challenging as state-of-the-art results without using additional training data barely reach 65% accuracy.


Equivalence with the ECOC decision rule thus follows from the fact that 3 is the Hamming distance between the appropriate row of the coding matrix and the concatenation of the bits returned from the binary classifiers.

if 7 © acts transitively on W then for all ¥ $ U¥ 21 ¢ W and I ¢ t . Proof.


In other words, we want to minimize H(z|s) and H(s) at every time frame.

the sparsity parameter β was checked for various values from 0 to 0.8, and we used trained-basis models with 5, 10, 20, 40, 80, 160 and 320 bases, as well as the proposed scenario where all the training data is used as a dictionary.


Recall our assumption that the scope of each B C is only a small subset of variables S s . Then, the scope of R x is P S i pQ ( ¢¡ P £ ¥¤ §¦ P ¨ParentsP (% R Q .

these value functions are a weighted linear combination of basis functions, as above, but each basis function is restricted to depend only on a small subset of state variables.


Reinforcement learning (RL) is often used to solve single tasks for which it is tractable to learn a good policy with minimal initial knowledge.

this can be highly inefficient when many identified subgoals correspond to the same underlying skill, but are all used individually as skill goals.


The same figure also shows the one-and two-dimensional marginal distributions for one pair (X, Y ).

checking that the total number of edges is nondecreasing (as a global measure of sparsity) works well as a practical stopping criterion.


Furthermore, we used a generic alphabeta search algorithm for learning.

both players start with a minute on the clock, and gain an additional second every time they make a move.


Using recent results on the properties of random projections, we proved that in sparse spaces, random projections of sizes logarithmic in the original dimension are sufficient to preserve linearity.

we collect 3000 sample transitions for training.


From any initialization point γ (0) ∈ R m + the sequence of hyperparameter estimates {γ (k) } generated via γ (k+1) ∈ A(γ (k+1) ) is guaranteed to converge monotonically to a local minimum (or saddle point) of ( 2).

at any non-minimizing γ the auxiliary cost function L z (γ) obtained from Step 3 will be strictly tangent to L(γ) at γ .


4 Model-Free PAC-Bayes Bound In this section we introduce a PAC-Bayesian bound for model-free reinforcement learning on discrete state spaces.

this time we assume that we are given a prior distribution on the space of value functions, rather than on transition models.


In order to predict units well, the model must have a good understanding of the dynamics of the game as well as the possible strategies taken by players in the game.

we can measure the prediction accuracy of all opponent buildings in a future frame.


A challenge for the interpretation of the principal components (or factors) is that they can be linear combinations of all the original variables.

to get sparse principal components, we add a sparsity constraint to the optimization problem: every column of V should have at most r non-zero entries (the sparsity parameter r is an input), The sparse PCA problem is itself a very hard problem that is not only NP-hard, but also inapproximable [12] There are many heuristics for obtaining sparse factors [2,18,20,5,4,14,16] including some approximation algorithms with provable guarantees [1].


Although it does not correspond to the loss+penalty formulation we have described, it does £nd a "decision hyper-plane" in the predictor space.

we present the resulting margin-maximizing versions of SVMs and logistic regression in section 4.


Eventually, we hope to fully integrate skeleton computation with f/g computation so that the more general problem of shape and surface estimation can be approached in a coherent and unified fashion.

2 shows the network structures for each of these four cases.


As described in Section 2.3, the CorrLDA model first generates topics for the pivot language part of a document, and for the other language parts of the document, the model then uses the topics that were already generated in the pivot language.

acknowledgments We thank Sinead Williamson, Manami Matsuura, and the anonymous reviewers for valuable discussions and comments.


This is because according to (10), when the primal-dual parameters (w, α) converge to the optimal parameters (w * , α * ), we have (∇φ i (w) + λnα i ) → 0, which means that even if the learning rate η t stays bounded away from zero, the procedure can converge.

3 shows more convex-case results (L2-regularized logistic regression) in terms of training loss residual (top) and test error rate (bottom) on rcv1.binary and covtype.binary from the LIBSVM site 2 , protein 3 , and CIFAR-10 4 .


Let r i be a n-dimensional vector defined by r i (v) = 1 if v ∈ V i , and 0 otherwise.

we generalize spectral clustering techniques to hypergraphs, more specifically, the normalized cut approach of [16].


We start by observing that Problem 5 really only depends on the integrals of monomials under the measure µ: for example, if , then we only need to know the integrals over the constituent monomials (y 3,0 : ) in order to evaluate the integral over f n . This suggests that we can optimize over the (parameter) moment sequence y = (y ↵ ) ↵2N P , rather than the measure µ itself.

in typical polynomial optimization, we are only interested in solutions ✓ ⇤ that actually satisfy the given constraints, whereas here we are interested in K solutions , whose mixture satisfies constraints corresponding to the moment conditions (3).


(3 and "(i are the inverse variances in the directions of contraction and elongation respectively.

consider a I-factor PPCA model, having a latent variable Si and visible variables x.


This problem can be cast as The complexity of this bound is XXX.

across the range of ρ, we note that the log-determinant bound is indistinguishable from its relaxed counterpart.


For instance, ENet authors rely on bottleneck residual blocks, sometimes employing dilation in its 3 × 3 convolution, or replacing it by two 1D convolutions (also possibly dilated).

our approach learns the coordinates of the boxes in an end-to-end manner, and provides a generic layer that can be inserted into a ConvNet architecture multiple times.


Definition 1 Two sets A, A ∈ A are said to be neighbors if only a single hypothesis (and its complement, if it also belongs to H) outputs a different value on A and A .

there exists a greedy procedure that yields query sequences that are within an O(log |H|) factor of the optimal search tree depth [GG74, KPB99, Lov85, AMM + 98, Das04], where |H| denotes the cardinality of H. The greedy procedure is referred to as Generalized Binary Search (GBS) [Das04,Now08] or the splitting algorithm [KPB99, Lov85, GG74]), and it reduces to classic binary search in special cases [Now08].


Formally, for any measurable function T : ⊗ k R n → {0, 1}, we have For k = 2, our result implies that, for β < 1, P 0 − P β TV is bounded away from 1.

in this context we establish a lower bound on the critical signal-to-noise ratio below which a rank-one signal cannot be detected.


Later, in our sampling schemes, we will use this lemma to bound the variance of sampling a vector.

a natural and fundamental question in this space, is when can we achieve faster running times by computing the gradients of f i approximately, thereby decreasing iteration costs.


At a high level BMM can be understood as an instance of the general assumed density filtering framework [14] where the algorithm finds an approximate posterior distribution within a tractable family of distributions by the method of moments.

define w k,j α k,j / j α k,j , then where the second equality is by Corollary 1 that the network polynomial is a multilinear function of w k,j and the third equality holds because T F is the set of trees that do not contain w k,j .


We decided to test the simple -model with the convolutional architecture ConvPool-CNN-C by Springenberg et al.

given a denoising function, one can draw samples from the corresponding distribution by creating a Markov chain that alternates between corruption and denoising [9].


3 In this section, we show that the policy gradient theorem does hold in the off-policy setting, when using function approximation for the policy, as long as we use emphatic weightings.

we repeated the experiment in 5.1, with a chosen from {0, 0.25, 0.5, 0.75, 1} and the step-size chosen from {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1}.


As we will see in section 6 , considering uncertainty does not improve the search in our problem.

we define context features at each loop level to represent loop characteristics.


Given a probability mass function P over X, x ∈ Val(X) is said to be a MAP instantiation for P if which means that x is the most likely value of X according to P . In principle a mass function P can have multiple (equally probable) MAP instantiations.

figure 3 shows the classification accuracy for varying values of * that were used to perturb the model (in order to obtain the curves, the technicality was to split the test instances into bins according to the computed value * , using intervals of length 10 −2 , that is, accuracy was calculated for every instance with * between 0 and 0.01, then between 0.01 and 0.02, and so on).


it uses a prior probability distribution ⇡ over its classifiers and keeps track of the current version space, i.e.


(See, for example, [3] and references therein.)

figure 1 shows the curves for a 3wise independent distribution on 8 random variables.


Our work distinguishes itself from these directions mainly in the objective, since we require the non-discrimination to happen in the long-term instead of at any time; this extends the classical batch definitions of non-discrimination in the online setting.

the main representative of algorithms that do not have such a property are the algorithms that achieve low approximate regret compared to a shifting benchmark (tracking the best expert).


From the observational data it is straightforward [12] to obtain the basic graph B(G), a mixed graph 2 obtained from the skeleton of G by orienting the edges in each v-structure.

for the average-case, the proof of Theorem 4.1 exploits the v-structure operation (F 1 ).


In this section, we provide several examples of cascade models that show that our theoretical bounds are applicable in a wide range of scenarios and provide the first results of this type in many areas, including two widely used epidemic models.

and, even more critically for decision makers: how can we modify its course in order to meet specific goals?


A high resolution, zero-dimensional data quantizer is presented as a proof-of-concept demonstration.

visual systems have perfected the art of sensing through billions of years of evolution.


The global three-dimensional structure into which the entire protein folds is referred to as the tertiary structure.

a convolutional neural network [7] with convolutions over (i, j), i.e.


We learn the inverse dynamic models of this robot manipulating M = 15 different loads c 1 , .

in our model all the latent functions share a common covariance function, which reduces the number of free parameters and should thus help to reduce over-fitting.


Spectral clustering can handle complex data of multiple distributions.

then from y i , messages are passed among S 2K i in the sense of minimum distances (or general dissimilarities), thus locally forming an acyclic directed subgraph at each point.


A natural and popular framework for the theoretical analysis of classifiers is the PAC (probably approximately correct) framework [11] which is closely related to Vapnik's work on the generalisation error [12].

we recommend: When training an SVM, always normalise your data in feature space.


coins of A, φ∼Uni(3MAJ n,∆n 1+µ ) (A(φ) = "typical") ≥ 1 − o(1) Assume first that φ ∈ 3MAJ n,∆n 1+µ is chosen at random.

an n-variables 3MAJ formula is a boolean formula of the form where the C i 's are 3MAJ clauses.


Hence, like classical regression trees (Breiman et al., 1984), our tree growing algorithm's time complexity is linear in the number of features and log-linear in the number of examples.

the complexity of finding the new pointer position J t and updating M t at Equations ( 14) and ( 15) varies depending on the nature of .


The entries in the matrix Kt are given by that is the sum of the products of the weights over all paths of length t that start at vertex i and finish at vertex j in the weighted graph on the examples.

such an approach suffers from well known limitations, mostly due to its inability to exploit semantic similarity between terms: documents sharing terms that are different but semantically related will be considered as unrelated.


reparameterization) z = µ + R , where ∼ N (0, I dz ), we can generate samples from any Gaussian distribution N (µ, C) by simulating data from a standard normal distribution, provided the decomposition C = RR holds.

each data point x follows a generative model p ψ (x|z), where this process is actually a decoder that is usually constructed by a non-linear transformation with unknown parameters ψ and a prior distribution p ψ (z).


In the second step the word context model generates all instances w i,j of w i together with their part-of-speech tags t i,j and context words (plate W in the figure).

we show that this also results in substantial performance improvement.


For example, [43,44,64] concatenate the input text to the penultimate layers of the discriminators.

in [38], we have shown that creating positive and negative pairs using source and target data is very effective for SDA.


A MAP configuration is an assignment of values to variables that maximizes the probability (or minimizes the energy) in the MRF.

theorem 2 states that, if exp(w i ) 1, AZ configurations have negligible probability.


To the best of our knowledge, we are the first to study the identifiability and inference of GRUMs with multiple types.

prior work in econometrics has focused on developing models that use data aggregated across types of agents, such as at the level of a geographic market, and that allow heterogeneity by using random coefficients on either agents' preference parameters [7,9] or on a set of dummy variables that define types of agents [6,27], or by imposing additional structure on the covariance matrix of idiosyncratic taste shocks [16].


A naïve approach would be to simply reduce the dimensionality of the gradient vector, gt ∈ R τ = Πg t . ADA-FULL is now directly applicable in this low-dimensional space, returning a solution vector βt ∈ R τ at each iteration.

we summarize the cost of each step in Algorithm 1 and contrast it with the cost of ADA-FULL in Table A.1 in Section A.


They are thus viable for production settings where accessing c is expensive (requiring human labeling), impossible (requiring underlying transformations), or legally inadvisable (sharing protected data).

here, the first term is constant, but expanding the second term provides the following: The last inequality is again up to a constant term.


That approach removes the need for the agents to perform any kind of filtering, but requires the specification of some particular class of policies that return actions for arbitrarily long histories.

in experiments, we demonstrate efficient filtering in a range of multi-agent domains.


We split the observed message sets into training (70%) and hold out (30%), and train and evaluate the random forests using the two datasets.

implementing a message-passing operator for a new function either requires technical expertise, or is computationally expensive, or both.


The average number of nonzeros is about 4000 which should be much larger than k (e.g., 500) for the hashing procedure.

in current practice, methods for approximate near neighbor search often fall into the general framework of Locality Sensitive Hashing (LSH) [10,1].


Recent examples where this has led to significant improvements include unsupervised morphology learning [8], language modeling [9] and image segmentation [10].

the SBP is not conjugate to Bernoulli process observations.


Our approach to policy extraction is based on imitation learning [27,1], in particular, DAGGER [25]the pretrained DNN policy (which we call the oracle) is used to generate labeled data, and then supervised learning is used to train a decision tree policy.

verifying stability of a cart-pole controller.


(Note that we must do this inference without knowing the value of δ.)

the probability that T δ will contain exactly one node in the path is Since, under this conditioning, the single node in the path will be uniformly distributed over the path itself, with half the probability it will be in the lower half of the path -causing the upper half of the path to be revealed.


The reason for choosing deep CNN features in this paper is that by doing so we can demonstrate state-of-the-art image classification performance.

the experimental results on this dataset are shown in Table 4.


The higher an action is ranked by the learner's current policy, the more it is preferred by the learner, thus easier to learn.

in this setting, features are acquired at a cost, such as computation time and experiment expense.


Given a possibly perturbed model M α , in which x ∼ N (0, Q α ), we have y ∼ N(0, S α ), where S α = rI + CQ α C T . Note that S α S α /r does not depend on r when is fixed, as Q α ∝ q ∝ r =⇒ S α ∝ r. Next, we aim to maximize the log-probability of y, which is a vector of N components (or pixels).

4e and f illustrate the procedure to find optimal q/r for a membrane and a plate, respectively, as explained in Section 2.3.


It is easy to verify that this is a smooth and convex function and therefore we can easily adapt ShareBoost to deal with this regularized objective.

the MNIST dataset has been extensively studied and is considered a standard test for multiclass classification of handwritten digits.


In the worst-case we can always bound X ∞ by 1 since X is an orthonormal basis.

the second condition is specific to the power method and requires that the noise term is proportionally smaller when projected onto the space spanned by the top k singular vectors.


As a central optimization problem with a wide variety of applications, online resource allocation problems have attracted a large body of research in networking, distributed computing, and electronic commerce.

applying submodularity of f j , we have α i ≥ f j (Gr j ∪ i) − f j (Gr j ).


FB15K contains 14,951 entities, 1,345 relations, and 592,213 facts.

haar matrices have many desirable properties.


The mixture weights, reported in [33], are similar between the original scVI and our modification (and therefore higher than other mainstream differential expression procedures) and saturate the number of significant genes in this experiment (∼23%).

the bias from the HSIC [17] is of order O( 1 n); it is negligible whenever the batch-size is large enough.


The algorithm recovers the hidden labels and alignments nearperfectly in this case.

this expectation is then used in the M-step to calculate the re-estimation equations for updating the model parameters The posterior p(Φ i , z i |y i ) can be factorized as p zi (Φ|y i )p(z i |y i ).


Here, we briefly discuss some concrete examples of graphs G, and show how the regret performance of our algorithms depend on their structure.

if ad i is for running shoes, and ad j is for wheelchair accessories, then a user who clicked on one ad is unlikely to clique on the other.


The dynamics of the system are nonlinear.

we restrain the policy search to a set of policies that have a low estimated Bellman error when their values are approximated using the provided features, knowing that the optimal policy has a low Bellman error.


The GRU controls the past information by having two gates: an update gate and reset gate.

our procedure P δ (•) has minimal impact on the minimization of the loss function.


Repeating this process log 2 m times gives rise to a partition of the unit hypercube into m d hypercubes of identical size.

finally, given {X j , Y j } i−1 j=1 the random variable X i does not depend in any way on f . Let fn : [0, 1] d → R denote an estimator based on the training samples {X i , Y i } n i=1 .


Moreover, RMHMC suffers from expensive inner iteration.

riemann manifold Langevin dynamics (RMLD) and Riemann manifold HMC (RMHMC) [13], are invented for better performance but still on the task of sampling in Euclidean space, where the target variable is treated as the global coordinates of some distribution manifold.


This usually results in about 10000 neural network training epochs, and takes about 2.5 hours to complete, depending on task parameters and number of nodes.

φ X is calculated by finite differencing.


In practice, the estimated transition matrix has only one eigenvalue with unit magnitude and lim e→∞ ( ĀP ) e converges to a global stationary distribution.

note that, in an actual implementation, one would use a low-rank reconstruction by zeroing-out the eigenvalues that are not equal to 1 in Λ to form ( ĀP ) r := V P ( ΛP ) r ( V P ) −1 = ( ĀP ) ∞ , where ( ΛP ) r ∈ R M K×M K is a diagonal matrix with only K non-zero entries, corresponding to the eigenvalues which are 1.


From a mathematical perspective, it would be interesting to know if it is possible to remove the logarithmic factor in our main result.

for r > m polylog(m) , this bound exceeds the number m 2 of possible observations.


The probability distribution that x t = [x t σµ ] is expressed as where ⟨. . .⟩ A,W t ,X t denotes the average over the graph A, the random linear transform W t , and the state X t of the previous layer.

the NMI is defined by We adopt this measure as the error function for the readout classifier.


Traditional winner-take-all network This is a special case of our network with N groups, each containing one of the N neurons.


In this scheme the estimate will be based on fewer samples, but the samples that are used will be less correlated because they are more distant from each other in the Markov chain.

2 Algorithms 1 and 2 represent two of the three key ideas behind our proposal: both Gibbs sampling and Rao-Blackwellized estimation can be implemented efficiently using message passing on a junction tree.


The action set depends on the task, as described in Figure 2.

no forces or motion are allowed in the third dimension.


As with the speech signals discussed in section 2.2, the value becomes smaller as ω increases, and thus, the gain of W (ω) tends to decrease.

figure 5 shows spectrograms of reverberant and dereverberated speech signals when rtime was 1.0 sec.


The sequential nature of decision making in RL is inherently different than the one-step decisions in supervised learning, and in general requires some form of planning [2].

in this section we introduce a general policy representation that embeds an explicit planning module.


In contrast with minimum cut, average cut and normalized cut tend to generate more balanced clusters.

let cut i be the minimal cut with the size of the smaller subset is i, i.e., Clearly, we have 4 is a constant.


The generative process of mGDMF is presented below and the graphical model of mGDMF can be found in the supplementary.

poisson-based dynamic matrix factorization models are recent advances for modeling dynamic data, such as dPF [16] and DCPF [34] for recommendations.


We believe that these shortcomings, as well as the weak spot of RL models in not taking into account the internal drive state of the animal, all arise from lack of an integrated view toward learning and motivation.

it has been argued by some authors [14] that even though habitual responses are insensitive to sensory-specific satiety, they are sensitive to motivational manipulations in a general, outcomeindependent way.


Putting all t he data in memory is simpler to code and results in faster running times.

maximize the margin (distance) between the parallel separating planes with respect to both orientation (w) as well as location relative to the origin b).


V in R is equal to the weighted fourth cummulant, and a component with a large cummulant should be split.

the key of our discussion is the following two symmetric properties, which are satisfied by mixture models; ).


In this case, the epigraph of Φ is a polyhedral cone.

by Lemma 3.4, As noted before, since W is a polyhedron, w t is (generally) attained at the vertices.


The log loss of the Bayesian predictor on data y ≤T := (y 1 , .

our algorithm simply maintains one weight per model/task pair and does not rely on sampling (often used for multitask learning).


. . , q ,K }, which means (q − a)/(b − a) ∼ Beta(K, 1) [19], from which µ max = E[x ] = (a + Kb)/(K + 1).

our results can be extended to multiple issues.


At a higher level, the algorithm partitions the n active queries evenly into log n epochs, and level sets of f are estimated at the end of each epoch by comparing (uniform) confidence intervals on a dense grid on X .

there is an explicit gap between local minimax rates of active and uniform query models.


We demonstrate that shape contexts greatly simplify recovery of correspondences between points of two given shapes.

the literature in computer vision and pattern recognition is full of definitions of shape descriptors and distance measures, ranging from moments and Fourier descriptors to the Hausdorff distance and the medial axis transform.


More precisely, we shall consider a variational distribution that consists of a recognition model [4,2,10,8,15] which is parametrized by a "reverse" sigmoid network that predicts the latent vector x i from the associated observation y i : The variational parameters are contained in matrix V (also the bias terms).

for such cases, reparametrization could be computationally more efficient than local expectation gradients since the latter approach will require to apply 1-D numerical integration to estimate the integral in (11) or the integral in ( 17) 2 which could be computationally more expensive.


In recent work, Chan et al [CDSS14] presented an approach employing an intricate combination of dynamic programming and linear programming which yields a poly(k/") time algorithm for the above problem.

in this terminology, our learning problem is exactly the problem of agnostically learning the class of k-flat distributions.


Cats, many species of monkeys, and humans exibit ocular dominance stripes, which are alternating areas of primary visual cortex devoted to input from (the thalamic relay associated with) just one or the other eye (see Erwin et aI, 1995;Miller, 1996;Swindale, 1996 for reviews of theory and data).

second, this value of C>w can be used to calculate the value of the normalisation parameter ).+ that affects the growth of 8W+ and 8W-.


The value of ξ i reflects the difficulty of task t i -a small ξ i suggests a large discriminant margin, indicating that the task is easy with a rare chance to make mistakes; while a large ξ i suggests that the task is hard with a higher chance to make mistakes.

many learning tasks require labeling large datasets.


Each silhouette subtends 12.5º to ensure that its entire shape cannot be characterized with a single fixation.

, where the entropy of a distribution P(x) is defined as .


Specifically: • We extend fast Kronecker-based GP inference (e.g., [14,15]) to account for non-grid data.

all patterns are shown in the supplement.


Following existing literature [1,9], we work with similarity graphs -where presence of an edge would mean two nodes are similar; and derive the following (supplementary material, Section C). . Then, for Proof.

we confine ourselves to specific sets of interest in our problem.


We can see that for larger updates of the synapses (κ = 0.1) the network converges faster.

we start approximating the terms N ǫ and (N − 1) ǫ by the sum of all pre-synaptic efficacies ǫ ik : This can be done for large N and if we suppose that the distribution of ǫ ik is the same for all i. E diss is now defined in terms of each individual neuron i as: An update of ǫ ij occurs when a spike from the pre-synaptic unit j induces a spike in a post-synaptic unit i.


However, most techniques for dimensionality reduction require a high computational throughput to transform images from the large input data space to the feature subspace.

a second network with userprogrammed coefficients performs classification with Manhattan distances.


Using GANs to generate simple colored objects, Figure 7a-d show sampled images and model collapse analyses.

in those works it is often seen as a minor detail in a larger architecture which is tuned to a specific task and experimental project, and discussions of this necessity are scarce.


RSA revealed that the representational structures in the inferotemporal (IT) cortex of natural objects are highly similar between human and monkey [12] and a continuum in the abstract representation of biological classes exist in human ventral object visual cortex [2].

if each single stimulus is modelled as a condition in X and regularization is used during regression, the correlation between β of temporally adjacent stimuli is higher primarily because of the autocorrelation property of the noise.


We applied our estimator in the SGD and SVRG frameworks, and analyzed convergence.

while it is usually possible to compute the gradient of Σ f (A(θ)), this is typically very expensive.


In the limit, Λn → Λ Y = Λ X + Λ Z , a sum of a rank-k matrix and a diagonal matrix.

we present an estimator which is appropriate when the conditional means E [y|u] lie in a low-dimensional linear space, and a maximum-likelihood estimator for additive Gaussian mixture noise.


As a result, instead of a single FV, describing the whole image, the image is represented by a large number of densely computed semi-local FVs, each of which describes a spatially adjacent set of local features, computed by the previous layer.

during training, high-dimensional FVs, computed by the 2nd Fisher layer, are compressed using product quantisation [23].


The QAP-SPE method uses AP in the outer-loop and exact inner-loop projections.

from the perspective of iteration cost, RCD is significantly more efficient, especially when R is large and computing Π(•) is costly.


Our algorithm solves the classification LP in a sub-optimal manner in the sense that it does not find a separator with an optimal margin.

there exists a separating hyperplane, if and only if the above linear program has a feasible solution.


Comparison of the optimal, true, generalised portraits to those based on the subject labels shows that classification has become more difficult: generalised portraits have moved closer to each other in gender space, narrowing the distance between the classes and thereby diminishing the gender typicality of the generalised portraits for all classifiers.

if we disregard the constant offset b, we can write the decision function as x , which is a prototype classifier using the prototypes µ ± after whitening the space with S −1/2 W . We combine the linear preprocessor (PCA) X = EB and the linear classifier (SVM, RVM, Prot, FLD) y( x) = w| x + b to yield a linear classification system: y = w T E T + b where b = b 1.


Define: Then δ i is the amount of ε-insensitive error that can be corrected for example i by keeping all α ( * ) j =i constant and changing α ( * ) i . Optimality is reached by iteratively choosing the example with the largest δ i and changing its α ( * ) i within the [0, c] limits to minimize the error for this example.

the form of the dual is max Note that the above expression conforms to the dual form of SVR.


Given the obtained representation h, the target y is predicted by a predictor M , which effectively models the distribution q M (y | h).

given observation/input x, we are interested in the task of predicting the target y based on the value of x using a discriminative approach.


Traditionally, in nonparametric factor models inference is done using Gibbs sampling, sometimes augmented with Metropolis Hastings steps to improve performance.

then, we denote with M h the number of columns in the matrix S that have the same history.


For example, the Infinite Relational Model (IRM) [8] represents simple laws consisting of partitions of objects and partitions of relations.

given a set of known relations S, we can learn the parameters by maximizing a penalized log likelihood log P (S|θ) − Reg(θ).


The goal of the agent is to maximize its cumulative reward by acting optimally in the environment.

compute the Q-values: Q( ✓S t , ✓a t ) = ( ✓a t ) T U ✓S t for a = 1, . . . , A t . 8: end for In this section, we develop an end-to-end learning algorithm for Q-LDA, by minimizing the loss function given in (7).


MMC has also shown its success in various computer vision applications.

our formulation can be easily generalized to handle more complex latent variables (e.g.


In such analyses, brain images are first spatially registered to a common stereotaxic space, and then mass univariate statistical tests are performed in each voxel to detect significant group differences.

we proposed derivations for both 3D image features, such as tissue maps, or surface characteristics, such as cortical thickness.


In this paper, we take another approach to this problem by constraining the network such that the corresponding optimization landscape has good theoretical properties without significantly compromising performance.

otherwise, it has a negative orientation.


So far, we have assumed that the firing rates for m observations are the same.

note that the zero-crossings of the derivatives of the log-likelihood function with respect to parameters provide an maximum likelihood estimator.


[6] suggested that the noise factor ⌘/B determines the sharpness of the solutions selected by SGD.

viewing SGD as SDE [8,15,6,5] cannot explain this, since noise-driven escape is exponentially slow [1].


Here, p is the total number of features (or covariates) and n is the total number of observations (or the sample size).

this approach, which we call TREEWEIGHT, calculates the feature importance score for a variable by summing the impurity reductions over all nodes in the tree where a split was made on that variable, with impurity reductions weighted to account for the size of the node.


We use these tests in section 4 to compute the statistical dependencies between simulated time series of various types of objects, as well as recordings of neural activity in the visual cortex of non-human primates.

the dependency between independent identically distributed (i.i.d.)


The complexity of the traditional LP solver is still at least quadratic in the problem dimension, i.e., the Interior Point method (IPM) with a weighted path finding strategy.

detailed applications can be viewed in Appendix.


Synchronization challenges include those reported for coevolutionary systems.

the reality gap is a well-known problem in robotics: Often, behaviors that work well in simulation do not translate effectively into real-world implementations [11].


In other words, regions in one signal (the "query" signal) which can be composed using large contiguous chunks of data from the other signal (the "reference" signal) are considered to have high local similarity.

(up to some local distortions which are also modelled by P (R|T, H ref ) -see algorithmic details in Sec.


In addition to reducing the number of training iterations, hierarchical training has been shown to lead to better parameter estimates [2].

6 requires parsing of the entire training corpus.


Assuming that the function f is twice continuously differentiable, it is strongly convex, if and only if its Hessian is positive semi-definite, for all feasible θ.

x 1 , x 2 refer to 1 , 2 vector norms respectively.


We consider this centralized ERM objective for m parties, each with a data set D j of size n j : i , y The parties can collaboratively learn a differentially private model via iterative learning by adding noise to the aggregated gradients within the MPC in each iteration with the following noise bound.


There are a few correlations, in particular between the first pose-and the "ink"-parameter, that are inherent in the dataset, i.e.

a user needs to define a grouping structure for the input data by informing the model which data-points belong together.


When both G AB and G BA are learned simultaneously, there is an analog expression L GAN (G BA , D A , pB , pA ), in which the domains A and B switch roles and the two losses (and four networks) are optimized jointly.

it requires that pairs of samples are transfered at once, which, while having little implications on the training process as it is currently done, might effect the ability to perform on-line learning.


see [4], their use is limited by a lack of efficient learning algorithms.

the so-called bag of visual words model is employed.


The proposed work here-which we dub matrix generation (MG)-extends the column generation technique to non-polyhedral semidefinite constraints.

we overview some relevant work in this section.


According to [1], the above condition is the weakest condition to guarantee that optimizing a surrogate loss function will lead to obtaining a model achieving the Bayes risk (in our case, the top-k Bayes ranker), when the training sample size approaches infinity.

it is easy to verify that Proposition 8 holds for this case while the opposite does not.


In order to accomplish this, we employ a technique proposed by [8], introducing a "global" utility variable (uG).

it is currently a critical, and quite open, question what the relevant computations within this part of the brain might be.


However, from a cognitive and neuroscientific perspective, there is one approach to solving MDPs that it seems particularly appealing to consider.

in the present paper, we advance a computational framework for goal-directed control in animals and humans.


Results in terms of minimum ESS are summarized in Table 2.

in addition, we show that ⇢(y t , y t+h ) is a non-negative decreasing function of the time lag in discrete steps h. The variance of a Monte Carlo estimator is determined by its Effective Sample Size (ESS) [18], defined as ESS = N/(1 + 2 ⇥ P 1 h=1 ⇢ x (h)), where N is the total number of samples, ⇢ x (h) is the h-step autocorrelation function, which can be calculated in a recursive manner.


This increases the size of the subgame compared to the inexpensive method because a strategy must be recomputed for every action a ∈ A(h) in addition to a.

formally, an imperfect-information subgame is a set of nodes S ⊆ H such that for all h ∈ S, if h h , then h ∈ S, and for all h ∈ S and all i ∈ P, if h ∈ I i (h) then h ∈ S. Define S top as the set of earliest-reachable nodes in S. h ∈ S top if h ∈ S and h ∈ S for any h h. This section reviews prior techniques for subgame solving in imperfect-information games, which we build upon.


samples from D will produce an -optimal solution x to the problem (namely, F (x) ≤ min x∈K F (x) + ) with probability at least 1 − δ?

let K be a unit 2 ball and F be the set of all convex sub-differentiable functions with Lipschitz constant relative to 2 bounded by 1 or, equivalently, ∇f (x) 2 ≤ 1 for all x ∈ K. Then, known algorithm for SCO imply that sample complexity of this problem is O(1/ 2 ) and often expressed as 1/ √ n rate of convergence (e.g.


This is a transition from viewing data as capital to viewing data as labor.

our focus is on the case in which C and F are arbitrary given sets in the data-clustering setting.


To change the size of the intermediate representation, one can replace x with x obtained by suitably sub-sampling or zero-padding x.

a plain feedforward neural network typically consists of L layers where the l th layer (l ∈ {1, 2, ..., L}) applies a non-linear transformation H (parameterized by W H,l ) on its input x l to produce its output y l . x 1 is the input to the network and y L is the network's output.


Second, the CSI algorithm selects inducing points in a single greedy pass using an approximate objective.

instead of evaluating the change in the objective exactly, we use an efficient approximation based on a small number, z, of training points which provide information about the residual between the current low-rank covariance matrix (based on inducing points) and the full covariance matrix.


In contrast, RSVD, which is equivalent to subspace iteration with a Gaussian random matrix, constructs a basis for A j 1 V 0 and then restricts A to this subspace to obtain the decomposition.

more specifically, suppose that we select the top-k i eigenpairs of A ii and construct an ki 's and form an n ⇥ k orthonormal matrix ⌦ as where P i k i = k and denotes direct sum, which can be viewed as the sum of the subspaces spanned by U (i) ki .


The results (Figure 4) showed that SPEEDUP was consistently higher for composite probes.

¥ ¢ ¤ ¥ £ , just as the principle of suspicious coincidences does.


Our model has two novel components: (1) A domain-invariant feature self-reconstruction task is introduced to the seen/unseen class data, resulting in a simple linear formulation that casts ZSL into a min-min optimization problem.

without any labels, the unseen class data has limited effect in overcoming the domain gap using existing transductive ZSL models.


Amortized inference allows for the recognition model to be used for inference in the same way as a network that was trained fully supervised.

due to the indirect nature of calcium imaging, spike inference algorithms must be used to infer the underlying neural spiking activity leading to measured fluorescence dynamics.


Here, we have analyzed the properties of MPOMDP models which can be exploited in order to increase the efficiency of communication between agents.

as we will show, it is possible to obtain bounds on the achievable value of any given vector, in local belief space.


We try to overcome these limitations by combining the replica method with a variational approximation.

the data generating process is unknown but assumed to be fixed.


Note that we can use other losses such as angular softmax loss [26] as the additional loss.

in [55], high precision weights, activations and gradients in CNNs are quantized to low bit-width version, which brings great benefits for reducing resource requirement and power consumption in hardware devices.


In practice a common way to deal with limited data is to "transfer" a model trained on a separate, but similar, large labeled dataset [12,51,9].

we use our reimplementation as a consistent testbed on which we carry out a series of experiments, each of which individually focusses on a single issue from section 2.


This experiment shows the real power of our active scheme.

for example, in multiclass classification, if we include all one-vs-one classifiers into H, |H| is quadratic in the number of classes.


In this case, the probability of observing llm, lml and mll can be different as it depends on the clusters to which items 1, 2 and 3 belong.

figure 5 shows the performance of spectral clustering for r = 0.2 and 0.3.


B 2 is the treatment given to mothers (in our case no treatment), and Y 2 is the mothers' outcomes.

since all observed variables in our example are binary, the saturated model has 2 5 − 1 = 31 parameters, and the model corresponding to Fig.


However, current practice in population genetics collapses the data to a set of summary statistics before passing it through the machine learning models.

for inference, we propose iterating the following algorithm.


Patient risk has an inherent temporal aspect; it evolves over time as it is influenced by intrinsic and extrinsic factors.

for training and classification, we employed SVM light [19] and Kevin Murphy's HMM Toolbox [20].


Our analysis applies to a generic noise setting as long as Y ij has bounded support.

the threshold η n trades off between bias and variance of the final estimate.


The rest of this paper is organized as follows.

moreover, the newly released ImageNet [12] data set goes a big step further, in that it further increases the number of classes to over 15000, and has more than 1000 images for each class on average.


To optimize a tensor operator, programmers must choose from many implementations that are logically equivalent but differ dramatically in performance due to differences in threading, memory reuse, pipelining and other hardware factors.

we use a batch of parallel Markov chains to improve the prediction throughput of the statistical cost model.


zeros) from valid co-evolution values, the indicator function of the valid region (1 in the valid L × L region and 0 in the padded region) is introduced as an additional feature channel.

parts of the community are adopting deep learning with certain hesitation, even in areas where it is essential for scientific progress.


Whenever a helper action h is executed directly before the corresponding agent action a, the agent receives a bonus reward of 1.

informally, the HAMDP provides the assistant with a helper action for each of the agent's actions.


Note that the technique is query-based because weightings depend on the query.

we propose a technique that computes a locally flexible metric by means of Support Vector Machines (SVMs).


Furthermore, due to introducing a smooth change with the correct time scale in the latent space (e.g., the posterior mean of h across trials shown in Fig.

2, we introduce our framework for constructing non-stationary neural population models, as well as the concrete model we will use for analyses.


The information contained in the negative part, reflecting the information coded by metric or l 2 violations, codes in this case for the individual weighting of the (dis)similarities.

similarity was rated on a discrete integer scale between 1 (very dissimilar) and 5 (very similar).


The goal is to generate input trajectories and output measurements which are informative for learning time-series models.

generating the data for learning a time series surrogate model by varying the actuation signal and engine speed is not simple, as an inappropriate combination of them would result in hazardously high rail pressures, damaging the physical system.


The transition and reward functions for a given policy are denoted by P π and r π .

a deeper understanding of the formulation and potential solution methods will be necessary in order to determine the full practical impact of the proposed methods.


the other uses the psuedo-Dirichlet regularizer [8], which is a bounded perturbation of the original Dirichlet model.


Any MBRL algorithm must select a class of model to predict the dynamics.

our method to predict plausible state trajectories begins by creating P particles from the current state, s p t=0 = s 0 ∀ p. Each particle is then propagated by: s p t+1 ∼ f θ b(p,t) (s p t , a t ), according to a particular bootstrap b(p, t) in{1, . . . , B}, where B is the number of bootstrap models in the ensemble.


The empirical distribution of actions of any no-regret sequence in a repeated game converges to the set of CCE of the static game.


2 For each data set all instances from the training, validation, and test set, if available, are combined to a large set of instances.

during training, node splitting and node merging are driven by the minimization of exactly the same objective function, here the weighted sum of entropies at the leaves.


This leads to a sequential monomial approximations of the original SP formulation: at each iteration y (k) , we linearize both terms in Eq.

despite the hardness of SP in general, the objective function in the MLE formulation of SPNs has a special structure, i.e., it is the ratio of two posynomials, which makes the design of efficient optimization algorithms possible.


In these applications there is a natural place where one might divide data into episodes: for type 1 diabetes treatment, one might treat each day as an independent episode, and for digital marketing, one might treat each user interaction as an independent episode.

if the behavior and evaluation policies are both options-based policies, then the PDIS estimator can be exponentially more data efficient compared to using primitive behavior and evaluation policies.


Neural parsing methods [16,17] are grammar-like models for scene understanding, but use precomputed superpixels and thus also do not permit arbitrary region shapes.

since there are an exponential number of subregions of an image, SFG-PARSE instead constructs a parse of the entire image for each production and reuses that parse for each of these subregions.


Moreover, the last propositions show that we indeed can estimate the correct hull of the sparsity pattern if the sufficient condition is satisfied.

if all Hilbert spaces are finite dimensional, our particular choice of norms corresponds to an "ℓ 1 -norm of ℓ 2 -norms".


A closely related baseline is the Deep Recurrent Attentive Writer (DRAW, [3]), which like AIR, generates data sequentially.

in this paper we take a Bayesian perspective of scene interpretation, namely that of treating this task as inference in a generative model.


We show that this model can significantly improve modeling efficacy, and has major advantages for model interpretability.

the subsets of kernels considered by this method are restricted to be a hull of kernels.


This strategy has not, to our knowledge, been applied either to multidimensional data or bounding-box prediction, as we do here.

it is entirely possible there are errors in the labeling: for instance, there is little agreement in the climate community on a standard heuristic for capturing Extra-Tropical Cyclones (Neu et al., 2013); Atmospheric Rivers have been extensively studied in the northern hemisphere (Lavers et al., 2012;Dettinger et al., 2011), but not in the southern hemisphere; and spatial extents of such events not universally agreed upon.


The animal receives a reward for the first response after the length of time tr .

here it is shown that the network activity obeys equation (1).


In this case, we use the filter methods to filter out e + 0.1 of the input features, where e is the desired proportion of the features that one wants to reserve.

if a pool is tested positive then at least one sample in the pool is positive.


For each of these approximations, we use stochastic gradient descent (SGD), stochastic meta-descent (SMD) and BFGS to learn the parameters.

in the following we consider the factor graph G = ∪ r G r which is the union of all factor graphs.


We first study the effectiveness of the algorithm, measured by the EV value of its output after the last sample, and compare it to the nuclear norm based online RPCA (OR-PCA) algorithm [8].


Then the margin condition (7) is satisfied if and only if there exists a constant C > 0 such that, for all ✏ > 0, (`, F ✏ , P ⇤ ) is ⌘-stochastically mixable for ⌘ = C✏ ( 1)/ .

let ⌘ > 0 and suppose `is a loss such that its pseudolikelihood set e ⌘S is closed and pre-supportable.


The proof can be referred to in the Supplementary Materials.

different classifier chains involve different classifiers learned on different training sets and thus the order of the chain itself clearly affects the prediction performance.


Training using standard support vector machine methodology gives accuracy that significantly exceeds the performance of state-of-the-art mean-squared error training for a speaker recognition task.

we decide based on the output of a discriminant function using a polynomial classifier.


The mid level priors j are drawn from an inverse-Wishart distribution centered on the top-level prior.

in this section we plot generalization gradients, which provide a good feel for how the priors we propose match with the mechanisms used in earlier models across a variety of conditions.


Those models are in many aspects more general than the approach discussed here.

additional parameters could also be introduced to model different prior probabilities for different arrangements in depth.


To systematically monitor skin disease activity, clinicians use the TSS which is a quantitative score between 0 and 55 computed by evaluating skin thickness at 17 sites across the body (higher scores indicate more active skin disease).

the joint distribution over y is a multivariate normal: where Σ DTM is a covariance matrix that depends on the times t 1:m (through design matrices B 1:m ) and representations x 1:m . Σ DTM is a block-structured matrix with m row blocks and m column blocks.


To ensure that random sampling can be used during inference time, the latent distribution is regularized using KL-divergence to be close to a standard normal distribution.

for example, a sketch of a shoe could map to a variety of colors and textures, which could get compressed in this latent code.


Their classifier was first pre-trained layer by layer as an autoencoder on unlabelled data, followed by a supervised fine-tuning with backpropagation on a much smaller labeled data set.

we hope to further improve the classification accuracy through higher data quality of the new EEG recordings.


Given the data at time t, t − 1, . . . , t − n, the hidden units at time t are conditionally independent.

we stop after one reconstruction, so the binary choice of hiddens from the reconstruction doesn't correlate with any other terms, and there is no point including this extra noise.


On-line learning algorithms, such as the Perceptron algorithm [17], the Winnow algorithm [14], and their many variants [16,6,13,10,2,9], are general methods for solving classification and regression problems that can be used in a fully incremental fashion.

1 The average hypothesis generates valid predictions whenever the decision space I is convex.


provides an exact solution for the ground state of a 2D lattice Ising model without a ferromagnetic field [13,8,9,10] in O(N Computing a lower bound: At a given iteration, prior to adding a newly generated set of constraints we can compute the total residual constraint violation over all layers of hierarchy by ∆ = l (θ l + λ l + ω l−1 − ω l ) • z l . In the supplement we demonstrate that the value of the dual objective plus 3 2 ∆ is a lower-bound on the relaxed closest ultrametric problem in Eq 9.

we optimize the dual of the objective in Eq 9 using an efficient column generation approach based on perfect matching.


In this paper, we examine a large scale energy disaggregation task, and apply a novel extension of sparse coding to this problem.

this criterion provides a better optimization objective for our algorithm, as we wish to obtain a sparse set of coefficients that can achieve low disaggregation error.


Under this scheme, the base measure quickly learns much of the basic structure of the data while the Dirichlet extension takes into account any deviations in the data which are not predicted by the parametric component.

uBM is capable of adjusting the probabilities of the most frequent words to focus on fitting the regularities of small probability events.


As revealed by the recent literature findings [28], the deep features in standard CNNs must eventually transition from general to specific along the network, and the feature transferability decreases while the task discrepancy increases, making the features in higher layers f c7-f c8 unsafely transferable across different tasks.

all three datasets are evaluated using DeCAF 7 [9] features for shallow methods and original images for deep methods.


We thus achieve superior performance over existing gradient matching approaches, as shown in the experimental section 5.

[2008] infer the parameters θ by first sampling the states (i.e.


For instance we can fit a 1D Gaussian Mixture Model (GMM) with two components and set ψ as the point of equal Mahalanobis distance between the two components.

the corrupted sequences are then subjected to the algorithms for motion segmentation.


In our experiments, we used Nesterov's accelerated gradient method [25] whose runtime is O(mtk/ p ✏) for a smooth objective, where ✏ is the desired accuracy.

in the case of learning a multiclass predictor, we shall learn a predictor v 7 !


with the knowledge that this assumption is a point of weakness for VR algorithms, future work may more purposefully exploit this to yield better speedups than SVRG and SARAH can currently attain.


let G := H, and let the complexity measure be I(g) = g H . Eq.


To address this challenge, reweighted amplitude flow effecting suitable gradient directions from all data samples {(a i ; ψ i )} 1≤i≤m will be adopted in a (timely) adaptive fashion, namely introducing appropriate weights for all gradients to yield the update The reweighted gradient ∇ rw (z t ) evaluated at the current point z t is given as for suitable weights {w i } 1≤i≤m to be designed next.

the losses (z; ψ i ) in (2) that are nonsmooth at points z will be eliminated, to prevent their contribution to the reweighted gradient update in (10).


Nomad did autonomously identify several meteorites.

human experts often have trouble explaining how they can identifY many rocks, and will refer to an example.


Given upper bounds on the dimension, volume, and curvature, we show that Empirical Risk Minimization can produce a nearly optimal manifold using a number of random samples that is independent of the ambient dimension of the space in which data lie.

for a fixed n, the quantity in the limits is a random variable.


Now focusing on the estimation of a conditional quantile, one can show that the target function [17].

following Koenker [15], this can be achieved by minimization of the pinball loss: τ (r) = max(τ r, (τ − 1)r), where r ∈ R is a residual.


These difficulties are circumvented by replacing |γ j + h j | by sign(γ j )(γ j + h j ).

then, it becomes necessary to find methods that retain meaningful factors instead of individual variables.


An important implication of Theorem 1 is that any iterative algorithm, such as EM or gradient ascent, that attempts to maximize the likelihood based on local updates cannot be globally convergent-that is, cannot converge to (near) globally optimal solutions from an arbitrary initialization.

since the log-likelihood is bounded from above, this neighborhood must contain at least one maximum of the log-likelihood.


If we know that the ratio of the false positive and false negative costs is approximately θ : (1 − θ), it is reasonable to solve the following cost-sensitive SVM [17]: where the weight w i (θ) is defined as When the exact false positive and false negative costs in the test scenario are unknown [4], it is often desirable to train several cost-sensitive SVMs with different values of θ.

we define w i (t) ∈ [0, 1], t ∈ N T as the weight of the i th instance for the t th task, where T is the number of tasks.


Multiresolution Matrix Factorization (MMF) MMF is a recently introduced matrix factorization algorithm motivated by similar multiresolution ideas as the present work, but applied at the level of individual matrix entries rather than at the level of matrix blocks [31].

it is clear from its form that the Nyström approximation is spsd preserving , so is augmented SPCA compression.


In our experiments, using the baseline model in such a way, as a replacement for the physics function, provided better results than using it in an unstructured manner, relying solely on the decoder loss.

if we could differentiate through the solution for the LCP as well, the system would be differentiable end to end.


This results in grass patches with different intensity and chromaticity (bright yellow and dark green) ending up in different subtrees.

[29]), this exponential growth poses a problem for implementing tree models on memory-constrained hardware such as embedded or mobile processors.


When the target conditional is close to all source ones, ↵ can be chosen to be very large and ✏ T is close to ✏.

more details are presented in Appendix C. These results are non-trivial and important, as they provide a guarantee for an accurate and robust predictor for a commonly used loss function, the cross-entropy loss.


Enticingly, this suggests that various settings of ψ lead to various imitation learning algorithms that directly solve the optimization problem given by Proposition 3.1.

if there were no cost regularization at all, the recovered policy will exactly match the expert's occupancy measure.


For this reason, we evaluate LL T = Σ using a rank one Cholesky updates in a specific order.

other robust observation models include, for example, mixtures of Gaussians, Laplace  distribution and input dependent observation models [7][8][9][10].


If there are only a few examples for each such class then it is almost impossible to learn the manifold structures using only local manifold learning.

then, it increases because of the curvature of manifold (further away neighbors form a larger angle).


The situation is complicated by the fact that decompositions like (3) and ( 5) are not unique.

as mentioned in Section 2, to go from multiresolution analysis to orthogonal wavelets, one needs to define appropriate bases for the spaces V 0 , W 0 , W 1 , .


Approximation algorithms for this problem are essential since solving the problem exactly is NP-hard [12,14], even when k = 1 and A is a binary matrix.

we allow the algorithm to output a matrix Although we do not obtain rank exactly k, many of the motivations for finding a low rank approximation, such as reducing the number of parameters and fast matrix-vector product, still hold if the output rank is O(k log(n/k)).


We denote by ω and σ the mean and width of each Gaussian kernel, and we denote by h Finally, for ν njk = f (a njk ) we form a neural network that takes as input the score s njk , the binned variables h nj , which summarize the information of the scores (s njk : k = k), as well as the target observation x nj and the prior probability π nj .

we report the approximate posterior probabilities in Table 3, for two query items (one from each type).


Additionally, this means that p(S) ≥ 2/3, so again with high probability, at least half of our m samples will lie in S. These first m /2 samples from S will be independent samples from (p|S), which is uniform, and therefore with 99% probability will pass the uniformity tester.

from the above, we derive an algorithm that approximates p r to a small relative error: Lemma 2.3.


The results here provide substantial insight into the nature of GAN optimization, perhaps even offering some clues as to why these methods have worked so well despite not being convex-concave.

g ) and other equilibria in a small neighborhood around it.


A model is said to be walk-summable if for each pair of vertices s, t ∈ V , the absolute sum over all walks from s to t in G converges: Here, W(s → t) represents the set of all walks from s to t, and φ(s → t) denotes the absolute walk-sum 2 over this set.

here, V 2 represents the set of all unordered pairs of vertices.


Supplying the model with additional binary indicators as inputs (one for each neighborhood pixel) did not solve the problem.

we found that conditionally whitening the data greatly sped up the training process of both models.


This is because, given a fixed-size training data, when using fewer machines, the size of training data per machine will become larger and thus a smaller k can already guarantee the approximation accuracy.

we collect the full-grained histograms of the globally top-2k attributes from local machines in order to compute their global distributions.


Instead, our bounds simply hold for general bounded loss functions and, when applied to classification, coincide with the tight classification bounds of Vapnik [1998].

this second stage is critical and distinguishes our method from other suggested ones.


The extracted code can be used for image translation guided by the reference image.

each sketch can be mapped into several photo-realistic images.


Classical theories of rational choice do not apply in such cases because they ignore information-processing resources, assuming that decision-makers always pick the optimal choice [10].

for each, we collected choice data from 15 anonymized participants living in the United States, totaling 30 subjects.


Note that the definition of complement generator implies that G is a function of f . By treating G as function of f , theoretically D can optimize the original objective function in Eq.

we develop a novel formulation of the discriminator and generator objectives to address these drawbacks.


We will demonstrate the utility of this new method on both simulated examples and on a real-world application, the latter in form of predicting the components of a magnetic field, as illustrated in Figure 1.

a solution may not just be hard to find, but one must also make sure that it is indeed a valid covariance function.


We consider twenty tasks in each environment, resulting |E| × |T | = 400 pairs of (ε, τ ) in total.

the agent is allowed to have a very limited amount of learning data in the target environment and/or task, for instance, from one demonstration, in order to transfer knowledge from its prior learning.


The results of the sweep are represented by the function DistF romAvg in Algorithm 1.

to date, there remains a considerable gap between the performance of 1-bit and 2-bit networks (compare rows 8 and 10 of Table 1).


Sampling a trajectory over a long interval will take more time than over a short one, and to more clearly distinguish performance for large values of t end , we scale each ESS from the left plot with t end , the length of the interval, in the right subplot of figure 5.

as this parameter varied from 0 to 1, the problem moved from sampling from the prior to a situation where the trajectory was observed (almost) perfectly at 10 random times.


A prototype chip was designed in a 0.35-µm CMOS technology and the fab-ricated chip generates an edge based image vector every 80 µsec, which is about 10 4 times faster than the software computation.

a number of algorithms developed for robust image recognition so far [1]- [3] are mostly implemented as software systems running on general-purpose computers.


In Table 1 we compare optimal value iteration using ADDs (SPUDD as presented in [8]) with approximate value iteration using different pruning strengths J.

al [8] to perform value iteration using ADDs.


We can see from Figure 1(c) and 1(d) that our algorithm FLASH converges faster with larger step sizes for negative curvature descent, which validates our theories on third-order smoothness can be helpful in the nonconvex stochastic optimization.

according to recent work by [34,5], one can extract the negative curvature direction by only using stochastic gradient evaluations, which makes the negative curvature descent approach more appealing.


Recursive Neural Networks have recently obtained state of the art performance on several natural language processing tasks.

next, we introduce our novel global belief model and hybrid unsupervised-supervised word vectors.


Note though that a low level implementation should give similar run times.

[20] proposed their dropout variant within the speech recognition community, where they did not have to consider embeddings overfitting (which, as we will see below, affect the recurrent layers considerably).


the data center recovers almost complete information if R exceeds the entropy rate of {X(t)}.


Following [18], we introduce a small perturbation ζ > 0 to replace M 2,1 by i m i 2 2 + ζ, which is smooth and differentiable with respect to M . Apparently, i m i 2 2 + ζ is reduced to M 2,1 when ζ → 0.

we evaluate the proposed method by applying it to the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort to examine the association between a wide range of imaging measures and two types of cognitive measures over a certain period of time.


Due to the size of the dataset, the analysis of [27] requires breaking the chain into several blocks, severing long range dependencies.

( 7), but with time indices restricted to the length L subchain y S : To compute these local beliefs, we use our current q(A), q(φ)-which have been informed by all previous subchains-to form π, A, p S = { p(y S |x S = k), ∀k, = 1, . . . , L}, with these parameters defined as in the batch case.


Bayesian people tracking requires dynamical models in the form of transition densities in order to specify prediction distributions over new poses at each time instant (e.g., [11,14]); similarly, data-driven computer animation requires prior distributions over poses and motion (e.g., [1,4,6]).

figure 1(a) depicts the graphical model.


Probabilistic graphical models [14] [11] are graphs in which nodes represent random variables, and the (lack of) arcs represent conditional independence assumptions.

our first scheme is to use an outer-loop of the Hill-Climbing algorithm (DML-HMM-HC).


Below, we demonstrate that our model can effectively transfer to different shapes, lighting conditions, and object categories without ground truth intrinsic images.

researchers have also explored reconstructing full 3D shapes through intrinsic images by making use of richer generative models [Kar et al., 2015, Wu et al., 2017.


(ii) After learning (with plasticity at the bottom-up synapses (W PP 1,0 )), the network successfully predicts the new teaching signal, reflected on no distal 'error' (top-down and lateral interneuron input cancel each other).

we postulate that the apical dendrite has an explicit error representation by simultaneously integrating top-down excitation and lateral inhibition.


This result is supported by the theoretical analysis in Armstrong et al.

a central assumption in inverse reinforcement learning is that the demonstrator is close to optimal.


If the algorithm guarantees a zero regret against the competitor with zero L 2 norm, then there exists a sequence of T vectors in X , such that the regret against any other competitor is Ω(T ).

i built upon ideas of [19], but I designed my new algorithm as an instantiation of OMD, rather than using an ad-hoc analysis.


Preliminary results reported in [13] in a related context suggest that the resulting predictor can outperform predictors based on the individual scalar scores.

the following information might help the reader in reproducing our results (in addition to our code being publicly available [9]).


Since there is no consensus on how to generate object tracking displays in the visual attention literature, we will assume simple linear dynamics, which can approximate prior experimental manipulations.

the resulting accuracy surface is shown in Figure 2 -an apparent tradeoff can be seen, when objects move faster, they must be farther apart to achieve the same level of accuracy as when they move slower.


After training, the VIN policy performed mildly better than the baseline on 2000 held-out test queries when starting from the root node, achieving 1030 successful runs vs. 1025 for the baseline.

the transitions were fixed based on the graph connectivity of the smaller VIN graph, which is known, though different from the true graph.


Then the space of all possible preference vectors is given by i becomes arbitrarily large for all i = i, then with high probability item i is ranked higher than any other item i and there is no way to estimate θ i to any accuracy.

in this paper, we study a statistical learning approach, assuming the observed ranking data is generated from a probabilistic model.


The controller generates this corrective submovement "on the fly," i.e., before the initial fast submovement is completed.

it faces high uncertainty in the plant behavior.


When our orientation network fails to predict the correct orientation, the output keypoints will be flipped as shown in Figure 5.


However, a subtlety of pLSIand the crucial difference between it and LDA-is that d is a dummy index into the list of documents in the training set.

we train the model on a fully observed set of users.


In the case of Problem (1.1), performing linear optimization over a trace-norm ball amounts to computing the top (left and right) singular vectors of a matrix, which can be done much faster than full SVD.

then we can apply the second running time in Theorem 4.3.


4 Practical Aspects From now on we will drop the logarithm terms to simplify presentation.

once the histogram is constructed, following Algorithm 1, we can view it as a set of h −d n = O(n 2d/(2+d) ) weighted data points a r , r ∈ {1, . . . , h −1 n } d associated with weights {n r }, where each data point a r is the center of cell B r as defined in Step 2 of Algorithm 1.


We conduct extensive experiments with several explanation methods across data sets and model architectures, and find, consistently, that some of the methods tested are independent of both the model parameters and the labeling of the data that the model was trained on.

these methods applied to a random convolution seem to result in visual artifacts that are akin to an edge detector.


Let K ∈ T and C be a cycle in G K . We denote by π For example, if the graph in Figure 1 is the adjacency graph of some K ∈ T and C is the cycle where the oriented cycles → C 1 , → C 3 and → C 5 are given above, and where we use the shortcut K ( → C j ) , where C j is the unoriented version of → C j .

the matrix K is called the kernel of the DPP, and we write Y ∼ DPP(K).


Regardless of the setting considered, it is not hard to construct a loss sequence such that obtaining sublinear dynamic regret is impossible (in general).

we are not aware of an analysis of EXP3 nor other algorithm equipped to handle such a harsh setting.


threshold for independence tests, and the number of neurons-per-layer were selected by using a validation set.


In the posterior, the model parameters and hyperparameters are strongly correlated.

compared to previous RMHMC methods, SSHMC yields simpler and more computationally efficient samplers for many practical Bayesian models.


The sample covariance spectrum will therefore show quite rich behaviour even when the data itself has no structure.

we have indicated with arrows the theoretical prediction for the top two eigenvalues and we see that there is a significant difference, although the separation is quite well described by the theory.


By Theorem 2.1 for kzc, C is a (k, z )-center solution to (P , w ) of cost at most 4 • 5L = 20L.

the (1 + , 1 + )-bicriteria approximation ratio comes with a caveat: our algorithm has running time exponential in many parameters such as 1 , k, D and m (though it has no exponential dependence on n or z).


The nominal classifier considers the missing values are well approximated by the mean (x j ), and there is no uncertainty.

we derive a robust formulation when the distribution is given by a normal distribution.


This choice of notation was deliberate; one may define elic C := min{k : ∃ Γ ∈ E k ∩ C, ∃f, Γ = f • Γ} to be the complexity with respect to some arbitrary class of properties C. Some examples of interest might be elic E for expected values, of interest to the prediction market literature [8], and elic cvx for properties elicitable by a loss which is convex in r, of interest for efficiently performing ERM.

while L must be concave, it may not be strictly so, thus enabling level sets which are potentially amenable to elicitation.


They proposed SDS MA and SDS OMP , and analyzed the approximation ratio using the coherence of the matrix A. Das and Kempe [10] introduced the concept of the submodularity ratio  Approximation ratio Running time Generalized sparsity SDS MA [22] m1ms M1Ms (1 − 1/e) [10] O((k + d)nT ) No SDS OMP [22] O Replacement Greedy [30] m2s Ms,2 O((n + ds)kT ) Yes and refined the analysis via the restricted isometry property [5].

we approximate a data point y t with a sparse representation in atoms in X, where the approximation quality is measured by u.


are density functions corresponding to P X and P X respectively.

for example, when calculating mutual information between input and output of a neural network, some of the neurons are deterministic functions of the input variables and hence they will have a joint density supported on a low-dimensional manifold rather than the entire space.


The main objective of this paper is precisely to tackle this issue in the context of image modeling.

. . , x n randomly extracted from various images and normalized to have unit 2 -norm, and perform a spherical K-means algorithm to obtain p 1 centroids z 1 , .


Step size h allows us to quantify the rate of change of intersection if τ is increased from 0 to ∞, and since z t is decreasing, k r will evaluate to a high value for two points from the same subspace.

without lost of generality assume that M is wholly divisible by h. Step size h is used to obtain the Difference of Intersection Kernel (DOIK) where indicates the set formed by the a-th to the b-th elements of θi .


Taylor and Lupker (2001, Experiment 1) instructed participants to name high-frequency words (easy items) and nonwords (hard items).

(1) From a purely computational perspective, the optimality-or even the behavioral robustness-of an MDM with an evidence criterion has not been established.


For function F and any U ∈ {U|σ min (X U) ≥ γ}, we have: Lemma 4.2 tells function f is smooth if spectral norm of U is not very large.


For efficiency,  we implemented the permutation using fast 2-universal hashing which is always recommended [18].

then we define the hash of x, h(x) as Our procedure can be viewed as a form of rejection sampling [30].


The modified TS policy is presented in Algorithm 3, and we have the following theorem about its regret and compensation.

we only provide proof sketches in the main text.


For any sequence {γ n } n≥1 such that where γ * n is defined in (3.4), any computationally tractable test is asymptotically powerless under the statistical query model.

then if where C � is an absolute constant, then test function φ is asymptotically powerful.


in a simple asynchronous Bayesian distributed system with S 2 G-MCMC, our theory indicates a linear speedup on the decrease of the variance w.r.t.


Our goal is to express the logical relationships between label assignments as constraints on the score function that hold universally over all x ∈ X .

more recently, several works have focused on coping with large label spaces by using low dimensional projections to label subspaces [3,17,22].


This paper presents a general framework for multiclass total variation clustering that does not rely on a recursive procedure.

we accomplish this task by implementing the primal-dual algorithm in such a way that each inner iteration always satisfies the constraints.


The objective function in (15) fits naturally into the framework of (1), with Ω(α) − Ω(β) and constraints corresponding to M , and the rest terms to K. The entropy function Ω is convex wrt the KL-divergence, which is in turn distance enforcing wrt the 1 norm over the probability simplex [23].

assume the proximal operator has been called #po number of times, then #pass := number of epochs so far We also compared with a "convex" approach.


It is easy to control the trade-offs between the complexity of the recognizer network, the information capacity of the codes, and the robustness of the recognition towards different adversarial effects.

in each case we show six markers: (1) -the marker corresponding to a bit sequence consisting of −1, (2) -the marker corresponding to a bit sequence consisting of +1, (3) and ( 4) -markers for two random bit sequences that differ by a single bit, ( 5) and ( 6) -two markers corresponding to two more random bit sequences.


Note that "separation condition" requirement refers to T 1 (x), T 2 (x) being small, so that eigenfunctions corresponding to the largest eigenvalues of convolution operator when applied to individual high density bumps are preserved in the case when convolution operator is applied to the mixture.

it has been shown ( [SBY08a,SBY08b]) that when data distribution P X has clusters, for each high density region there is a unique representative eigenfunction of a convolution operator that takes positive values around the chosen cluster and is close to zero everywhere else.


A fast associative memory has several advantages when compared with the type of memory assumed by a Neural Turing Machine (NTM) , Neural Stack [Grefenstette et al., 2015], or Memory Network [Weston et al., 2014].

this overcomes the objection that these models can only do recursion by storing copies of neural activity vectors, which is biologically implausible.


They have been extensively analyzed and are the most commonly used methods.

aBP addresses some important issues with ALP: 1) ALP provides value function bounds with respect to L 1 norm, which does not guarantee small policy loss, 2) ALP's solution quality depends significantly on the heuristically-chosen objective function c in Eq.


Roughly speaking, we require N (ε) = O(ε −2 ) random points to cover the unit circle with the resolution of ε.

we may write for some choice of b i s. This means that we can write (5) as if we knew the set of complex poles Z p = {z 1 , .


In this setting, [14] introduces safety guarantees in terms of constraint satisfaction that hold in expectation.

it is not clear how one may find these policies in the first place.


( 1) is not convex; hence, it is likely to be trapped by local minima.

via the Schur lemma, this constraint expresses the lower bound ≥ Y AY, and the SDP is seen to be equivalent to the optimization in eqs.


As can be seen, the first few splits lead to the most significant decreases of the held-out risk.

while it is easy to estimate G(x) at any given x, it requires global smoothness of the mean and covariance functions.


The compact and explicit polynomial form reveals important insights in the program semantics (e.g., the internal program loop that affects program execution time the most).

condition 4 is a little bit tricky; it says that the irrelevant predictors (X S c ) are not very correlated with the "residuals" of E(Y ) after its projection onto X S . Condition 5 is always needed when considering LASSO's model selection consistency [26,28].


In this paper, we address the problem of whether cortico-cortical synaptic systems encode information efficiently.

this input structure is rather broad in terms of stimulus-specificity: cortico-cortical connections between neurons tuned to dissimilar stimulus orientation also exist [4].


For instance, in roulette our initial action value estimate of $0 can be considered optimistic, since no action has an actual expected value higher than this.

in this section, we analyze two methods to find an approximation for the maximum expected value of a set of random variables.


This gain results in a kernel whose computation is numerically unstable.

then, (after an additional hold period of 1.0-1.5s) one of eight targets appeared at a distance of 4 cm from the origin and monkey had to move and reach the target in less than 2s to receive liquid reward.


The expected profit function Π(r, c) is quasi-concave in r for each c. The previous result shows that the reserve price of the single-period constrained model is larger or equal than the one of the multi-period constrained model.

so all the gains from reserve price optimization are already accounted for in our baseline.


To study the consequences of Theorem 3, observe that when the covariance matrix Σ is generated randomly, the amount of correlation is much larger than in the idealized case that Σ is diagonal.

a fundamental instance of the general two-sample problem is the two-sample test of means with Gaussian data.


The present contribution studies to what extent we can omit this brief calibration period.

given two distributions in a high-dimensional space, the (supervised) CSP algorithm finds directions (i.e., spatial filters) that maximize variance for one class and simultaneously minimize variance for the other class.


The computation results are closest to the F P 32 baseline with the chunk size between 64 and 256.

in the context of deep neural networks, we find that the swamping is particularly serious when the accumulation bit-precision is reduced aggressively.


For a large or continuous action space, one needs to draw a finite set of actions {a 1 , .

the Beetle algorithm is however capable of handling finite state and action spaces only.


Similarly, work on target/conditional shift focuses on matching marginal distributions on labels Y and adjusting conditional distributions P (X|Y ), such that P (X) can be matched across domains.

as part of the future work we are working on faster ways to solve the proposed objective.


Each simulation is no longer an isolated path in an exponentially growing tree, but instead value backups can impact many non-visited beliefs and states.

existing algorithms only update the nodes that are directly traversed in each simulation.


While this approach has proven successful to group HMMs into similar clusters [4], it does not allow to generate novel HMMs as cluster centers.

acknowledges support from the Research Grants Council of the Hong Kong SAR, China (CityU 110610).


uniformly sampled from X , the n ´α{p2α`dq global minimax rate also applies locally regardless of how large β is.

we however remark on several differences between our work and [34].


Then, if γ is fully known, p γ (z|a obs , u) is computed with an extension to the Kalman smoothing algorithm to sequences with missing data, after which samples from p γ (a un |z) could be readily drawn.

while the focus in this work is to define a generative model for high dimensional videos of simple physical systems, several recent works have combined physical models of the world with deep learning to learn the dynamics of objects in more complex but low-dimensional environments [3,4,9,34].


The first row of Figure 3 contains similar plots that allow comparison of the four models we considered.

figure 5 shows that the mean rankings of participants in Cluster 1 (N = 8) were best fit by the absolute utility model, the mean rankings of participants in Cluster 2 (N = 12) were best fit by the relative utility model, and the mean rankings of participants in Clusters 3 (N = 3) and 4 (N = 6) were better fit by feature-based models than by either the absolute or relative utility models.


This motivates us to propose a new approach to detecting the systematic changes when the segment lengths have dramatic differences.

when s is small, the Bayes factor vanishes slowly and hence the algorithm picks more spurious change points.


The common choice is principal component analysis (PCA) feature, which is able to reduce the data dimension and identify the most important features [1].

since the differences between the pixels of the unrelated "baboon" image or "tiger" image and the pixels of the images from two datasets are relatively small, the contiguous occlusion caused by these unrelated images is much more challenging than by random black or white dots.


Thus a linear PSR model is specified by Q and by the weight vectors in the above equation m aoq for all a ∈ A, o ∈ O, q ∈ Q ∪ φ (where φ is the null sequence).

this is the first nonlinear PSR that can be used to represent a general class of problems.


Motivated by statistical modeling of biological sequences, Apostolico and Bejerano [1] showed that the bound on the maximal depth can be removed by devising a smart modification of Ron et.

in this paper we describe a variant of prediction trees for which we are able to devise a learning algorithm that grows bounded-depth trees, while remaining competitive with any fixed prediction tree chosen in hindsight.


Theorem 1 now follows from Lemmas 1 and 2 and a union bound over γ ∈ Γ := {0, 1/T, 2/T, .

the results in Figure 4 confirm our hypothesis.


A training procedure based on pointwise log likelihood, for example, would prefer to reduce the posterior probability for a correct label from 0.6 to 0.4 in return for improving the posterior probability for a hopelessly incorrect label from 0.0001 to 0.01.

unlike Och's algorithm, our method does not require one to provide a small set of candidate parses, instead relying on efficient dynamic programming recurrences for all computations.


where V ∈ R m×dv denotes the visual features of the top-ranked m detection boxes and Q ∈ R dq denotes the question embedding.

one-step relational reasoning can only construct pairwise relations between initial objects, which is not always sufficient for complex questions.


Thus, by choosing η = O(1/ √ T ), OGD achieves an O( √ T (1 + P T )) dynamic regret, that is universal.

in Step 3 of Algorithm 2, each expert submits its prediction x η t to the meta-algorithm, and receives the gradient ∇f t (x Observe the loss function f t (•) 7: Update the weight of each expert by 8: Send gradient ∇f t (x η t ) to each expert E η 9: end for Algorithm 2 Ader: Expert-algorithm Require: The step size η 1: Let x η 1 be any point in X 2: for t = 1, . . . , T do 3: Submit x η t to the meta-algorithm 4: Receive gradient ∇f t (x η t ) from the meta-algorithm 5: x η t+1 = Π X x η t − η∇f t (x η t ) 6: end for to get the prediction for the next round.


In this case, the number of information sets |I 1 | = |S|H, and so polynomial in both states and the horizon.

we take the Bayesian approach to uncertainty where the true MDP parameters are assumed to be distributed according to a known distribution, i.e., the true MDP M * is distributed according to an arbitrary distribution P(M).


The proof above uses our assumption that the clustering function f is defined on the set of all distance functions on n points.

we then define a distance function to be any function d : S × S → R such that for distinct i, j ∈ S, we have d(i, j) ≥ 0, d(i, j) = 0 if and only if i = j, and d(i, j) = d(j, i).


However, SMO works usually with a single linear constraint and needs heuristics to run efficiently, which are quite difficult to find (even though an implementation exists for two linear constraints [25]).

this one guarantees that the ratio of observations lying below a predicted quantile is close to the quantile level of interest.


We compare our method with CRF and SSVM models.

let p i be a vector with length k, where its a-th element contains P (ŷ i = a|x), and let Q i,j be a k-by-k matrix with its (a, b)-th cells store P (y i = a, yj = b|x).


A naive simple Monte Carlo estimator of the KL divergence between the output distributions of two inference algorithms requires evaluating output probabilities for both algorithms.

second, BREAD estimates divergences between the target algorithm's sampling distribution and the posterior distribution, but the exact posterior samples necessary for BREAD's theoretical properties are only readily available when the observations y that define the inference problem are simulated from the generative model.