Motivated by these two ideas, we propose a novel interpretation of the notion of asymmetry between cause and effect.

when we combine multiple kernel hyperparameters under the majority vote approach, we see that our method outperforms other methods by a significant margin.


This is particularly important when using linearized dynamics fitted to local samples, since these dynamics are not valid outside of a small region around the current controller.

in this paper, we show that guided policy search algorithms can be interpreted as approximate variants of mirror descent under constraints imposed by the policy parameterization, with supervised learning corresponding to a projection onto the constraint manifold.


The recent work by Sopyła and Drozda [18] suggested several variants of this idea to compute an estimated BB step size using the stochastic gradients.

in all sub-figures, the dashed lines correspond to SVRG with fixed step sizes given in the legends of the figures.


For the unnormalized model (2) and distributions p(x) and p(x) in P , probability functions r α,θ (x) and rα,θ (x) on X are defined by The distribution r α,θ (r α,θ ) is an e-mixture model of the unnormalized model (2) and p(x) (p(x)) with ratio α [11].

the estimating equation of the MLE is written as which is a moment matching with respect to the empirical distribution p = r1,θ mle and the normalized model qθ = r0,θ mle .


This is expected, as there is no way an adversary can perturb any input x into a misclassified x ′ .

we denote the error region of a hypothesis h and the target concept c with E (h, c).


Surprisingly, it was able to exactly find the 50 top solutions for all cases, using up to 4 standard spanning tree inequalities per second-best calculation.

such a characterization requires variables whose cardinality is exponential in the tree-width and is thus tractable only for graphs of low tree-width.


The resettable position embedding alone cannot identify the language of a word token.

we evaluate our proposed model on the five translation tasks and compare with the previous models that are under the typical encoder-decoder framework.


The best model fit from 200 random restarts (lower bound of −2.24 × 10 4 , no crossvalidation, results not shown) only used 3 out of the 8 possible states (the other 5 states had a probability of less than 0.5 %).

the model allows state-transitions to be dependent on an external input x t -this can e.g.


In the remainder of the text, we consider θ to be an [n(n + 3)/2]-dimensional column vector consisting of the elements of w and the upper-right elements of C, i.e., Here, C k:n,k is the sub-matrix in C at row k to n and column k. Previous natural policy gradient methods [9] use the empirical FIM, which is estimated from a sample path.

in this approach, the action of the agent is the parameters of the controller, and the policy is represented by where Σ is the n × n covariance matrix and the agent seeks θ = w, Σ .


In practice, neither the form of C nor the form of Σ is known a priori and hence needs to be inferred from data, fitting a set of corresponding covariance parameters θ C and θ Σ .

in the following, we will refer to a Gaussian process model with this type of sum of Kronecker products covariance structure as GP-kronsum 1 .


In our setup, the output of the neuron during learning is clamped to the teacher spike train S * which is the output of a neuron with the target weight vector w * .

on the other hand experiments in vivo have shown that neurons can be taught by suitable teacher input to adopt a given firing response [2,3] (although the spiketiming dependence is not exploited there).


moreover, at the fixed points, x W `Y Fa 8 a vu ti H . Corollary 5.5 When § ¤¢ every algorithm which finds a fixed point of 8 , induces a fixed point of u with ¥¢ , and vice versa.


Most existing tracking algorithms construct a representation of a target object prior to the tracking task starts, and utilize invariant features to handle appearance variation of the target caused by lighting, pose, and view angle change.


Coreset generation [1,15] is another technique for generating reduced size datasets that can well approximate results generated from fitting a model on a full dataset.

leverage-based sampling throws away two pieces of available information, the effect of the regression design on points other than the i th point and more importantly, the information about the response Y i .


At first, this model might seem quite restrictive.

to this end, we create categories for "all days", "weekends", "weekdays", and "Sundays" through "Saturdays".


We refer to them as Parametric-sequential and Parametric-parallel respectively.

then a nested M -tuple (y m ) M m=1 minimizing the Joint-DivMBest objective (2) can be found as the solutions of the following M problems: where .


Adversarial training techniques that aim to build feature representations that are indistinguishable between source and target domains have been proposed in the last few years [2,17].

we train MTAE on a combination of three source domains (20, 000 images for each).


Thus, all paths through ordinary neural networks are of the same length.

the forward and backward pass is only performed on those modules.


Fixed points of the belief propagation message passing algorithm correspond to local minima of the KL divergence between a kind of trial function and the posterior distribution [17].

we adopted the initialization method of the K-means++ also for the AMP algorithm, because random initialization often yielded empty clusters and almost all data were assigned to only one cluster.


The classical setting is well studied, and the following question has recently received attention: do we gain anything if data are obtained sequentially, and the learner is allowed to modify the design distribution Π of the predictor variable before receiving the next pair (X i , Y i )?


The kernel elements Kij are computed between the p basis vectors X i and the 1 training data Xj.

the use of the "kernel trick" allows projection of inputs into a nonlinear kernel induced feature space of very high (possibly infinite) dimension which is never explicitly represented or accessed.


Previous generative approaches include modeling worlds of painted polyhedra [11] or constructing surfaces from patches taken out of a training set [3].

the difference in orientation between a horizontal graph edge and image contour, φ, is found from the orientation of the image gradient, φ.


According to our notation, for every i, Theorem 2.1 Assume 0 < E(h 2 ) < ∞, then under H A , ηk converges in distribution to a Gaussian according to where This in turn implies that For an average of {η k (i)} i=1,..., n B , the central limit theorem implies that under This result shows that the distribution of H A is asymptotically independent of the block size, B.


As the drift v was fixed in CONST, this variant explained coherence-dependent behaviour with large and almost identical changes in both diffusion s and bound b such that large parameter values occurred for small coherences and the relation between parameters and coherence appeared to be quadratic.

the brain, therefore, must had adapted reliability within trials even on the short timescale of a few hundred milliseconds.


In this case, each feature vector Xn at time n is considered as a fixed length sequence, which has supposedly been generated by a temporal HMM state specific HMM for which each state is emitting individual feature components that are modeled by, e.g., one dimensional Gaussian mixtures.


Let f ∈ R V and denote by C t := {i ∈ V | f i > t}, then it holds under both conditions, Theorem 3.1 can be generalized by replacing the cut with an arbitrary other set function.

if F : A → g(s(A)) is submodular for all s ∈ R V + , then g is concave.


Otherwise, TE between the two electrodes is estimated to be greater than zero solely due to volume conduction effects from source s 3 .

it is important to properly address possible volume conduction effects, not confine the analysis to a small subset of electrodes, and consider a broad range of frequency bands.


Approximate dynamic programming (ADP) is an approach which attempts to address this difficulty.

the relaxation in this case is clearly beneficial; it allows us to compute a better approximation to J * than the point Φr SALP .


Because the color likelihood p C (y | x i , z i ) factorizes across pixels u, the BP approximation to p C (y | x i ) may be written in terms of these marginal occlusion probabilites: Intuitively, this equation downweights the color evidence at pixel u as the probability of that pixel's occlusion increases.

this research was supported in part by DARPA Contract No.


. . , i k , together with the rows e i1 , .

bob, who has [1, 0 d ] together with the output P , can compute the second row of AP , which necessarily reveals a lot of information about x (e.g., if AP ≈ [1, x/2; 1, x/2], its second row would reveal a lot of information about x), and therefore one could hope to embed an instance of the Index problem into x.


T y M maps a vector v 2 T x M to y x v 2 T y M, while preserving norm, and roughly speaking, "direction," analogous to translation in R d . A tangent vector of a geodesic remains tangent if parallel transported along .

for the problem of computing the leading eigenvector, i.e., min existing analyses for state-of-the-art algorithms typically result in O(1/ 2 ) dependence on the eigengap of A, as opposed to the conjectured O(1/ ) dependence [29], as well as the O(1/ ) dependence of power iteration.


Some other works on conditional graphical model estimation [20,4] are based on similar structural sparsity assumptions.

for sparse Σ −1 case, we use the same values of λ 1 and λ 2 that were selected for non-sparse case, and only the third parameter λ 3 is selected by crossvalidation.


We treat skip-thoughts in the framework of encoder-decoder models 1 .

we restrict ourselves to linear classifiers for two reasons.


Let {P k } ∞ k=k1(T ) be an increasing sequence of partitions of T , where for each Note that in Theorem 4 if we let T W and X w gen(w) for all w ∈ W, then for each k ≥ k 1 (T ), due to the Markov chain and the data processing inequality, we have I([W ] k ; X T ) ≤ I([W ] k ; S).

the fact is that we are not dealing with infinite number of independent random variables: the random variables h t (G 2 ) and h s (G 2 ) are actually quite dependent on each other when t and s are close.


By jointly optimizing the feature extraction steps with the rest of the network, the feature extraction can be modified to be optimal for the classification task at hand.

the data is provided mean-centered and normalized and a training/testing split of the data is set.


This makes visual recognition tend to be a dynamic procedure.

table 4 reports the final results of our best model and its fusion with spatial stream on the three splits of both datasets.


We use a mean-squared error objective, which optimizes for the mean pixel values.

we trained for 8 future time steps for all recurrent models, and test for up to 18 time steps.


In [6], two algorithms to solve the bilinear saddle-point formulation are proposed based on mirror descent and the extragradient [9], such as the Mirror-Prox algorithm.

tD is only guaranteed to converge in the on-policy setting, although in many off-policy situations, it still has satisfactory performance [21].


The static plane is represented using 5,000 particles with a practically infinite mass.

moreover, representing every object with hundreds or thousands of particles would result in an exploding number of pairwise relations, which is both computationally infeasible and cognitively unnatural.


In general, the TD model has learned that the radar screen and direction finder (toward the bottom left of the game screens) are usually the relevant locations, as illustrated by the elevated activity at those locations in the sample TD maps in row g. Most of the time, that is indeed a good prediction of eye position, reflected by the fact that the TD NSS scores are typically higher than the BU NSS scores outside the event window.

we annotated the video game clips with several pieces of additional information that we could use to identify interesting events (see Figure 2) which would serve as the basis for event-locked analyses.


To learn a DPP for this problem, assume we have a parameterized kernel L(θ), where θ is the parameter to be learned.

rather, we assume that one of these techniques has been applied to learn a DPP kernel L for a recommendation task, and we focus on how to best use that kernel.


The sparsity of the ground truth inverse covariance matrix of the synthetic data is 6.76%.

since the practical performance of this algorithm was not attractive, Lu gave a variant (VSM) of it that exhibited better performance.


of equation ( 15) is just a scaling factor of U.

if each Gaussian has a simple structure, the product can have a richer structure.


[58] establishes a connection between robust optimization and regularization for linear classification.

as predicted by our theory, the networks achieve good adversarially robust generalization with significantly fewer samples when thresholding filters are added.


We consider tractable representations of probability distributions and the polytime operations they support.

we finally multiply the PSDDs of these factors.


We thank Vijay Balasubramanian, Curtis Callan, Adrienne Fairhall, Tim Holy, Jonathan Miller, Vipul Periwal, Steve Strong, and Naftali Tishby for useful discussions.

there will be an important distinction from the "correct prior" cases.


Our goal is to compute the top k principal components of the data: the k-dimensional subspace that offers the best squared-error estimate for the points.

without loss of generality, we can assume that A 2 = λ 1 = 1.


Thus all the information in the population spike train can be summarized in the random vector ∆(r), which is a simple linear function of the observed spike train data.

in this paper, we study information transmission and optimal decoding in what we would argue is a more biologically-relevant "intermediate" regime, where n is large but the total amount of information provided by the population remains finite, and the problem of decoding the stimulus given the population neural activity remains nontrivial.


This is one way to build a neural network implementation of the VB algorithm.

in the example below we will take advantage of this flexibility in order to build biologically plausible neural network implementations.


With this notation Y = AX −1 + G . We can apply Corollary 1.1 directly once we have suitable bounds on G and U G . The result of [MCJ13] is specific to the spiked covariance model.

this step loses control of the coherence of the original matrix and hence results in suboptimal bounds.


As discussed in Section 2, there are many links between content based attention, kernel based nearest neighbor and metric learning [1].

neither the words nor the sentences used during test time had been seen during training.


A useful property motivating the use of GPs is that linear projection preserves normality, so that the posterior distribution for the integral p[f ] is also a Gaussian, characterised by its mean and covariance.

require: function J, initial state g 1 = ḡ1 ∈ G (and, for FW only: step-size sequence {ρ i } n i=1 ).


Furthermore it is noticeable that all descriptors that model the object boundary rely on image statistics that are primarily based on edge orientation.

in this paper we explore a orthogonal direction to these extensions and focus on how one can improve on the basic system by extending the straight line representation of HOG to a more discriminative description using curvature self-similarity.


When t = 1, our proposed EP for the t-exponential family is reduced to the original EP for the ordinary exponential family and t-factorization yields the ordinary data-dependent factorization.

as shown in the previous section, ADF has been extended to EP (which resulted in moment matching for the exponential family) and to the t-exponential family (which yielded escort moment matching for the t-exponential family).


For BCIs, it is very desirable to have fast transfer rates.

the input vector for the classifier was extended by combining data from the same epoch but from different electrodes.


We assume instead that a set of action models are available.

as an example, ⇠ = 10% suggests there are 10 activities deleted from a team trace with 100 activities.


Here (2 is useful to single out the triple wise interaction (()3 = 8123 ), while (I is to single out the pairwise and triplewise interactions together (()2; ()3).

for example, when we compare firing patterns in two periods, as control and 'test' periods, there may exist a weak correlation in the control period.


A first attempt might be to define them in terms of energy (1), as this is ultimately what we wish to minimise.

when a sample is revisited, its old assignment is first removed before it is reassigned.


A very similar approach was also used by Ray and Page [10].

otherwise, ddt+1 > ddt , which means that a different set of instances are selected.


The better accuracy comes from the fact Co-teaching further takes the advantage of different learning abilities of two classifiers.

a good robust training method should stop or alleviate the decreasing processing.


One of the simplest processes that can operate over a semantic network is a random walk, stochastically jumping from one node to another by following edges.

in our analyses we consider only the first time an animal node is visited, which we denote as τ (k) for the k th unique animal seen on the random walk (out of the K unique animals seen on the random walk).


We hope this work will form a foundation toward a mathematically grounded initialization scheme for state-of-the-art architectures like the original He et al.

and indeed, the solutions p (l) to these difference equations behave asymptotically exactly like so (Thm B.16).


Input: Empirical second-moment matrices Σ x,y for all pairs {x, y} ⊂ V obs computed from N iid samples from the distribution over V obs ; threshold parameters ∆ x,y for all pairs {x, y} ⊂ V obs .

suppose the Spectral Recursive Part of this work was completed while DH was at the Wharton School of the University of Pennsylvania and at Rutgers University.


Recently, a type of attractor networks, called continuous attractor neural networks (CANNs), has received considerable attention (see, e.g., [2,3,4,6,7,8,9,10,11,12,13,5]).

g max defines the maximum trackable speed of a moving stimulus.


Finally, knowing the actual resources needed to estimate a parameter J..tj with some uncertainty defined by pdf (J..tj ), we are able to estimate (5).


Both the Z step and the free embedding use the spectral direction with a fixed step size γ = 0.01.

the beginning of the path is the direct fit to the free embedding.


The symnet control points in the first layer were arranged in three concentric rings in translation space, with 8 points spaced across rotation (200 total points).

the affine net can represent these transformations and so it benefited from larger filter patches.


Different choices for the (mini-)batch size b can lead to different algorithms.

in the above, p * is the number of 'passes' over the data, which is defined as bt m at t iterations.


As we might expect, the performance of ANTICOR w depends significantly on the window size.

within the proportional commission model (see e.g.


Third, for the same reason (because R P (P, X) depends directly on P rather than particular data X 1:n ), it detect lack-of-diversity issues such as mode collapse.

to ensure that the summation is well-defined, the order of summation will need to be specified, depending on the application (as in, e.g., Section 6).


LB-1 optimizes the right objective but over the wrong feasible region (the set of matrices with σ 1 ≤ 1).

linear dynamical systems can also be viewed as probabilistic graphical models.


Note that although the predicted configurations are not the true MAP labelings, they correctly match the training labels.

for positive constants λ ij , define edge potentials ψ ij (y i , y j ) = exp(λ ij ) whenever y i = y j and ψ ij (y i , y j ) = 1 otherwise.


In future work, we will determine the number of topics automatically by extending the proposed model to a nonparametric Bayesian model such as the Dirichlet process mixture model [24].

each annotation is associated with a latent variable r dm with value r dm = 0 if annotation t dm is not related to the content; r dm = 1 otherwise.


Part of this work was completed while the second author was at the Simons Institute at Berkeley.

the results of these methods are presented as baselines.


#@ ) C ED GF 1 98 ¡ %$ & R C GD EF 1 98 ¡ %$ P " D 8 ¡ %$ P ' , PF enables us to compute i particles ¡ ) C GD EF 1 98 ¡ R C GD EF 1 98 ¡ ¢ H D EP approximately distributed according to !

this discrepancy is what causes the well known problem of sample impoverishment in all particle filters [11,15].


This estimates to which extent the last k experiences help to learn a better model as evaluated over the complete data.

. . , s T , r T . We start by considering an empirical estimate of the current model accuracy.


If ∂ θ k F (A) exists for all A ⊆ V the approximate Jacobians J σ are equal and do not depend on the choice of σ.

the directions v where we will compute the directional derivatives will have in general non-negative components v j , unless F j is modular.


Bertsimas and Goyal [8] show that affine policy is optimal for the adjustable problem (1) when the uncertainty set U is a simplex.

in such instances, the bound b/µ can be quite loose.


If we can control the bipolarity of the activation distribution, we may have an opportunity to reduce the quantization error.

for quantized activations shown in Figure 2(f), only 2 states are valid due to the activation functions.


We note, however, that a weaker result, that still suffices for answering Question 1 in the affirmative, can be proven using a naive improper learning algorithm.

concretely, they studied the problem of sparse PCA, namely, finding a sparse vector that maximizes the variance of an unsupervised data.


At the core of our proof technique is the first-order stability condition on the population loss function.

nevertheless, in LVGGM, there is no closed-form solution for the sparse matrix due to the log-determinant term, and we need to use gradient descent to update S. both the algorithm in [40] and our algorithm have an initialization stage.


To provide some understanding of this phenomenon, we show that this method can be actually recovered by an inexact Uzawa method [11].

let z x , z y be the Lagrange multipliers for constraints Ax = b, x = y,respectively.


The following claim, proven in the supplementary material, relates D + to D L+ .

the weight w for label ∈ {1, . . . , L} is generated uniformly at random in [0, 1], independently of other weights.


This will almost inevitably lead to overfitting (in a maximum likelihood context) or inflated inference uncertainty (in a Bayesian context).

the conjugate prior for the hyperparameters a, b is a beta distribution, P (a, b|α, α, γ, γ) ∝ a 1) , which allows the hyperparameters to be integrated out in closed form: .


The OE dataset collected by us is more comprehensive, including 10183 images with groundtruth masks.

we set c = 200 in our experiment, and we only need to perform over-segmentation for superpixels once as preprocessing for training.


Inferences using the Gaussian Sum approximation had consistently higher area under the ROC curve and lower equal error rates than the FHMM.

there has also been much prior work on condition monitoring in intensive care; here we give a brief review of some of these studies and the relationship to our own work.


To tackle GAN's problem of mode collapse, in what follows we present our main contribution of a framework that seeks an approximated distribution to effectively cover many modes of the multimodal data.

alternatively, around the same time, there are various attempts to employ autoencoders as regularizers or auxiliary losses to penalize missing modes [5,31,4,30].


One of the disadvantages of this approach, from an image coding perspective, is that it may only be applied to small sub-images (e.g., 12 x 12 pixels) extracted from a larger image.

moreover, the resulting coefficients achieve higher coding efficiency (higher SNR for a fixed bit-rate) than traditional wavelet bases which are typically designed "by hand" according to certain mathematical desiderata [5].


3) We provide optimized parallel implementations for FA, CMS and our proposed Topkapi algorithm.

without identifiability, we need another pass over every item, estimate its count, and then report top-K.


If furthermore the number of component vectors is set to B = |T | and the hash function h 1 (w) is the identity function, hash embeddings are equivalent to standard embeddings.

the hash embedding models used in this article achieve equal or better performance than previous bag-of-words models using standard embeddings.


Both models have a power-law distribution with an exponent approximately equal to -3/2, although the exponent is somewhat smaller for small network sizes.

we consider time being measured in discrete steps, t = 0, 1, 2, . . .. Because synaptic values are essentially determined presynaptically, we assume that all synapses of a neuron are identical, i.e.


In this paper, we assume that each w i has a multivariate Gaussian N (0, σ 2 I n×n ) distribution.

b 3 (ξ, ρ n , n, s) (ii) If the support minimum B min > 2b 3 (ξ, ρ n , n, s), then the primal support method successfully recovers the support union J = S(β 1 )∪S(β 2 ).


Our analysis, though asymptotic in nature, leads to growth conditions that are sufficiently weak so as to require only that the number of observations n grow logarithmically in terms of the graph size.

we assume in this section that θ 1 corresponds to the unregularized bias term, and omit the dependence on sample size n in the notation.


Here the aim is to create recursive equations for the relations between documents and between terms.

the first method exploits the fact that the standard representation of text documents as bags of words gives rise to an interesting duality: while documents can be seen as bags of words, simultaneously terms can be viewed as bags of documents the documents that contain them.


For instance, in their setting, there are statistical barriers so that no algorithm can achieve an optimization error below some fixed threshold, no matter how many samples are taken.

in the same setting as Theorem 4.4, no algorithm can output x so that f Remark 4.6.


A natural question is the accuracy of the linearized model Eq.

any estimated parameters from an observation should be stable under small perturbations such as object, viewpoint or light positions.


This is formalized as follows: we are given a compact convex set K that contains a global minimum of f , i.e., ∃z ∈ K such that z ∈ arg min x∈R d f (x).

this project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no 725594 -time-data).


In terms of ability to predict the top and bottom 10 names, the multinomial models are both comparable and vastly superior to the naive approaches.

in our example, each row z m of Z corresponds to the year, latitude, and longitude of an observation, and K is the number of names.


Rank-k Projection-Cost Preservation: Let A ∈ R n×d be a matrix of at least rank k and τi (A) be defined as in Eqn.

dRLS selects fewer columns with the same accuracy in Eqn.


If the conditions (3) hold, then for sufficiently large n (and thus sufficiently large p), assumptions ( 5) and (6) hold.

then it holds with probability at least 1 − the extended BIC with parameter γ selects the smallest true model.


We have used the results in Lemma 1 and a common statistical approximation: E(max(x, y)) ≈ max (E(x), E(y)).

the estimates of the original CRS are, strictly speaking, biased.


We show that a Bayes-risk minimizing decision policy that minimizes not only error rate but also average decision delay naturally exhibits the experimentally observed Go bias.

experimental evidence also indicates that there is a curious choice bias toward the overt (Go) response in the GNG task [11,16,2,15], in the form of shorter response times and more false alarms for the Go response, than when compared to the same stimulus pairings in a 2AFC task [2,16].


As a first step towards end-to-end learning, hand-crafted descriptors like SIFT [9,10] or detectors [9,11,12] have been replace with learned ones, e.g., LIFT [13], MatchNet [14] and DeepCompare [15].

in this paper, we focus on descriptor learning and, using a novel method, train a convolutional neural network (CNN), called HardNet.


(c) shows that the two gray arcs in (a) and (b) are overlapping on the dark arc.

it means that the more overestimation an inference algorithm makes, the larger estimation error it may suffer.


Like QPEs, EFPEs impose a lower bound on the realization of every sequence.

these extra pivoting steps need to manipulate extremely small constants due to the values of , hence introducing a large overhead.


In brief, the sampling distribution f 1 (j) and the model dependency control scheme with threshold ρ allow STRADS to speed up the convergence rate of Lasso.

because our experiments feature very large vocabulary sizes, even a small fraction of the word-topic table can still be too large for a single machine's memory, which caused YahooLDA to fail on the larger experiments.


This accuracy is due to the additional input required by the K2 algorithm, namely a correct topological ordering of the variables according to the true network structure.

first, it is the (exact) bias induced by the bootstrap procedure, while Eq.


However, MLE of the multinomial distribution is spiky since it assigns zero probability to the events that did not occur in the observed sequence.

moreover, we use 10-fold cross validation with a binary C-Support Vector Machine (SVM) where the C value for each fold is independently tuned using training data from that fold.


The data center then collects the L codeword sequences, z 1 , • • • , z L . Since all the L codewords are of the same length m, the combined data rate will be R = L × m/n.

in this paper, we introduce a new analytical model for a massive sensing system with a finite data rate R. More specifically, we assume that the sensors use LDGM codes for rate distortion coding, while the data center recovers the original sequence by using optimal "majority vote" estimation [3].


We apply this RL based interactive retrieval framework to the task of image retrieval, which we call dialog-based interactive image retrieval to emphasize its capability in aggregating history information compared to existing single turn approaches [13,14,15,16].

for example, if the "shiny" value of the candidate image and the target image are 0.9 and 1.0 respectively, then the rule-based feedback is "more shiny."


Note that a D input lattice interpolated with simplex interpolation has D!

in this paper, we proposed combining three types of layers, (1) calibrators, (2) linear embeddings, and (3) multidimensional lattices, to produce a new class of models we call deep lattice networks that combines the flexibility of deep networks with the regularization, interpretability and debuggability advantages that come with being able to impose monotonicity constraints on some inputs.


The second bound is much more useful (and, as we show below, tight) in the data-sparse regime N << m. The resulting minimization problems have a polynomial approximation flavor: we are trying to find an optimal set of weights g j such that the sum in the definition of f (t) (a polynomial in t) will be as close to H(t) + t as possible.

the first is nearly tight for N >> m (it is actually asymptotically possible to replace m with m − 1 in this limit, due to the fact that p i must sum to one; see (7,8)), but grows linearly with m and thus cannot be tight for m comparable to or larger than N . the optimizer doesn't depend on m, only N (and hence the bound can't help but behave linearly in m).


However this is out of the scope so we do not extend it in this paper.

from (6), the choice of sampling method has no effect on the decreasing rate of the bound, r −1/2 , but influences the constant C. a theoretical measure of efficiency for some sampling method is whether it can make the constant C attain its minimum.


These FDR procedures are widely used but they ignore additional information that is often available in modern applications.

the bias in (2) is much smaller than E[F D(t)].


Our model then decodes the answer y t from the encoded representation e t (Figure 2 (g)).

a fc layer with fixed weights would always result in the same type of combination although the merging process should, as we argued previously, depend on the question.


In the document example, the feedback yields predictive features: the presence of the word "filibuster" is a moderately-strong predictor of the label "politics".

the clusters in the feedback formalism reflect the level of categorization at which the labeler is operating.


It is clear that the finite-dimensional gamma process satisfies such a construction with J k = G k and T K = G θ .

we demonstrate the effectiveness of our approach on both synthetic and real-world datasets.


We now have the notation to consider a popular class of M -estimators studied in the papers above for these superposition-structured models: where {λ r } k r=1 are regularization penalties.

. . , d (k) ] = argmin The quadratic subproblem (8) cannot be directly separated into k parts because the Hessian matrix ( 7) is not a block-diagonal matrix.


After propagating evidence multiple times, average the results together according to their scale factors, to get the final marginals and separators of q.

this gives the same result as TreeEP, because these clusters are exactly the off-tree loops.


. . , f (x N )}, are jointly Gaussian with a fixed covariance function k : R D × R D → R. The conditional distribution of y is obtained via the likelihood function p(y|f ).

in terms of the number of inducing points (the inducing inputs are always shared across the latent dimensions), we tested two variants.


where I w (t 1 i , t 2 j ) is a function that returns 1 iff t 1 i = w and t 2 j = w, and 0 otherwise.

the sequence and tree kernel with feature selection (SK,TK+FS) can be defined as follows: (2) The difference with their original kernels is simply the condition of the first summation, which is τ ≤ χ 2 (u).


NSGS learns to understand long-term dependencies from GRProp, and finds shorter path by also considering the observation.

we tested agents on larger subtask graphs by varying the number of layers of the subtask graphs from four to six with a larger   1).


The deformation features φ stich d (p i , s, θ) between the face p i and the stitching point s are defined as Here, (u(s, i), v(s, i)) is the position of the stitching point in the rectified coordinates corresponding to face i and level l. We define the deformation cost between the faces to be a function of their relative dimensions: with e i and e k the lengths of the common edge between faces i and k. We define the deformation of a face with respect to the stitching point to also be quadratic.

object-centered approaches represent and reason about objects using more sophisticated 3D models.


We select the training input density Ô Ü ´Üµ from the independent Gaussian density with mean Å Ä and standard deviation Å Ä , where In this simulation, we can not create the training input points in an arbitrary location because we only have ½ ¾ samples.

for each run, the test errors of (A) and (B) are normalized by the test error of (C), and then the values are averaged over ½¼¼ runs.


At such a point, one of two conditions must hold for each element v * i : either The first condition applies to the positive elements of v * , whose corresponding terms in the gradient must vanish.

in this paper, we have derived simple, closed form multiplicative updates for solving the nonnegative quadratic programming problem in SVMs.


In real world applications, it may happen that certain controlled experiments cannot be conducted in the source environment (for financial, ethical, or technical reasons), so only a limited amount of experimental information can be gathered.

we were able to decompose R into subrelations such that each one is separately z-transportable from the source domains, and so is the desired target quantity.


Typically, the structure should not only reduce memory requirements, but also dramatically accelerate inference and training via fast matrix-vector products and gradient computations.

we hope that such ideas might lead to new generalizations of Convolutional Neural Networks.


The key result is that, when testing between two multivariate Poisson distributions of means log(n)λ 1 and log(n)λ 2 respectively, where λ 1 , λ 2 ∈ Z k + , the probability of error (of maximum a posteriori decoding) is n −D+(λ1,λ2)+o (1) .

proving that the number of non-backtracking walks is close to its expected value is difficult.


In this section, we discuss how the PixelGAN autoencoder can be viewed in the context of learning cross-domain relations between two different domains.

the adversarial training pushes the output of the encoder to the corners of the softmax simplex, by which it ensures that the autoencoder cannot use the latent vector z to carry any continuous style information.


For the case of a single tree, performance decreases (presumably due to overfitting) on the stochastic problem for increasing budget.

we complete the proof by noticing that SOP spends at least half of its budget on shallowest leaves.


The evaluation result is consistent over multiple runs and is insensitive to the specific NDB clustering mechanism (e.g.

6(a), adding a column-vector to the mean with either a positive or a negative sign results in a realistic image.


Gaussian noise, i.e., p(y|x) = N y|Φx, σ 2 I , where σ 2 is the unknown noise variance.

a particular non-zero coefficient occurs within a distance of N α of its predecessor with probability 1 − ǫ/K.


We consider a class of iterative stochastic policy optimization problems and analyze the resulting expected performance for each newly updated policy at each iteration.

sample M trajectories (ξ j , τ j ) ∼ p(•|ν i ) for j = 1, . . . , M 2.


It returns a list of list of (variable,function) pairs.

and nodes are labeled with x i and correspond to assignments to X i .


Most of the methods above involve estimating the entire graph matrix which is computationally challenging if the number of vertices is extremely large.

settings: We investigate Algorithm 1 for various disconnected graphs under the null hypothesis.


The problem of learning a (k, `)-binary-biclustered matrix, corresponds to the assumption that the row indices and column indices represent k and `distinct object types and that there exists a binary relation on these objects which determines the matrix entry.

the number of margin violations in a sequence S at complexity is defined to be, merr(S, ) := inf note that merr(S, ) = 0 if  1 mc(S) .


Again, it can be seen that both the objective values and the solutions converge linearly.

then, it can be shown that prox τ (X) = S τ (X); (6) see, e.g., [11,Theorem 3].


Typically, an edge in this graph indicates the expectation that the joined data points are more likely to have the same label.

in the limit of zero temperature, a rich combinatorial structure called the Picard-Queyranne graph [9] emerges.


In this section, we report the results of empirical studies comparing the algorithm we propose in Section 4 (referred to as Opt-D&S) with a variety of existing methods which are also based on the generative model of Dawid and Skene.

the MV-D&S and the Opt-D&S algorithms consistently outperform the other methods in predicting the true label of items.


While the 2D recurrence model can directly infer the latent representations, it is not guaranteed to output disentangled representation.

in fact, [6] specifically stated that DRNet is unable to get good results when the two digits have the same color.


To address this dilemma, the ResNet paper's detection pipeline [10] inserts the RoI pooling layer into convolutions -this region-specific operation breaks down translation invariance, and the post-RoI convolutional layers are no longer translation-invariant when evaluated across different regions.

with pre-computed region proposals, it is easy to end-to-end train the R-FCN architecture.


Second, the variance terms involved in Lepski's method are not completely explicit.

using the Stoke's formula, ∆ is the unique linear operator satisfying Replacing the volume measure µ by a distribution P which is absolutely continuous with respect to µ , the weighted Laplace-Beltrami operator ∆ P is defined as where p is the density of P with respect to µ.


This is strictly worse than the complexity O( max{L 0 , M 2 /(2 )} 1/ ) of our approach.

see Example 1 and Example 2 for details about the nonsmooth function f . We note that S-APG has been demonstrated with superior performance on both problems in [13], therefore we will only concentrate on comparing with it.


Markov random fields (MRFs) [12] have been applied to a wide variety of real-world problems.

for example, the constraint satisfaction community has studied several special-purpose constraint types that can be solved more efficiently than using generic methods [4]; it would be interesting to explore whether these constraints arise within MRFs, and, if so, whether the special-purpose procedures can be integrated into the COMPOSE framework.


In 3IC, if X 1 and X 2 are in the same cluster as X 3 , then all three of them are in the same cluster.

in practice, there is certain function B(X) ∈ B(X ) of the items that is of interest in crowdsourcing and is here considered as the source.


For example, if G 1 and G 2 are social networks, then k might capture to what extent their clustering structure, degree distribution, etc.

writing the kernel explicitly in terms of A 1 and A 2 , we must have k(A 1 , A 2 ) = k(A 1 ,P A 2 P ) for any permutation matrix P . Permutation invariance has proved to be the central constraint around which much of the graph kernels literature is organized, effectively stipulating that graph kernels must be built out of graph invariants.


Unfortunately, computing the gradients exactly seems very complicated for arbitrary parametrizations F θ , and we will focus our attention to mixture models of the form given in eq.

while we could train a network θ : x → v ∈ R n to output per-pixel scores, it would be helpful, especially in domains with limited data, to bias the predictions by encoding some prior beliefs about the expected output.


In a first step, the learner applies to its input data S a fixed function ϕ : Examples Using the notations above, when S = X tr × {±1}, n = N , ϕ is the identity function and S is drawn i.i.d.

we need a result on more general functions than sums of random variables, but which also takes into account the known dependency structure of the variables.


Ultimately, we would prefer to integrate r out.

the intrinsic dimensionality d of the data manifold can be estimated from the growth process of point-to-point distances.


Our method sets a new state-of-the-art IoU SegNet [28] 46.4 FCN-8 [29] 57.0 DeepLab-LFOV [24] 61.6 Bayesian SegNet [22] 63.1 Dilation8 [30] 65.3 Dilation8 + FSO [31] 66.1 DenseNet [20] 66.9 This work: on this dataset with mean intersection over union (IoU) score of 67.5%.

these results show that aleatoric uncertainty is able to capture many aspects of this task which are inherently difficult.


Theorem 1 shows that γ k is the negative of the optimal L-risk (where L is the linear loss as defined in Theorem 1) associated with the Parzen window classifier.

first, it is established that MMD corresponds to the optimal risk of a kernel classifier, thus forming a natural link between the distance between distributions and their ease of classification.


Here we apply a supervised learning approach to this problem and show that convolutional networks can achieve near-human accuracy and superhuman speed.

t was equalized to 50 for all image stacks in the V1 dataset and 5 for all image stacks in the MEC dataset using averaging and bicubic interpolation.


Since we have chosen conjugate priors, we can analytically marginalize out from the joint distribution all the parameters {π n }, {θ k }, {m n } and {Σ n } and obtain p(X, S, Z, α).

the probability of [Z] is We assume that the first K + features are represented i.e.


EP can be understood as a generalization of loopy belief propagation.

for a Bayesian network, the energy term simplifies into a sum over local terms: the entropy term is as intractable as the normalization in (3) that we try to prevent.


( 11) for the "DIRECT 5-Mixture SGD" model which uses a mixture distribution with r 5 components, and t 3000 Monte Carlo samples for the entropy gradient estimator.

while the Bayesian integrals that arise in GLMs can be easily computed in the case of conjugate priors, for general priors inference is challenging.


We first notice that Pr(jlx) is a function of x.

we use a Chi-squared distance analysis to compute a flexible metric for producing neighborhoods that are elongated along less relevant feature dimensions and constricted along most influential ones.


Let I ⊂ {1, . . . n} be set of size n ′ < n. The subsampled loss Loss I will be computed only for the points k ′ ∈ I.

if the weights are computed as in (1), it is easy to see that the loss function in (3) is the finite sample version of the squared L 2 distance between h and g 0 on the space of Riemannian metrics on M, w.r.t base measure πdV g0 Defining Loss for embeddings with s > d dimensions Consider G, G 0 ∈ R s×s , two symmetric matrices with G 0 semipositive definite of rank d < s. We would like to extend the G 0 norm of G to this case.


Our image representation is agnostic to any specific type of object detector; we take the "outsourcing" approach and assume the availability of these pre-trained detectors.

while the OB representation offers a rich, high-level description of images, a key technical challenge due to this representation is the "curse of dimensionality", which is severe because of the size (i.e., number of objects) of the object bank and the dimensionality of the response vector for each object.


Theorem 4 illustrates the difficulty of SIS.

we show a necessary and sufficient condition for a screening method to be strong screening consistent is that the screening matrix is restricted diagonally dominant (RDD).


Fixing Ψ and x and minimizing (3) with respect to a produces a vector a(x) that approximates a sparse encoding for x.

this basic model can help us explore the effects of repeated communication by ACS.


The maximum likelihood estimator, which is logistic regression for MNL, has been known to be consistent in large sample limit, cf.

the rank order for each component is a uniformly random permutation.


We will assume an infinite sequence of training data (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ), .

finally it is worth noting that L ramp and L probit are meaningful for an arbitrary prediction space S, label space Y, and loss function L(y, s) between a label and a prediction.


Two datasets are used to evaluate performance on Electroencephalography (EEG) data: SEED dataset and an Autism Spectrum Disorder (ASD) dataset.

this makes sense particularly in medical contexts, as nearly all diagnoses address a multi-factorial disease.


To the best of our knowledge, this is the first exact algorithm to the D.S.

from the graphs, we can see the following: First, exact solutions (by PRISM) always outperform approximate ones (by SSP).


Our use of policy iteration generally results in a small number of very large steps directly in policy space.

these runs always produced immediate crashes in trials.


In the following we present our approaches to estimate a causal order on the variables of the system.

for each chain component C, we denote its vertices by V (C) and denote the set of parents of V (C) by P a(V (C)), and define .


Let n be the number of training instances, n + the number of positive training instances, and n − the number of negative training instances.


Proposition 7 relates these errors to the clustering loss.

inference is usually tractable since not all features are relevant to the learning task at hand.


An equivalent formulation expresses (6) as the minimizatioin of w.r.t.

other recent work [7,8] show that in the noiseless setting with isotropic Gaussian inputs, an Alternating Minimization algorithm initialized with the Tensor Method leads to exact recovery of the true parameters.


For two measures µ and ν, their bounded Lipschitz (BL) metric is defined to be their difference of means on the set of bounded, Lipschitz test functions:  Theorem 3.2.

a set of measures {µ t } is called the weak solution of ( 13) if it satisfies (15).


The sequential and hierarchical computer vision pipeline Visual processing has long been understood to follow a hierarchical process from the analysis of simple to complex features.

when a single layer is removed, the only viable path is corrupted.


• We develop a method for efficiently discovering new regions.

perhaps the most troubling assumption is that we can determine the attacker's payoffs for different outcomes.


Our work has strong connections to the analysis of minimax lower bounds in local differential privacy.

this assumption is often unrealistic as it requires insider knowledge of the learner or for the attacker to solve the same estimation problem the learner faces to identify the data-generating distribution.


Our theoretical findings are complemented by empirical evidence which shows that our method delivers state-of-the-art performance.

p can be described algebraically as All vertices of P lie on the hypercube {0, 1} n . We let x ⇤ denote the (unique) minimizer of f over P, and we let D denote the Euclidean diameter of P, namely, D = max x,y2P kx yk.


This can become quickly intractable if both x and yare longer than, say, 1000 frames.

4See the appendix of [1) for more details.


In deriving lower bounds in the next section, we make use of the following result on networks with product and sigmoidal units that has been previously established (Schmitt, 2002).

we assume that the input nodes remain unchanged during the computation.


This work is supported by SenseTime Group Limited and the Hong Kong Innovation and Technology Support Programme.


In this respect, the two approaches may prove complementary, and it will be interesting to further consider their interrelations.

we take three empirically motivated points as founding premises: (1) Neurons in dorsolateral prefrontal cortex represent action policies, (2) Neurons in orbitofrontal cortex represent rewards, and (3) Neural computation, across domains, can be appropriately understood as performing structured probabilistic inference.


The decision boundary is approximated with first-order Taylor series to avoid complex non-convex optimization.

if is too large, then the attack will not be accurate.


After solving for p A|x , we can obtain f A,x using Eq.

then: this means that if there is only one parent shared between (a, b) and (c, d), M is the sum of two rank 1 matrices, and thus is at most rank 2.


This leads to the following approximate auxiliary function (based on the law of large numbers) which is merely the update rule for EM for θ n with s = 1, . . . , S virtual samples x m,s obtained from the m'th model p(x| θm ) for each of the other We now have an efficient update rule for latent variable models (mixtures, hidden Markov models, etc.)

a large family of alternative information divergences exist to relate pairs of distributions (Topsoe, 1999) and are discussed in the Appendix.


Otherwise, it is accepted with probability α.

the performance is evaluated on three datasets: 8D5K [2] , Iris [4] and Pen-Based Recognition of Handwritten Digits (PENDIG) [5].


This value is too large for an exhaustive search.

( 1) is modified to become: For a probabilistic treatment with EM, we make a standard normal assumption of all distributions in form of: where 1 = [1, 1, .., 1] T . While this model is still identical to OLS, notice that in the graphical model, the regression coefficients b m are behind the fan-in to the outputs , we can view this new regression model as an EM problem and maximize the incomplete log likelihood log p(y|X) by maximizing the expected complete log likelihood log p(y, Z|X) : where Z denotes the N by d matrix of all z im .


The unnormalized graph Laplacian L of an undirected graph G has the following properties: (i) L is symmetric and positive semi-definite; (ii) the smallest eigenvalue of L is 0; (iii) L has n non-negative, real-valued eigenvalues 0 = λ 1 ≤ .

we want to ascertain whether the effort of modeling the conditional independence structure of the overall network through the FRF formalism is justified by a suitable gain in prediction accuracy with respect to statistical models that do not focus explicitly on such dependence structure.


Developing methods to directly estimate the difference of two DAGs that do not share a topological order is of great interest for future work.

to define these assumptions it is helpful to view (σ   v,w|S and σ w|S for all v, w, S. For consistency of the DCI algorithm we assume that the converse is true as well, namely that differences in B ij and σ j in the two distributions are not "cancelled out" by changes in other variables and result in differences in the regression coefficients and regression residual variances.


We show that the new algorithm, like Isotron, has theoretical guarantees, and significant new analysis is required for this step.

to prevent a large number of such notes accumulating at any given node we show that these notes satisfy certain commutative and additive relations, thus requiring us to keep track of no more than 2 notes at any given node.


We then estimate θ from this synthetic data using the variational method described in Section 3 using OMP and phase 1 only.

in the case of natural images, this is not the case.


These trajectories come from one of two different populations; either P 0 , when the label is Y n = 0, or P 1 , when the label is Y n = 1.

there are important points for which this quantity does not attain a maximum.


The value function u wv of an FSC P is the expected discounted sum of rewards for executing its policy P , and can be computed by solving a set of linear equations: Given an initial belief state B , an FSC's value at node Y is simply the expectation u ¤ HY rB D 5 B ¤ &¦ C u ¤ HY r¦ x ; the best starting node for a given B is determined by u ¤ §B D E u E¤ Y rB .

many point-based algorithms including PBVI [12] (which is perhaps the best such algorithm) optimize the policy for a single initial belief state, capitalizing on a hopefully small reachable belief region.


Although MLMLT-NC is perhaps the closest algorithm to ours, we applied it only to simulated data.

studying the theoretical and experimental properties of this approach is beyond the scope of this paper and is left for future work.


In a highly volatile environment, one will be expected to have a high learning rate estimated by RL model, and a belief of low stationarity estimated by DBM.

lose shift rate in all conditions (Fig 3b) have an inverted U shape as a function of alpha, where α = 0 leads to a random lose shift rate (1/3), and α = 1(fixed belief model) leads to the minimal lose shift rate.


Let n = 2 and consider RCD (Algorithm 3) with probabilities p 1 > 0 and p 2 > 0, p 1 + p 2 = 1.

for every n ≥ 2 and T > 0, there exists A such that: (i) The rate of RCD with p i ∝ A ii is T times worse than the rate of RCD with uniform probabilities.


Using Proposition 3, we get for our part the following result: Then, for any > 0, we have asymptotically almost surely when n → ∞, This result is to our knowledge the first to bound the expected size of the largest connected component in general arbitrary networks.

in this section, we show that the bounds given in Sec.


Being completely general, we leave many details unspecified.

a helpful teacher can simply teach with n = 2 items (θ − /2, white), (θ + /2, black) to achieve an arbitrarily small error .


Choose suitable joint kernels on the maximal cliques.

we apply this new criterion to independent component analysis and sequence clustering.


In addition, for ν = 1 the required scalar value λ B/0 is |r| here since V B ∩ V0 = {j, r} ∩ {r} = {r} noting that value λ B/0 is the same for ν = 2, 3.

by alternating between Z 1 and Z 2 , we can maximise the log-likelihood iteratively; indeed this alternating maximisation is standard for solving matrix factorisation problems.


In these cases, the approach in [8] is only a bit faster than directly solving the entire problem.

if a partition {V c } k c=1 satisfies the assumption of Theorem 1, Θ and Θ * will be the same, and the last step of Algorithm 1 is not needed anymore.


Let {x i } T i=1 be a sequence of observations generated by the process (1).

when we increase T to 50, the difference between the two methods vanishes, even though there is still much room for improvement as indicated by the result of our model sanity check before.


Also if the prediction density matrix is diagonal, i.e.

first, the time horizon T must be specified in advance, so the minimax algorithm can not be used in a purely online fashion.


This can be mitigated by using a denser sequence of { [m] } along the solutions path.

we define the largest and smallest s-sparse eigenvalues of r 2 L(✓) as for any positive integer s. We define as the s-sparse condition number.


Our goal is to accurately infer the true labels of the tasks without restricting workers' strategies.


The four coarse regions, down-sampled to 7 × 7, along with their the four 7 × 7 quadrants are presented in a single sequence as shown in Figure 1.

convNet is able to perform better than the multi-level attention model on this near frontal face dataset.


Consider a element-wise positive kernel matrix G standardized to be element-wise bounded 0  g i,j < 1 with unitary diagonal g i,i = 1 8 i 2 [n].

in a question that asks to compare Proto and Criticism Condition and Proto Only Condition, a subject said that "The addition of criticisms made it easier to locate the defining features of the cluster within the prototypical images".


Note that the soft assignments r i need to be computed only once after the algorithm has converged.

more sophisticated initialization methods have been proposed to improve the results but the challenge of finding good initialization for EM algorithm remains [4].


[18] study properties of the set of persistence diagrams when endowed with the p-Wasserstein metric.

it is unclear whether k σ is universal with respect to the metric d W,q .


Let (X(t), Z(t)) be the unique continuous solution to SAMD η,η/r,s .

we show how the asymptotic rate of covariation affects the choice of parameters and, ultimately, the convergence rate.


When using the full learning rule for both features, the learning rate needs to be decreased until an agreeable signal-to-noise ratio between the drift introduced by the first term and the diffusion caused by the other terms is reached.

an interesting alternative is that the trial mean is calculated by a prediction system, e.g., by topdown signals that use prior information or an internal world model to predict the expected value of the coding feature.


We want to stress the importance of the last point.

factored bandits with uniformly identifiable actions generalize rank-1 bandits.


p(a, s 0 |s) is the joint distribution of action sequences and the final state, !

we then apply our algorithms to a broad range of high-dimensional problems for which it is not possible to compute the exact solution, but for which we are able to act according to empowerment -learning directly from pixel information.


Each event occurs at an unknown time and an unknown location.

the argument in the quadratic expression is still non-linear, due to the non-linear trigonometric functions involved.


Given a belief b, after executing a and receiving o, we can compute an updated belief b a,o using Bayes' theorem: b a,o (s) = kb(s) Pr(s |s, a) Pr(o|s a).

in many realworld scenarios, planning can be simplified by decomposing the task into a hierarchy of smaller planning problems.


This leads us to view the structural equation model and its corresponding graph as a data generating model.

the work does not provide a formal mechanism to articulate why and how these scenarios should be considered different.


they display surround suppression as well 12 .

it seems unlikely that a reasonable receptive field expansion of LGN cells would not be at least partially transferred to V1.


The present study mainly focuses on information processing at MSTd and VIP, where visual and vestibular cues are integrated/segregated to infer heading direction.

when only cue x 2 is applied to module 2, the congruent neuronal network at module 1 receives a reciprocal input and generates a bump at x 2 , whereas the opposite neuronal network receives an offset reciprocal input and generates a bump at x 2 + π (Fig.


For this example, applying the Smooth-CG or Semi-SPG would require two smooth approximations, one for hinge loss term and one for ℓ 1 norm term.

since the computation cost of these two algorithms mainly come from the LMO calls, we present in below the performance in terms of number of LMO calls.


As mentioned in the introduction, the output of a speech recognition system associated to a speech utterance is a weighted automaton called a word lattice representing a set of alternative sentences and their respective probabilities based on the models used.

in the remaining of this section, we will omit the subscript and v since our results are independent of the choice of these parameters.


We call a policy feasible if it is guaranteed to uniquely determine the correct hypothesis.

. . , h n , and two equivalence classes H 1 := {h i : 1 ≤ i < n} and H 2 := {h n }.


We observe that the existing algorithms, although theoretically sound, are suboptimal from the performance perspective because of their limitations in exploiting parallelism in modern distributed compute settings.

as different threads are working on their own local copies of the sketch, we do not need locks to update a counter anymore.


Its probability is , whereas the direct path (x, z) simply has probability P xz = 1 3 .

cTMCs are used in a wide variety of domains.


One possible explanation for this is its high computational complexity.

let DK a = P a be |A| stochastic factorizations of order m and let ra be vectors in R m such that Dr a = r a for all a ∈ A.


In this paper, we exploit contextual correlations between the object classes by introducing Boosted Random Fields (BRFs).

standard applications of MRFs/ CRFs to images [7] assume a 4-nearest neighbor grid structure.


The neural network has 100 hidden units.

the normalization by ||x t − x j || 2 is to avoid giving more weight to the neighbors that are further away.


This allows a direct comparison of the algorithms proposed here with previously studied approximate 1-step greedy algorithms.

namely, our bounds consist of concentrability coefficients C (1) , C (2) , C (2,k) and C π * (1) from [19,11], as well as two new coefficients C π * κ and C π * (1) κ .


However, solving (3) with this Y is generally NP-hard.

here, we use unsupervised multiple partitionings (quantizations) from baseline superpixels.


Furthermore, the risk functional can be simplified further by considering Our framework, on the other hand, alleviates the problem by minimizing the risk functional R µ (f ) = P ℓ(y, E P [f (x)]) dP(P, y) for f ∈ H with corresponding empirical risk functional the discussion at the end of Section 2).

images of different scenes tends to generate distinct set of patches.


Our GEM algorithm achieves 0.51% and 2.22%, respectively.

where φ = (φ (1) , ..., φ (K) ) is the set of parameters of the generative models of classes.


In the first we show that whenever all f t 's are SLQC, there exists some t such that f t (x t ) − f t (x * ) ≤ .

it is well known that quasi-convex optimization tasks can be solved by a series of convex feasibility problems [4]; generally solving such feasibility problems may be very costly [6].


To learn the hash functions for multiple bits, one could repeat the same procedure and treat the learning for each bit independently.

it is clear that CRH outperforms its two counterparts by a large margin.


• -1.00 0 .00 1.00  This work was supported partly by the Human Brain Project grant P20 MH57180, the Danish Research councils for the Natural and Technical Sciences through the Danish Computational Neural Network Center (CONNECT) and the Technology Center Through Highly Oriented Research (THOR).

( 9) and that ul B_ j = 0 (since uluo = 0) we get ( 12) We note that this distribution is degenerate because the covariance is of rank N -l. For a sample Zj from the above distribution we have that UJ B_jB_;Uoz j = UJ B_jB_;UoUJ B_jB_; Xj = UJ B_jB_; Xj = Zj ( 13) As a second approximation, assume that the observed Zj are independent so that we can write the likelihood of A where we have used Eq.


It is only weakly adaptive in the sense that only the stopping criterion for ML-RP is determined by monitoring the nature of the projected data.

let Φ be a random orthoprojector Suppose M < N . Then, with probability exceeding 1 − ρ, the following statement holds: For every pair of points x, y ∈ M, and i ∈ {1, 2}, where d 1 (x, y) (respectively, d 2 (x, y)) stands for the geodesic (respectively, ℓ 2 ) distance between points x and y.


But both the log determinant and the derivatives are needed for efficient GP marginal likelihood learning: the derivatives are required for gradient-based optimization, while the log determinant itself is needed for model comparison, comparisons between the likelihoods at local maximizers, and fast and effective choices of starting points and step sizes in a gradient-based optimization algorithm.

a Python implementation of our approach is also available through the GPyTorch library: https://github.com/jrg365/gpytorch.


Performance varied continuously with thresholds for radial motions (φ=0, 180 o ) significantly lower than those for circular motions (φ=90,270 o ), (p<0.001; t(37)=3.39).

where w ij is the strength of the recurrent connection between i th and j th units, (x i ,y i ) and (x j ,y j ) denote the spatial locations of their receptive field centers, σ Re (=10 o ) and σ Ri (=80 o ) together define the spatial extent of a difference-of-gaussians interaction between receptive field centers, and S R and S φ scale the connection strength.


For this paper, our experiments are conducted under the assumption that the mainchain atoms of the protein were known to within some error factor.

fffear [4] has had success finding rigid elements in very poor resolution maps, but is unable to locate highly flexible "loops".


This model was introduced in relation to DBM [7], inspired by related work showing that monkeys' choices when tracking reward biases that undergo change points are discounted in an approximately exponential fashion [2].

the constant G t approximation is valid for arbitrary environments and does not depend on whether humans truly have mis-specified generative assumptions, as having been previously suggested [7,11,12].


So we generically get slow logarithmic learning, consistent with the observations in [12].

[4]) that the posterior mean for GP regression can be obtained as the function which minimizes the functional where f H is the RKHS norm corresponding to kernel k. (note that the GP framework gives much more than just this mean prediction, for example the predictive variance and the marginal likelihood p(y) of the data under the model.)


Since our model is a POMDP solver and POMDPs are, in general, intractable (i.e., solution algorithms require an infeasible number of computations), it is clear that our model must ultimately fail to achieve optimal performance as environments increase even to moderate complexity.

we replicated these results, as shown in Figure 2B.


Simulation results over ten independent runs are summarized in Figure 5.

using Bayes' rule, the posterior distribution P (x * |{y t }, {x t }) can be rewritten as Since this posterior is equal to (6), one concludes (using ( 5)) that Note that this expression corresponds to the joint P (x * , {y t }|{x t }).


Here we construct an alternative to Theorem 1 based on exponentially sparse stopping times.

we call a bound that holds for all possible stopping rules J an adaptive bound.


Therefore, in our experiments we set these two parameters large enough to ensure that they outscore the published DQN scores, but not so large that they make our computational experiments unreasonably slow.

method 3: UCTtoClassification-Interleaved (for UCT to CNN via Classification-Interleaved).


Given the local surface geometry and the oriented line segments extracted from the image, we now create multiple hypotheses for possible spatial layout of the room and object layout in the room.

we use stronger parameteric models for rooms and objects in indoor scenes, which are more structured, that allows us to do more explicit and exact 3D volumetric reasoning.


Then clearly `is stochastically mixable relative to F. This is, of course, a trivial case.

we provide another piece of the puzzle by showing that an important concept in sequential prediction, the mixability of a loss, has a natural counterpart in the statistical setting, which we call stochastic mixability.


The fact that our model is able to capture an interaction between set size and target presence in terms of the number of fixations needed for detection lends support for our method.

the final color histogram was normalized to be a unit vector.


An alternative approach is to view the problem as estimation of a stochastic model, combining a scoring metric on candidate graph structures with a goodness of fit measure to the data.

our set-up includes the important situation in which the number of variables p may be large relative to the sample size n. we allow the graph  For many problems of interest, the graphical model provides a compact representation where the size of the neighborhoods are typically small-say d s p for all s ∈ V n . Our goal is to use 1 -regularized logistic regression to estimate these neighborhoods; for this paper, the actual values of the parameters θ ij is a secondary concern.


The expectations of these distributions are used in the calculation of Q w (W I ), Q w (W r ) and Q z (z) (Eqs.

the peripheral reconstruction was poor and often lacked shapes of the presented images.


Then it holds that Pr[lim t (x t , y t , x t−1 , y t−1 ) = (x * , y * , x * , y * )] = 0.

a time indexed vector x at time t is denoted as x t . We denote by ∇ x f (x, y) the gradient of f with respect to variables in x (of dimension the same as x) and by ∇ 2 xy f the part of the Hessian in which the derivative of f is taken with respect to a variable in x and then a variable in y.


Because the structured sparsity-inducing norms enforce the correlations along two directions of the learned coefficient tensor, the parameters in different sparsity norms are tangled together by distinct structures and lead to a difficult optimization problem.

our algorithm reaches one of the optimal solutions.


We first complete the dataset by filling last value, zero value, mean value and GAN generated value.

each value of the β should be bigger than zero and smaller than one, and the larger the δ, the smaller the decay vector.


While we define the spectrum and mismatch feature maps without any reference to a generative model for the positive class of sequences, there is some similarity between the ¡ -spectrum feature map and the Fisher scores associated to an order ¡ Markov chain model.

for two methods: the SAM-T98 iterative HMM, and the Fisher-SVM method.


In the single world approach, we generate a single perceived world W based on segmentations -a unique interpretation of a visual scene.

we introduce a novel dataset of more than 12,000 question-answer pairs on RGBD images produced by humans, as a modern approach to a visual turing test.


Both PCA and E-PCA reach near-zero error at 3 bases (E-PCA hits zero error, since an -basis E-PCA can fit an ( ¡ £¢ 2 -parameter exponential family exactly).

finding a value function this way is usually computationally intractable.


We cannot yet prove this conjecture, although numerical experiments strongly suggest it.

as of yet, the picture is still very incomplete in the online setting.


However they are typically only applied to static binary classification tasks.

the original score-operator in [4] was the 1st-order derivative operator applied to HMMs with discrete output distributions.


Bayesian sequential updating or belief propagation, implemented in the form of particle filtering, has recently been used in estimating the hand trajectories of monkeys based on M1 neuron's responses [4] and the location of a rat based on the responses of the place cells in the hippocampus [3].

at each time step of of decoding scheme, we can now filter a hypothesis particle (x 1 , x2 , .


A column vector of ones of arbitrary dimension will be denoted by e. For A ∈ ℜ m×n and B ∈ ℜ n×k , the kernel K(A, B) maps ℜ m×n × ℜ n×k into ℜ m×k .

in order to learn such a function we are provided with training data, A, containing S sets (or classes) of training samples: A = S j=1 (A j = {x j i } mj i=1 ), where the j-th set A j contains m j samples, so that we have a total of m = S j=1 m j samples in A.


By sampling drift only at endpoints, we will fail to sample some of the internal structure that is possible in drifts, e.g., we will fail to distinguish between a linear drift and a spiral pattern with the same endpoints.

the best algorithms can only extend the distance that the robot travels before experiencing drift.


POSS compares two solutions based on the domination relation as shown in Definition 3.


It is interesting to note that while using solely source training images yields very low accuracy (14.5% for SVM s ), adding even just a single labeled target image produces a significant improvement (TSVM achieves 18.5% accuracy with n t = 1, and 27.1% with n t = 5): this indicates that the method can indeed adapt the classifier to work effectively on the target domain given a small amount of strongly-labeled data.

we note that in work concurrent to our own, Saenko et al.


Unfortunately, we can not directly apply the smooth optimization method to problem (4) since the hinge loss there is not continuously differentiable.

lMCA controls the sparsity by directly specifying the dimensionality of the transformation matrix and it is an extended version of LMNN.


This improvement is even maintained over TNN-RPCA and MC which require prior knowledge such as the true rank and exact outlier locations respectively.

on the surface it may appear that the PB-RPCA objective (14) represents a rather circuitous route to solving (1), with no obvious advantage over the convex PCP relaxation from (3), or any other approach for that matter.


If the graphon W is piecewise Lipschitz, Algorithm 1 is a consistent estimator of the graphon cluster tree of W. We have presented a consistency framework for clustering in the graphon model and demonstrated that a practical clustering algorithm is consistent.

darker shades correspond to higher values of W. Figure 1b depicts a graphon W φ which is weakly isomorphic to W. W φ is the relabeling of W by the measure preserving transformation φ(x) = 2x mod 1.


At the region level we label pixels as belonging to one of a number of background classes (currently sky, tree, road, grass, water, building, mountain) or a single foreground class.

we conduct experiments on the challenging Street Scene dataset [2].


We denote E[f (x k ) − f (x * )] by V k , and we use W k to denote the last expression in (23).

we ran Acc-Prox-SVRG using values of η from the range {0.01, 0.05, 0.1, 0.5, 1.0, 5.0, 10.0}, and we chose the best η in each mini-batch setting.


There are interesting tradeoffs associated with the choice of parameters.

we highlight the CoSaMP algorithm [20] for sparse vector recovery and the ADMiRA algorithm [17] for low-rank matrix recovery in this paper.


Verbal fluency for two semantic categories, animals and foods, was administered in the last two testing rounds (2005 and 2010), yielding a total of 4714 lists for animals and 4624 lists for foods collected from a total of 5674 participants ranging in age from their early-60's to mid-70's.

furthermore, FE cannot estimate the transition probabilities from an item that does not appear as the first item in the lists, which is common in real-world data.


To predict the distance between r s and a previously-recorded response vector r nj , we extend kernel regression to account for the paired nature of distances.

we found that, using 500 CNN neurons for each layer, all layers had some predictive ability (Fig.


To avoid an error, we must have: y = sign(v;;,(x)) = sign(wlixli +WTXT).

hI order to verify that the margin bound is as tight as possible, it would also be instructive to study lower bounds.


However, as pointed out in [2], it makes little sense to solve an easier problem by 'reducing' it to a much more difficult one.

it would be interesting to see if tighter transduction bounds can be obtained by reducing the "slacks" in the inequalities we use in our analysis.


Hence, ( 8) and ( 9) impose desired constraints on both the marginal and joint distributions.

new images synthesized by VAEs tend to be unspecific and/or blurry, with relatively low resolution.


In Gridworld, it is interesting to see that Φ good and Φ opt are quantitatively very similar, yet both have similar effects on the rate of convergence in the tabular case, whereas Φ opt considerably outperforms Φ good in the deep learning case.

one reason for doing so is that expert demonstrations or advice can often be biased or incomplete, so being able to identify good advice from bad is critical to guarantee robustness of convergence.


Historically, multi-matching has received relatively little attention.

further, we identified 6 interest points in each image that correspond to the frame of the bicycle.


More specifically, we extend IRM for time-varying relational data by using a variant of the infinite HMM (iHMM) [15,3].

( 4) η k,l is the strength of a relation between the objects in clusters k and l. Generating the observed relational data x i, j follows Eq.


Note that most connections in this circuit are local, just like in a biological neural circuit.

"Research for this article was partially supported by the the Fonds zur Forderung der wissenschaftlichen Forschung (FWF), Austria, project P12153, and the NeuroCOLT project of the EC.


Lacking recursive features, it essentially must analyze long, rare constructions using only contexts.

one aspect of grammar induction where there has already been substantial success is the induction of parts-of-speech.


2(b) shows that for the large data regime the performance of pseudo-max learning gets close to that of the other methods.

we take a fully connected graph over n = 10 binary labels.


For each study 2 , i, we divided the MR images into D L i , D U i , and D S i , where an MR image (a.k.a slice) has three modalities available -T1, T2, and T1 contrast.

considering the fact that MR images contain much noise and the three modalities are not consistent among slices of the same patient, our improvement is considerable.


This will be investigated in detail in Section 3.

let h be a uniformly essentially strongly convex regularizer on X with modulus γ and let (η t ) t≥1 be a positive non-increasing sequence of learning rates.


This can be seen if we combine Table 2 and Table 1.

the distribution of activations is very different from weights.


We will denote π 0 (a | s) ≡ p(a | s) and refer to it as the "base policy," whereas we will refer to π g (a | s) as simply the "policy."

we trained Alice with action information regularization as in the previous section (see section S2.2 for training parameters).


We generated random data with 5 known rectangles and N additional random points and computed the average wall-clock running time (over ten trials) for each algorithm.

we limit this search to just those points required to define, and thus bound, the models currently under consideration.


Under the above assumptions and definitions, assume that the sequence of true random vectors x 0 and denoisers g 1 (r 1 , γ 1 ) satisfy Assumption 1.

for illustration, we repeated the previous experiment, but A constructed using the SVD A = UDiag(s)V T with Haar distributed U and V and geometrically spaced s. Also, to make the problem more difficult, we set b 1 = 1.


Efficient coding theory posits that one of the primary goals of sensory coding is to eliminate redundancy from raw sensory signals, ideally representing the input by a set of statistically independent features [1].

the distribution of the spatial-frequency tuning of the analysis vectors does not correspond to this trend; instead, it is bell-shaped (Figure 4b).


As training continues, Eve becomes better at her task, but then so does Alice as her weights are updated, in part, based on the loss of Eve.

they do not measure performance against state-of-the-art steganographic techniques making it difficult to estimate the robustness of their scheme.


Let Ω sample the observed entires of Ã so that A1 through A3 hold.

corollary 7 in the appendix can be used to establish the above conditions are necessary to recover A from a set of its principal submatrices which can be aligned in a overlapping sequence (e.g., submatrices running down the diagonal of A), which might be encountered when constructing a covariance matrix from sequentially sampled subgroups of variables.


Other connections of this type are discussed in [15].

for this model ξ(z, n) can be calculated exactly, because T (1) has only one non-zero row.


can also be handled under the paradigm of this paper.

in matrix completion, elementwise sparsity conflicts with Assumption 1 (and more traditional incoherence assumptions).


1 These labels are generated independently across pairs according to the distributions µ and ν.

this model is a special case of our labeled framework.


We establish their optimality by developing an upper-bound on their regret for each ↵; this nearly matches the lower bound (for BE), and exactly matches the lower bound (for BE-AE).

then the regret of the BE algorithm is as follows: observe that if w k = ln ln k, then we conclude .


This is unsurprising because these models have a built-in assumption that images are very smooth with occasional strong violations of smoothness [8,14,15].

for instance, we can define potentials on a small subset of input variables but, unlike Conv, each potential can have its own set of parameters, as shown in fig.


Meanwhile, mixed tabulation is 40% faster than both MurmurHash3 and CityHash, which showed similar performance as mixed tabulation.

again, we observe that this is not the case for mixed tabulation, which systematically out-performs the faster hash functions.


The key idea is that, in the market from our first result, only about (log T ) 2 of the T participants can be informational traders; after this point, additional participants do not cost the designer any more budget, yet their transaction fees can raise significant funds.

the market price update follows a natural kernel-weighted FTRL algorithm, where the learning rate λ is the price sensitivity of the market.


This term is in turn increasing in k with asymptote ϕ/(β − 1), which can therefore be taken as a k-independent bound.

let φ be the potential resulting from selecting βk cluster centers according to Algorithm 1, where β ≥ 1.


Accuracy value at coverage 100% is just the normal classification error.

for example, in Figure 2a, the normalized hybrid algorithm with R = 1 has a coverage of over 40% at 95% accuracy, while naive Bayes' coverage is 0 for the same accuracy.


Recently, several studies have explored AG methods for non-convex optimization [15,19,3,12].

none of these studies provide an explicit complexity guarantee on extracting NC from the Hessian matrix for a general non-convex problem.


We assume M = ZZ > for some matrix Z 2 R d⇥r .

moreover, even if we could have a reasonable approximation for the critical points (the solution of rg(x) = 0), it would be difficult to examine the Hessian of these critical points without having the orthogonality of the eigenvectors.


assumption 1 holds in expectation and the generalization performance of XNV is controlled by Theorem 1.


Based on the theoretical anslysis, we propose a novel solver GGM, which achieves remarkable performance in both synthetic and real-world image tests.

our method focus on one path no matter the path following or multiplicative strategy is used.


this number multiplied with the frame size at layer 6 will give the input dimension the first fully-connected layer accepts.


Using the phase coherence relation of Eq.

the detection precision is limited by the accuracy of phase measurement, rather than the highest spatial sampling density.


This assumption is important in view of the applications.

in this section, we explain how to use a stochastic version of the EM algorithm to produce maximum a posteriori estimates of the parameters.


Annotation (precision P, recall R, and f-score F) and retrieval (mean average precision MAP, and top-10 precision P@10) are reported in Table 3.

we illustrate the benefits of the proposed algorithm on hierarchical clustering of motion capture sequences as well as on automatic music tagging.


For example, both input neuroimaging measures (samples × features × time) and output cognitive scores (samples × scores × time) are 3D tensors.

first, because LR and RR methods by nature can only deal with one individual cognitive measure at one single time point at a time, they cannot benefit from the correlations across different cognitive measures over the entire time course.


Let M be the network obtained by grounding M with its reduced domains (which corresponds to the cluster centers) and let M G be the ground Markov network of M using the original domains.

the data complexity (fixed formula-size, variable domain-size) is polynomial.


Overall, these results yield the insight that the shape of the entire distribution of a deep network's Jacobian singular values can have a dramatic effect on learning speed; only controlling the second moment, to avoid exponentially vanishing and exploding gradients, can leave significant performance advantages on the table.

for hard tanh networks, p(q ⇤ ) = erf(1/ p 2q ⇤ ).


(The original version of LMM used a max of truncated exponentials mechanism, which gives the same guarantees up to constant factors.)

as these algorithms rely on the exponential mechanism and the max-of-Laplaces mechanism, their utilities degrade with the total number of possible itemsets.


. . f (x N )) is shorthand for the vector defined by evaluating f at the points in X = {x 1 , .


Formally, suppose f in (4) is convex; for such f , FBS performs the iteration where {η k } is a suitable sequence of stepsizes.

fBS is particularly attractive because of its simplicity and algorithmic structure.


Hence, when d = Ω(n), the introduced overhead reduces to O(log n) per iteration.

the algorithms that are used for data analysis face the difficult challenge to cope with the enormous amount of data or the vast dimensionality of the problems.


However, these works have focused mainly on stochastic optimization problems.

furthermore, we show that any distributed algorithm that implements (approximate) counters to additive error k/10 on all sites 4 is at least Ω(T ).


Indeed, as we show in the experimental study (Section 5), popular probabilistic modeling systems such as JAGS [7] or Stan [8] reify the graphical model, resulting in unreasonable memory consumption for models such as LDA.

indeed, it takes the collapsed LDA implementation 6.7 hours longer than Augur to draw 2048 samples.


Given state s and action a the next state s ′ is generated by s ′ = mod(s + 0.33a + 0.1randn, 1), where mod(x, 1) is the fraction part of x, and randn is a Gaussian random variable independent of the other variables in the problem.

the distribution over the initial state is uniform.


As we will show (in Section 3), in this setting the path is no longer piecewise linear.

the optimization problem is the following 1 : where λ > 0 is a regularization parameter and ||w|| is the 2-norm of w, defined as ||w|| = (w w) 1/2 .


Non-convexity immediately creates the risk of local minima, which unfortunately is not just a theoretical concern: EM often does not produce very good results in practice, and can sometimes fail to improve significantly upon initial parameter settings [9].

joint) EM algorithm, and to supervised training on fully observed data.


This method does not use user features, and captures similarities between users with a hierarchical GP model.

the posterior for f can then be used to make predictions on the user preferences for new pairs of items.


We first learn a set of "optimal" model parameters θ * by tuning g on H t with a standard loss function.

the associated k-shot regressor should be easy to learn because it is similar to an identity mapping.


In what follows, we present two algorithms that describe how to perform noiseless queries and noisy queries with outliers in order to seed the clusters.

the second performance measure is the query complexity, for which we once again have analytic upper bounds.


When δ, ζ and µ −1 min are fixed, C 1 = O(p), which is intuitive as one needs to update p functions at a time.

we set the discretization level δ = 0.05, the window size z = 3, the step size η k = (kδ/20 + 100) −1 , and the regularization coefficient ζ i,j ≡ ζ = 10 −8 .


The bound in (2) shows the potential of the two-layer coding scheme in achieving higher order approximation power than single layer coding.

if f (x) is smooth with relatively small α, β, ν, the error term becomes smaller (locally when x − x ′ is small) if we use a higher order approximation.


For ρ > 0 and 0 < α ≤ ∞ we say that h has geometric ρ-exponent α if Since {h > ρ} and {h ≤ ρ} are the classes which have to be discriminated when interpreting the DLD problem as a classification problem it is easy to check by Proposition 2.2 that h has geometric ρ-exponent α if and only if for P := Q s µ we have The latter is a sufficient condition for P to have geometric noise exponent α in the sense of [8].


The generator actually outputs a pair of sequential images, but we discard the second image in the pair.

we focus on discrete and deterministic dynamics models, which can be used with graph search methods, and on continuous models where planning is done by linear interpolation, though our framework can be generalized to other model types.


Experimental results demonstrate the comparative efficiency of our algorithms for sensor selection in high-dimensional distributions.

full parallelization, wherein each node i ∈ V is viewed as separate computing resource, incurs a multiplicative overhead of O(diam(G)) due to each i having to send This overhead can be alleviated by instead assigning to every computational resource a connected subgraph of G. It should also be noted that if the quantification is instead performed using serial BP -which can be conceptualized as choosing an arbitrary root, collecting messages from the leaves up to the root, and disseminating messages back down again -a factor of 2 savings can be achieved for R 2 , .


This has been one of the major criticisms of this type of encoding scheme as this result does not seem to be borne out experimentally (e.g., [19,2]).

intuitively, expending more resources on accurately approximating the complete density of natural sensory statistics is inefficient (from an optimal control perspective) if the behaviorally relevant signals live in a compact subspace.


For any Each observed variable x ∈ V obs is modeled as random vector in R d , and each hidden variable h ∈ V hid as a random vector in R k . The joint distribution over all the variables V T := V obs ∪ V hid is assumed satisfy conditional independence properties specified by the tree structure over the variables.

in the discrete case, suppose that the observed variables take on d values, and hidden variables take k values.


With the above definitions, we show in the following theorem that when X and Y are both full row rank, (G 0 , E 0 ) is the unique solution to Eq.

then models were obtained by applying each method to the remaining entries with a specific choice of λ from 10 −3 , 10 −2 , ..., 10 4 .


In fact, they differ only by some constants.

we now present the application of our stability bounds to several algorithms in the case of an algebraically mixing sequence.


our results hold regardless of what U is.

the paper is organized in the following sections.


We follow this particular approach since, first, CDFs can be easily estimated consistently using empirical CDFs without any free parameter, and second, standard tests on CDFs such as Kolmogorov-Smirnov (K-S) test [7] and Cramér-von-Mises (C-M) test [8] are well studied in the literature.

other methods should be investigated that allow two spike trains to interact irrespective of their spike counts.


Equipped with this new tool, we prove a series of theorems for missing data recovery and matrix completion.

are reserved for left singular vectors, right singular vectors and index set, respectively.


Next, since L i,t−1 is not assured anymore to be an upper bound on g t,i , we do not have any guarantee that the wealth Reward t,i is non-negative.

we encode the gambler's bet in round t by a single number w t . The sign of w t encodes whether he is betting on heads or tails.


The following lemma gives a lower bound on the correlation between the good groups and the residuals from the OLS prediction where the coefficients have been restricted to a set of good groups.


In this paper, we considered a new class of bandit problems with unobserved confounders (MABUC) that are arguably more realistic than traditional formulations.

the payout given by coin flipping is the same for both machines, P (Y = 1|do(X = M 1 )) = P (Y = 1|do(X = M 2 )) = 0.3, which means that the arms are statistically indistinguishable in the limit of large sample size.


This important property implies that, for large enough β, a random sample that is drawn from the tempered posterior would be close to the global optimum and can therefore be used as a MAP estimate.

it tries to find the absolute poses that best fit the relative pairwise measurements.


Only 4 landmarks were needed, and they correspond to very distinct face expressions.

the data must lie on, or near (accounting for noise) a manifold embedded in observation, or ambient space.


The model mesh X = (V X , E X ) is a complete model of the object, in a particular pose.

this model enforces preservation of local mesh geometry, as well as more global constraints that capture the preservation of geodesic distance between corresponding point pairs.


In multidimensional scaling, for example, pairwise distance measurements are used to form a kernel matrix and PCA is performed on this matrix to embed the data in a low-dimensional subspace.

in real world scenarios, the constraints that make it difficult to observe a whole matrix often also constrain which particular entries of a matrix are observable.


For any arms a = e|S ∈ A, we define the unit gap of a (i.e., the gap for one phase) as For any arms a = e|S ∈ A, we define the sunk-cost gap (irreversible once selected) as where for two feasible sets A and B, A ≺ B means that A is a prefix of B in some decision sequence, that is, there exists a decision sequence σ = S 0 = ∅, S 1 , . . , S k such that S k = B and for some j < k, S j = A.

online combinatorial learning problem can be formulated as a repeated game between the environment and the player under stochastic multi-armed bandit framework.


though its global solution attains the optimal statistical rate of convergence, such solution is computationally intractable to obtain.


In future work we aim to close the loop by providing end-to-end algorithms that both cluster data efficiently and give BTRs for the resulting C. Second, our work grounds this area of research.

the SDP relaxation for K-means has been instrumental to obtaining tight guarantees.


Let M n,P H (θ) = n −1 r nr m(a r , θ), where a r ∈ [0, 1] d is the center of B r , with a r (j) = (r j − 0.5)h n for all 1 ≤ j ≤ d. Comparing to θ * n,P H obtained by minimizing the exact integral, the only term in (8) impacted by using g(a r , θ) instead of h −d n Br g(x, θ)dx is the histogram bias term.

. . , x n } ∈ X n , where X is the data universe.


There are also many studies that directly train convolutional neural networks (CNN) using binary weights [3,4,20].

lastly, we used WRN-16-1 and WRN-16-2 to test the applicability of knowledge transfer methods for the architectures with the same depth but different widths.


Let p k denote the value f (σ k ), for 1 ≤ k ≤ N . Without loss of generality we assume that the permutations are labeled such that p k ≤ p m for k < m. We write f (•) to denote the function and f to denote the vector (f (σ k )) N ×1 .

consider a function f : S n → R. Suppose that f ℓ1 = 1 and we are given its corresponding Q.


In this paper, we consider multi-armed bandit problems with a continuum of strategies, parameterized by one or more real numbers.

two such applications are online auction mechanism design [8,15], in which the strategy space is an interval of feasible prices, and online oblivious routing [5], in which the strategy space is a flow polytope.


Interestingly, the assumption in Corollary 1 is satisfied by taking κ to be an empirical estimate of the curvature of the planar curves in Fig.

we first check the accuracy of these results in different classification settings.