Leveraging coefficients ([LC] in ULS) are approximated up to 10 −10 precision.

the second property met by ULS is illustrated in the second example below.


Together, they provide a reference flow, indicating a referential connection between one topic and another.

this coupling allows the model to take evidence about link structure into account when making predictions about document content and vice versa.


We considered the objective functions ¢ !'

to ensure G BC & e we distribute weight down the tree from level g (the root, C ) to levels e ¢ &% H¢ ¥¤ ¦¤ ¦¤ by a convergent series; where for simplicity we set the total weight allocated at level ' , G # C , to be G # C ¡ § # )( ¡ § # )( 10 .


The Maximum a Posteriori (MAP) estimation of network parameters W given training data {X , Y} for learning multiple tasks is where we assume that for prior p (W), the parameter tensor of each layer W is independent on the parameter tensors of the other layers W = , which is a common assumption made by most feedforward neural network methods [3].

the above updating equations ( 11) are computationally prohibitive, due to the dimension explosion of the Kronecker product, e.g.


In linear regression, we want to minimize x A b and hence, we can apply the framework of SVRG [12] (stated in Theorem 14) for solving it.

our running times depend only on the size of the input and natural numerical measures of the matrix, i.e.


Note that L-KM uses much less memory compared to OSM, converges at almost the same rate in iterations, and its running time per iteration improves as the iteration count increases.

subsequent work on the proximal setup uses trust regions, penalty functions, level sets, and other more complex algorithmic tools; we refer the reader to [18] for a survey on bundle methods.


Further for the Pascal dataset we do not have any initial depth estimate.

as shown, our joint approach achieves an improvement of almost 2.3% , and 1.2% in the overall accuracy and average intersection-union (I/U) score over the model of AHCRF [9], and almost 1.5 % improvement in the Algorithm Av.


We selected 953 genes with significant changes in expression, using their full set of 93 experiments.

much of the work on analyzing gene expression data [3] has focused on creating gene hierarchies.


Moreover, as seen in Section 2.1, f being roughly injective ≈ f giving high precision retrieval.

while precision is a natural measure in an information retrieval setting, it does not measure "how" wrong the retrieved data is.


(F2) is more stringent and we show that it is satisfied for convex nondecreasing and concave nonincreasing functions.

. . , w m ) ∈ R m be a random vector with independent components w i which satisfy Ew i = µ and w i − µ ψ2 ≤ K. Let imp(w) := m 2 −1 1≤i<j≤m (w i − w j ) 2 be the empirical variance of w. Then, for u ≥ 0, We can immediately apply this result when k / ∈ S. for k ∈ S, a more careful application is needed since we can only guarantee an exchangeable distribution for y k [m] in this case.


We then have to solve the prediction problem, i.e.,  We now notice that if the scalar c j = c(j), where c is a non-increasing function of rank position j, then ( 17) can be solved simply by sorting the values of h i , ✓i in decreasing order.

in the case of tractable graphical models, dynamic programming can be used to efficiently perform inference.


in this paper, we will consider two types of noise: , where is the elementwise product of two vectors.


obviously, (3) includes marginal MAP (2) as a special case by setting weights τ A = 1 and τ B = 0.


For example, both convolutional and recurrent operations process a local neighborhood (several nearest neighboring neurons) in either space or time.

define the following discrete nonlocal operator for where the superscript h is the discretization parameter.


Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function.

we generated N = 100 pairs of curves (x n , y n ).


For example, if P 1 is close to one, L ≈ C2 p(x)dx, while P e ≈ C1 q(x)dx.

in such an inner product space, the Cauchy-Schwarz inequality holds, that is, p, q 2 f ≤ p, p f q, q f . Based on this discussion, an information theoretic distance measure between the two pdfs can be expressed as We refer to this measure as the Laplacian pdf distance, for reasons that we discuss next.


We note that we can also impose both U T x == 0 and U T Px == 0, or even U T pBX == 0, S > 1.

they are distributed across the image and often have distinct local features.


This is not surprising since they are solving almost the same problem.

we show that a simple modification of Auer's UCB algorithm  achieves with high probability constant regret.


To deal with the computational demands imposed by such applications, high performance implementations of stochastic gradient and batch quasi-Newton methods have been developed [1,11,9].

similar behavior was observed on other datasets, in regimes where r • o was not too small.


These studies show that frequency and AoA are highly correlated (typically r = -.6) explaining the confound of older studies on frequency.

recently, Ellis & Lambon-Ralph (in press) have shown that when pattern presentation is staged, with one set of patterns initially trained, and a second set added into the training set later, strong AoA effects are found.


Modulo logarithmic factors, we require 1 λ machines to run 1 ηλ time, which is the same order of computation, but a dramatic speedup of a factor of 1 λ in wall clock time.

in all experiments, we fixed the learning rate to η = 1e −3 .


Using a Lévy flight proposal distribution will straightforwardly produce power-law flight distance if the posterior distribution is uniform over the entire space (i.e., every proposal will be accepted).

note that, from effective sample size perspective, DS is clearly the best among three sampling algorithms.


[22] recently derived identical minimax rates for divergence estimation.


The work of [5] provides the first differentially private algorithms for FIM.

finally, we show the applicability of our algorithm to two problems from data mining and machine learning: frequent itemset mining and private PAC learning.


For instance, we may not know a priori which sequence of fixations provides most information about an unknown image, but the total reward at the end of an episode will give us an indication whether the tried sequence was good or bad.

in line with its fundamental role, the guidance of human eye movements has been extensively studied in neuroscience and cognitive science literature.


These techniques are applicable to an unspecified spike sorting algorithm.

this maximally reduces the broad band noise without sacrificing the signal integrity.


We also need to calculate |X| and |E|, which are model counts that are in general difficult to compute exactly.

these techniques introduce approximation error that can be made arbitrarily small at the expense of lower efficiency.


This is because RPCA ignores clustering structures of the data which are ubiquitous in applications.

the magnitudes of the nonzero entries in S 0 may be arbitrarily large.


In the simplified case discussed in Section 2.2, with linear kernel on X = R d and H = R k finite dimensional, we have F = R d and this assumption corresponds to require the existence of a matrix W * ∈ R k×d = H ⊗ F, such that g * (x) = W * x for any x ∈ X .

as it is standard in statistical learning theory, we can impose regularity conditions on the learning problem, in order to derive also generalization bounds for f . if we denote by F the RKHS associated to the kernel k, we will require g * to belong to the same space H ⊗ F where the estimator g introduced in Eq.


This result is based on the intuition that IBAG never selects an action that is too uninformative relative to the other actions.

we define the principal set of an action w as J w ⊆ J .


We now turn to theoretical analysis of the joint method for parameter estimation and prediction illustrated in Figure 2.

the behavior of the TRW method is extremely stable, consistent with our theory.


Because the feature space is so small we can exhaustively search for all classifiers on single, pairs and triplets of segments.

we approximate every segment in a face image with a small number of representative pixels (a) (b) Figure 1: Face segmentation and representative pixels.


This makes the problem a non-linear ICA problem.

the learning mechanism is effective in producing approximately exponential firing rate distributions as observed in neurons in the visual system of cats and primates.


Given fixed base distributions, we can optimise the KL bound with respect to the parameters A = LU and b.

provided we choose a base distribution class that includes the Gaussian as a special case (for example generalised-normal, skew-normal and asymptotically Student's t) we are guaranteed to perform at least as well as classical multivariate Gaussian KL approximate inference.


Even with the delay in responding to event detection, the detectors have more than doubled the amount of reliable data collected from the estuary.

the estimated mixing coefficient should be well correlated with salinity, S m ≈ αS o .


Among earlier work, only PTP has looked at this problem (both search and sampling).


Recently, [7] separated PAC learnability and uniform convergence for large label sets by exhibiting PAC learnable hypothesis classes that do not satisfy the uniform convergence property.

in fact, this is derived for a loss function that takes just three values.


[21] developed a differentiable surrogate to the L 0 norm by smoothing the expected L 0 and using approximately binary gates g ∈ R n to determine which parameters θ ∈ R n to set to zero.

the regularization does very little to prevent the pairwise interactions from entangling within the neural network.


Thus, to find temporally correlated pixels all we need to do is run a clustering algorithm on the rows of the design matrix A.

in our experiments we have 8 segments, each represented by its mean and variance, giving rise to a 16D feature space.


Moreover, at high dimensions, the relative error made as considering E||X|| instead of the random variable ||X|| becomes asymptotically negligible [2].

under this assumption correlation between W and noise W − Q(W ) = ( 0 , 1 , ..., N −1 ) is negligible, and can be approximated as an additive noise.


Proof: Expected Generative Solution is ML Solution In the case of a generative model which has no constraints (i.e., can model any distribution), the maximum likelihood solution will have distribution px(a) = .J y Ef':18(yi -a), i.e., the model will produce only the observations and all of them with equal probability.

without Green's function, one might expect local optima in which clusters of points collapse onto a single location.


Our ablation studies (Section 4.3) support the hypothesis that the increased performance is due to the uncertainty-dependent reweighting of targets, as well as demonstrate that the performance of STEVE consistently increases with longer horizon lengths, even in complex environments.

we show that we can do still better by weighting the candidate targets in a way that balances errors in the learned Q-function and errors from longer model rollouts.


The goal of information bottleneck with side information (IBSI) is therefor to find a stochastic map of % to a new variable , @ 9¦ ¢¡ D © , in a way that maximizes its mutual information with & ' and minimizes the mutual information about & £) .

is supported a grant from the ministry of Science, Israel.


Posterior distributions depend on the modeling assumptions and can rarely be computed exactly.

the set of candidate densities no longer needs to be truncated, thereby easing its implementation and improving on the convergence guarantees.


In the Newton-LASSO Method, we approximate the objective function F at the current iterate P k by the piecewise quadratic model ) where g k = L (P k ), and similarly for H k . The trial step of the algorithm is computed as a minimizer of this model, and a backtracking line search ensures that the new iterate lies in the positive definite cone and decreases the objective function F . We note that the minimization of q k is often called the LASSO problem [18] in the case when the unknown is a vector.

the NL-FISTA algorithm terminated the FISTA iteration when the minimum norm subgradient of the LASSO subproblem q F became less than 1/10 of the minimum norm subgradient of F at the previous step.


We select the criticism points as the maximizers of this cost function: Where [n]\S denote all indexes which not include the prototypes, and c ⇤ is the number of criticism points desired.

it has quickly developed into an important part of model design, and Bayesian statisticians now view model criticism as an important component in the cycle of model construction, inference and criticism (Gelman et al., 2014).


Our work addresses this issue, giving the first gap independent bound for a Krylov subspace method.

as discussed in Section 6, for high dimensional data problems where is set far above machine precision, gap independent bounds more accurately predict required iteration count.


Consider a matrix of spike counts, S ∈ N T ×N , for T time bins and N neurons.

where ρ(•), µ(•), and Σ(•) are functions that output a probability, a mean vector, and a covariance matrix, respectively.


This work was in part funded by an NSF CRCNS grant (BCS-1309346) to AJY.

2a;b), since the persistent prior influence in Eq.


The above formulation requires the server to explicitly obtain predictions for each user, i.e., solve for X.

we express the error Σ − Σ F as a function of the total number of observations.


Therefore the expected regret comparing to the best hypothesis in H can be as large as O(1).

the optimal arm to pull should be a function of the context x, but this is not captured by the standard bandits setting.


For the CoffeeScript-JavaScript task, CoffeeScript employs a Python-style succinct syntax, while JavaScript employs a C-style verbose syntax.

such a correspondence makes it a natural solution to locate the referenced sub-tree in the source tree when expanding a non-terminal in the target tree into a sub-tree.


For each fold, we randomly initialized the location of the object in each image (the initialization was the same for the two methods).

a hidden variable h specifies a forest over the nouns such that each tree in the forest consists of all the nouns of one cluster.


In Gibbs+MH1+MH2+MH3, after a split the new clusters often move into separate regions; so it takes longer before they can merge again.

we describe inference procedures based on Gibbs and Metropolis-Hastings sampling in Section 4 and report experimental results in Section 5.


This can be intuitively understood as a safeguard against overfitting.

a hypothesis h ∈ H makes predictions by sampling from the conditional distribution y ∼ h(Y | x).


In this paper we present a slice sampling approach that requires little tuning while mixing well in both strong-and weak-data regimes.

if latent variables are required they can be sampled directly from the conditional posterior P (f |θ, data).


This is a rough match for the data in figure 2C.

c;D) Experimental and model proportion of reports of Adam when adaptation was to anti-Adam; but various strengths of Henry are presented.


We confirm its validity by reproducing a previously found effect -the influence of orientation on other images in the scene [12].

there is one reference frame shared by all the objects in a group.


following a classic approach in clustering by [13], we reduce the problem of finding a clustering with low cost to the problem of finding a coreset of small size.


Moreover, as the codebook size grows, non-linear classifiers, represented by RBF SVM in our experiments, suffer from the curse of dimensionality partially due to the large dimensionality of the over-complete feature representation.

we propose a new stacking technique for building a deep architecture, using a linear SVM as the base building block, and a random projection as its core stacking element.


Algorithms which treat the observation pairs {(x t , y t )} ∞ t=1 as iid will consider the random variables x, y as independent.

unfortunately, it typically involves density estimation or at least a nontrivial optimization procedure [11].


D-TS + : Implement the same operations as D-TS, except for the selection of the first candidate (Line 11 in Algorithm 1) is replaced by the following two steps: a (1) ← arg min R( 1) i ; D-TS + only changes the tie-breaking criterion in selecting the first candidate.

corollary 1 provides an upper bound for the regret of D-TS + .


Assuming the adjacencies X -Y -Z -W have been found, conditional-independence tests will reveal that (X Jl Z) and (X .,il Z I Y), which is a sufficient condition for the V-structure X ---> Y f -Z.

it contains spurious links to its spouses, to members of its district, to members of its children's district, and to parents of nodes in those districts, which we all call SD links (for Spouse/District).


The reason why these factors are less than the 3000 in the previous setup is that, for the larger proteins, the number of tied states is typically much higher than that for the small ones.

there always exists a maximizing µ that is integral and corresponds to x M . Although the number of variables in this LP is only O(|E| + |V |), the difficulty comes from an exponential number of linear inequalities typically required to describe the marginal polytope M(G).


Our MPGP framework does not only estimate the function value successfully, but it also provides a new technique for learning the unknown static hyperparameters by online estimating the marginal posterior of hyperparameters.

in [3], it is mentioned that SSGP model seems to be overfitting for this data due to the gradient ascent optimization.


For each attribute a d , we define a coverage set U d ⊆ U which covers all the combinations of pairwise classes that attribute a d can differentiate.

it would be beneficial to use a smaller subset of attributes while achieving comparable or even improved performance.


Every time a leaf makes 1 ǫ mistakes, TrackIPTree splits that leaf into its children, and instantiates and initializes the relevant path-node experts and node-label experts of the children.

we effectively plot the true positive rate against the true negative rate.


The update of φn in (11) indicates the key difference between the LSB-CMM model and traditional clustering models.

then z n is drawn from this distribution.


This prediction is consistent with single unit recordings on feature-based attention which show that the gain in neural response depends on the similarity between the neuron's preferred feature and the target feature [3,4].

finally, the gains g i on each saliency map can be found using eqn.


In detail, [14,8,9,10] view alternating minimization as a perturbed version of the power method.

since the alternating exact minimization algorithm updates U and V in a symmetric manner, we can establish similar results for a complete iteration of updating U in the next corollary.


Our first task is to derive an indirect Bayesian model for the optimal test point that builds its estimate via the underlying function space.

we aim to model directly the distribution of the maximum of (2) conditioned on observations.


Didea's resulting conditional Fisher kernel is benchmarked against the DRIP Fisher kernel and the previously benchmarked scoring algorithms using their respective standard Percolator features sets.

while DRIP significantly improves several facets of MS/MS analysis due to its parameter learning capabilities, these improvements come at high runtime cost.


Hence, even if the underlying form utility matrix is of low-rank, the overall purchase intention matrix is likely to be of high-rank, 2 and thus cannot be directly recovered by existing approaches.

we propose an extremely efficient optimization algorithm by effectively exploring the sparse structure of the tensor P and low-rank structure of the matrix X.


Another short-coming of the Ising model is that it can only model binarized data and cannot be normalized for integer y-s [6], so either the time bins need to be reduced to ensure no neuron fires more than one spike in a single bin or the spike counts must be capped at 1.

comparison with the output distribution derived for the Gaussian RLM suggests that this choice would fail to capture the instantaneous covariance that the LDS formulation transfers to the output distribution (and which appears in the low-rank structure of S above).


The computational challenge is how to reduce the space of possible edits effectively, and how to select the product from among the resulting candidates.

the overall pipeline is summarized in Figure 2.


In fact, the use of ensembles of CART trees [4] not only inherits all positive aspects of gradient boosting (robustness, speed and insensitivity to hyper-parameters) but is also a natural match for metric learning.

they often demand high computational expense, not only in parameter fitting but also in model selection and hyper-parameter tuning.


Neurons coding the same depth experienced common inhibition early in their responses for stimuli presented at their nonpreferred disparities.

using bootstrapped samples of stimulus trials, we estimated 95% confidence intervals for these three measurements [4].


Consider ✓ defined as follows: ✓t = ✏, and ✓t = Using the fact that log(1 z) 2z for z 2 [0, 1 2 ], it follows that We have ✓t ✓ ⇤ t for t 6 = t, and so Recall from Lemma 3 that, for each word i and t = arg max t it ✓ ⇤ t , we have ✓ t > K(↵, T, N ).

it is important to note that we only restrict the maximum number of topics per document, letting the Dirichlet prior and the likelihood guide the choice of the actual number of topics present.


Now, if parameter a in a,c is very close 6 to 1, then |Y * t | = K, and the algorithm itself will produce ordered subsets Ŷt such that | Ŷt | = K. Moreover, it does so by receiving full feedback on the relevant classes at time t (since Y t ∩ Ŷt = Y t ).

the algorithm is not directly dealing with the original loss when making exploration.


In [17] it is investigated that certain spectral features of ECoG signals can be used across subjects to classify movements.

we run 5000 epochs with a fixed learning rate 0.001.


This class of models strike a nice balance between their representation power (e.g., ability to model cliques) and the complexity of learning and inference processes on these structures (e.g., message passing is exact on trees).

a commonly used kernel function, which we will focus on, is the Gaussian RBF kernel k(x, x For Gaussian RBF kernel, there exists a feature map φ : R → F such that k(x, x ) = φ(x), φ(x ) F , and the feature space has the reproducing property, i.e.


Third, they may have different latencies, so they 'say' the same things at slightly different times.

the information that words provide about the visual stimulus then is if we know the identity of the fly to be i, we gain the information that its spike train conveys about the stimulus, Ji(W ~ s(t) j T), Eq.


The covariance between f x and f z is fully determined by the coordinates of the data pair x and z, and is defined by any Mercer kernel function K(x, z).

we employ the linear kernel K(x, z) = x • z or the Gaussian kernel K(x, z) = exp − κ 2 x − z 2 2 , and shift the origin of the kernel space to the empirical mean, i.e.


However, using the Kronecker factored approximation, the network achieves good performance relative to the individual networks across all five tasks.

they update this approximation to the posterior as the Gaussian that minimizes the KL divergence with the individual posterior approximations.


To this end, we intersect the confidence intervals: Given these high-probability confidence intervals, the system is stable according to Theorem 1 if v(f (x, u)) ≤ u n (x) < v(x) for all x ∈ V(c).


We thank Rob Goldstone, Karen Schloss, Stephen Palmer, and the Computational Cognitive Science Lab at Berkeley for discussions and the Air Force Office of Scientific Research for support.

figure 4 (d) and (e) show the results of applying the rational model with a noisy-OR likelihood to these two object sets.


For brevity, the proofs of the lemmas have been omitted and can be found in the supplement, where we in fact prove them for the more general setup of Theorem 3.

the following lemma summarizes the conclusions: ) and recall that δ was introduced in the definition of y k i .


We can then consider a quadratic regularizer of the form cV n /2kwk 2 to define the regularized empirical risk R n (w) := L n (w) + (cV n /2)kwk 2 and the corresponding optimal argument Since the regularization in ( 4) is of order V n and (3) holds, the difference between R n (w ⇤ n ) and L(w ⇤ ) is also of order V n -this may be not as immediate as it seems; see [22].

in the main paper we only use the protein homology dataset provided on KDD cup 2004 website.


Of course, this does not correspond to a realistic use of boosting in practice but it allows to check if the algorithm behaves consistently in terms of gradient steps number.

then, in section 3, the 55MBoost algorithm is presented.


The inter-agent communication and the LP avoid the exponential blowup in the state and action spaces, having computational complexity dependent, instead, upon the induced tree width of the coordination graph used by the agents to negotiate their action selection.

rather than placing a priori restrictions on the communication structure between agents, we first choose the form of an approximate value function and derive the optimal communication structure given the value function architecture.


For instance, consider a situation where the King of Hearts and the King of Spades, both on the pile, are vying for an empty build stack and there is a face-up Queen of Diamonds on a build stack.

the computation time required grows exponentially in the number of iterations, so this may not be practical.


Moreover, provided that is not too close to 1, dropout behaves similarly to an adaptive L 2 regularizer with parameter /(1 ) [6,12], and at least in linear regression such L 2 regularization improves generalization error by a constant factor.

here, we provide a heuristic argument for intuition.


It is an exciting direction of future work to determine which of these possibilities is true and to understand better as to why.

among all adaptive methods, AdaGrad's rate of improvement flatlines the earliest.


Theorem 2.3 presents an instance of a deep model that would be tractable to train with direct greedy optimization, such as gradient-based methods.

4 are the first-order and second-order conditions sufficient to prove Theorem 2.3 and Corollary 3.2?


The RADAR system [1], one of the first indoor localization systems, is an inverse modelling approach using a nearest neighbor technique.

one is very much interested in keeping the number of calibration points as low as possible.


Intuitively, if at least 100ρ% of all policies are feasible, L(v; ρ) is less than the objective value for the unconstrained CE method and greater than the expected G-value over the 100ρ% policies of the highest H-values.

a policy π ∈ Π is an optimal policy in Π with respect to ] be the expected cost over trajectory distribution P π .


Less well-known is a generalization of this result to renewal processes [13].

instead of using a single constant λ * , one could use (say) a piecewise linear function λ * (t) The more segments we use, the more flexibility we have; the price being the complexity of resampling this function, and slower mixing because of correlations it introduces.


Formally, a task τ ∈ T is defined as an MDP, and a policy π(s) is a function that outputs an appropriate action a given state s. The return, or utility, generated from interacting with the MDP environment by following π over an episode of k steps, is defined as the cumulative reward u = k i=1 r i , where r i is the immediate reward received by acting at step i − 1.

so, detecting from only one single perspective of policy's performance is not enough to exactly reason about the opponent's policy.


Principally, we have been assuming that each individual signatory of the petition exposes her petition copy independently with probability δ.

in this work, we have developed techniques that allow us to reason about the full tree along which the information spreads from the portion that is observed; as a consequence, we are able to propose estimates for the size of a network cascade from a sample of it, and to deduce certain structural properties of the tree that it produces.


All algorithms in consideration performed poorly on the mountaincar and acrobot testbed-none of them showing significant improvement in performance through learning.

it has four states [θ 1 , θ1 , θ 2 , θ2 ] and parameters K = [K 1 , .


We compared our optimized BP algorithm using FFT summation cliques with inference based on MCMC and regular BP, using the model and data from [8].

in the context of place labeling, [8] showed how to use non-zero mean priors in order to transfer weights learned for one person to another person.


We assume that each observation y i,j is a point on a N -dimensional Riemannian manifold M embedded in R P (with P ≥ N ) and equipped with a Riemannian metric g M . We denote ∇ M the covariant derivative.

each data point consists in four normalized scores, which can be seen as a point on the manifold M =]0, 1[ 4 .


Information of non-anomalous instances that cannot be handled by a single latent vector is modeled in Gaussian noise which is controlled by α.

they are rated by not only users who likes 'Comedy', but also who likes 'Romance' and 'Action-Thriller'.


(a) RFs in inferotemporal cortex are indeed very large, allowing for the possibility of distractor interference in the low load condition; and (b) even under the attentional load hypothesis, the only reason that an unattenuated distractor stimulus would interfere with target processing is that there is something in common about them, since it is known that there is more to the effects of distractors than just competition at the stage of the actual responses (Driver, 2001).


• If h✓ h0i , ✓ ⇤ i < 0, then for all t > T , Theorem 2 implies that if we use random initialization for ✓ h0i , with probability one, the Population EM 2 estimates converge to the true parameters.

in the M-step of EM, when the mean of the estimated component Ĉ is updated, it is pulled rightward towards +1.


. . Training examples recognized with high confidence usually do not appear in the SVM solution (2) because they do not become support vectors.

editing alters the apparent distribution of training examples such that the class distributions P (x | y = 1) and P (x | y = −1) no longer overlap.


Next, we consider the challenging case where the manifolds are close to each other.

one can see that the data are reasonably well separated according to their classes.


Given a source sentence with visible words x vis and missing words x miss , we want to find the settings of x miss and y which maximize p(x miss , y|x vis ).

most closely related to our work is Variational Neural Machine Translation (VNMT) , which introduces a latent variable z with the aim of capturing the source sentence's semantics.


(2006) has shown that banded Toeplitz matrices asymptotically approach circulant matrices as the size of the matrix grows.

since the distance from the origin during the initial random walk phase grows as √ n, the process will start to deviate from a random walk after n c ∼ (α(2 − α)) −1 steps.


On average, the mode is as good or better of an estimate than 68% of participants.

we also applied probabilistic models where the group answer is based on a pure rank ordering.


3(i)-(l) show the responses for drifting random dot stimuli at different velocities and coherence levels.

with position shifts, the neurons become speed tuned.


Hence, the posterior distribution 𝑝(ℎ|𝑥) has the form 𝑝(ℎ|𝑥) = 𝑝(ℎ)𝑝(𝑥|ℎ) 𝑝 (𝑥) .

there is a base function 𝑓 0 : R 𝑑 → R, centers 𝜇 1 , 𝜇 2 , .


The idea of much prior work on low-rank kernel approximation is to find K which is nearly as good as K k , but can be computed much more quickly.

2.1 Lower bound for low-rank approximation of MM T . We first illustrate our lower bound technique by showing hardness of direct approximation of MM T . Theorem 3 (Hardness of low-rank approximation for MM T ).


We run experiments on the biological interaction (Bio) and Reddit datasets (Figure 2).

the projection operator can be implemented using any composable, embedding-based edge prediction model, as defined in Guu et al., 2015 [18].


of the k-th variable of the input x j at time step j  i, for predicting y i as follows, where the index i of y i is omitted in the ↵ j and j .

rNN+↵ R model only provides scalar visit-level attention, which is not sufficient for healthcare applications.


This would make it easier for arbitrary regions of space to share the same covariance structures; at present the areas 'controlled' by a particular expert tend to be local.

in section 5 we present the results of several simple simulations that highlight some of the salient features of our proposal, and finally in section 6, we discuss our work and place it in relation to similar techniques.


We compare against running EM on the full set, as well as on an unweighted, uniform sample from D. Results are presented for three real datasets.

we use our approach for density estimation for acceleration data, motivated by an application in earthquake detection using mobile phones.


Now we can rewrite the first term of Eq.

formally, we need to display two models M 1 , M 2 such that the following relations hold (as implied by Def.


If S ( ) = 1, we reject the null hypothesis H 0 : ↵ ⇤ = 0.

in the context of high dimensional generalized linear models, [26,32] impose similar sparsity assumptions.


(and the corresponding predictions for the other 2 cards) at any history.

the "No Timestamps" model cannot fully represent a model of the tail's movement (which requires remembering what the head did when it was in the tail's position).


We show the tight relationship between Houdini and the task loss of the problem considered.

they can be used in combination with our proposal which derives a consistent approximation of the task loss having an analytical gradient.


Our convergence time analysis involves two steps.

2 the work Yu and Neely (2018) shows that when the dual function has Lipschitz continuous gradient and satisfies a locally quadratic property (i.e.


Furthermore, to evaluate the computational speedup gained by using random features, we compare against Nyström method [Drineas and Mahoney, 2005] as a secondary baseline.

the spectrum of C plays a crucial role in our results through the following key-quantity: Essentially, we will see that the constant κ(B k , k, m) is the dominating factor when bounding the excess risk, and, therefore, will determine the rate of convergence of our algorithms.


Besides the aperiodicity requirement, this assumption results in no loss of generality because transient states can be eliminated.

the TD(l) solution is equivalent to the optimal approximate solution.


The nontenninals A, B, C are elements of the non-terminal alphabet Vnt , which includes the start symbol S. t is a string of tenninal symbols from the terminal alphabet Vt 1 • For determining the language L of a certain grammar G I use simple depth-first exhaustive search of the derivation tree.

unlike in usual interpretations of this proof, these constraints are not strict (some grammars are better learnable than others, allowing for an infinite "Grammar Universe"), and they are not a-priori: they are the outcome of iterated learning.


A similar formulation was studied in Greenwald and Boyan [8], but without budget constraints.

it has been shown to be successful experimentally in simultaneous auction games [24] and other large games of imperfect information [7].


In fact, for the single-layer coding, our experiment shows that further increasing the codebook size will cause overfitting (e.g., with L 1 = 8192, the classification error deteriorates to 1.78%).

first, at the intuitive level, the first layer (traditional single-layer basis) yields a crude description of the data at each basis function, and multi-layer basis functions provide a natural way to zoom into each single basis for finer local details -this intuition can be reflected more rigorously in our nonlinear function approximation result.


To make the above framework more explicit, we consider the case of continuous hidden units and discrete, binary visible units, v i (t) ∈ {0, 1}.

training of these models by learning A, B, C, D (σ 2 was set to 0.02 throughout) is straightforward using the forward error propagation techniques outlined earlier in section (2).


For this particular subject, p(ŝ 1 , ŝ2 ) exhibited a significant correlation for 12 of 36 configurations.

on average, the k-th neuron has the highest firing rate in response to s 1 .


These bags reflect a fundamental ambiguity about the correspondence of patterns and the associated label which can be expressed logically as a disjunction of the form: x∈X (x is an example of class y).

it is often considerably less challenging to provide weakly labeled data, where labels or annotations y are associated with sets of patterns or bags X instead of individual patterns x ∈ X.


The practical problem is potential model over-flexibility 1 .

the MCMC scheme we discuss in the next section does not sample V n directly, but is based on local modifications of V n based on birth, death and reallocation moves.


Our first step is proving an analogue of Lemma 1, using the regret bound of the GEOMETRICHEDGE algorithm proved by Dani et al.

then, EXP3 cannot be used in the blinded bandit setting because the EXP3 update rule cannot be called on rounds where a switch occurs.


In the single-task learning setting maximizing the model evidence with respect to P is not expected to be effective to improve the prediction accuracy.

after EP has converged, q can be used instead of the exact posterior in (8) to make predictions.


Second, how does PGCN compare to an actorcritic where ∇ θ π(s, a, θ) is known?

equation 9does not hold for natural gradients: where θ = θ 1 , θ 2 , .


Complementing our theoretical analysis, the experiments clearly demonstrate that regardless of the actual stability measures per fixed sample size, they seem to eventually follow roughly constant and differing convergence rates, with no substantial degradation in performance.

2 as a guideline for when a stability estimator might be useful for arbitrarily large sample sizes.


In addition, it is worth mentioning that when performing the SVM, each x n was normalized to be V i=1 x n i = 1 because discrimination is much easier in the V − 1-dimensional simplex than in the original V dimensional space.

this is very efficient because it requires the calculation of the posterior probability at most L(L + 1)/2 times, while the exhaustive search needs 2 L − 1 times.


Given a strategy profile, σ, we define a player's best response as a strategy that maximizes their expected payoff assuming all other players play according to σ.

the vanilla form presented by Zinkevich and colleagues requires the entire game tree to be traversed on each iteration.


This offers a particularly simple way for solving problems of a size that would otherwise be out of reach for SVMs.

case 2 is indeed the best choice for initialization, because it represents the final solution.


There are no plates for the observation text (bottom part of the figure) because there is only one observation text document at each time step.

note that the objective ( 7) is a function of the MAP estimates of ✓ S t and ✓ at t . we start with a recursion for computing ✓S t and ✓at t and then introduce our learning algorithm for ⇥.


All experiments presented here were benefited by correlated sampling on top of stratification.

asymptotically, f i ( G m ) is normally distributed around its true value with a variance that depends on both the gradient of f and the covariance matrix of the approximated arguments in G m . This being the case, uniform sampling of the recursively estimated f i is equivalent to sampling from a distribution Pf that gives weight 1 n to a normal distribution centered on each f i .


The DITC algorithm minimizes this objective function by alternating computation of the cluster distributions and assignment of compound visual words to their closest cluster.

experiments demonstrate that assuming independence of visual cues given the categories provides a robust estimation of joint-cue distributions compared to direct empirical estimation.


If uniform probabilities are used, no pre-processing (for computing probabilities) is needed.

there are situations where by enriching the set of directions used by RCD by a single eigenvector only, the resulting method accelerates dramatically.


While the first call ( = 2.5) is identical to the A* call with the same , the second call to the ImprovePath function ( = 1.5) expands only 1 cell.

in addition to our theoretical analysis, we demonstrate the practical utility of ARA* with experiments on a simulated robot kinematic arm and a dynamic path planning problem for an outdoor rover.


To the extent that our model offers an accurate account of human object detection behavior, it should be able to predict the average number of fixations made by human subjects in the detection task.

each training image was represented by a set of SIFT features {F i,j , j = 1, ...n i }, where n i is the number of SIFT features in sample I i .


Given the current estimate θ, we form the quadratic approximation of the smooth loss function: where G = ∇L( θ) is the gradient of L and H is the Hessian matrix of g(θ).

they only consider the squared loss in their paper, whereas we consider a logistic loss which leads to better performance.


We therefore emphasize the importance of small datasets for standardized comparison among models.

we are only reasonably able to First, we address the critiques of Jozefoqicz et al.


In the PBM, each position in the list is also endowed with a binary Examination variable [8,19] which is equal to one only when the user paid attention to the corresponding item.

we consider the binary stochastic bandit model with K Bernoulli-distributed arms.


Simultaneous Perceptron: The simplest of the update forms generalizes the famous Perceptron algorithm from [8] by setting α t j to C if the j'th instance is incorrectly labeled, and to 0 otherwise.

we now use the mistake bound model to derive an upper bound on the number of trials on which the predictions of SimPerc and ConProj algorithms are imperfect.


Differentiable fingerprints can be optimized to encode only relevant features, reducing downstream computation and regularization requirements.

in the worst case, it can take a depth N 2 network to distinguish between graphs of size N . To avoid this problem, [2] proposed a hierarchical clustering of graph substructures.


Strong image edges could correspond to internal object structures, such as a window or a wheel of a car.

as noted by several authors and illustrated in Figure 1, the major stumbling block of all the scene-matching approaches is that, despite the large quantities of data, for many types of images the quality of the matches is still not very good.


For any link function f in (1.1) with µ 0 , φ(f ) defined in (3.2) and (3.1), and φ(f ) > 0 1 .

as we will describe below, our algorithm is based on a novel moment-based estimator, and avoids requiring such a condition, thus allowing us to handle even link functions under a very mild moment restriction, which we describe in detail below.


The same pathology exists for the broader class of power EP (PEP) algorithms [12] that includes variational message passing [13].

the accuracy of the methods is quantified in Fig.


Inspired by properties of the loss function discovered by our procedure, we also propose a new state-of-the-art ensembling method that can be trained in the time required to train a single DNN, with compelling performance on many key benchmarks (e.g., 96.4% accuracy on CIFAR-10).

to find these curves they used a different approach inspired by the Nudged Elastic Band method [12] from quantum chemistry.


(a) We provide an analysis of k-means for the case in which the data-generating distribution is supported on a manifold embedded in a Hilbert space.

indeed, as pointed out in [4], "The exact dependence of the minimax distortion redundancy on k and d is still a challenging open problem".


For any given ω ∈ Ω (the abstract probability space), projectiveness holds if θ I = Θ I (ω) for all I ∈ F(E).

a Bayesian nonparametric model places a prior distribution on the infinite-dimensional parameter space.


Treatment X is generated by first sampling a function f i (z i ) for every covariate from a Gaussian process, summing over 1 ≤ i ≤ 25 and adding Gaussian noise.

competitor III is particularly bad at lower signal-to-noise ratio problems, where sometimes it is overly confident that f (X ) is zero everywhere (hence, we ignore large likelihood discrepancies in our evaluation).


To save space, we defer this part to Appendix B.

probabilistic matrix factorization models have lend themselves naturally to leverage recent advances in Bayesian nonparametrics to bypass explicit model selection [17,1].


Note that for other algorithms M that do not satisfy (8), additional analysis and possibly a different initialization z 0 may be necessary (see Appendix D for example).

such methods should be contrasted with stochastic gradient methods [15,12], which minimize a different non-deterministic function.


The GCV criterion seems to work sufficiently well on the simulation data.

for the remaining portion of the algorithm we will use the kernel notation.


If S ⊆ X is a subset of demonstrations and A is a chain in (Φ S , ) then: Observe that if the lattice, (Φ, ) is itself a chain, then there are at most |X| + 1 non-empty demonstration partitions, Φ S . In fact, the non-empty partitions can be re-indexed by the cardinality of S, e.g., Φ S → Φ |S| .

in contrast to quantitative Markovian rewards, learning Boolean specifications enabled encoding compositional temporal specifications that are robust to changes in the environment.


This might be beneficial for preventing overfitting on outliers in the training set, since artifacts that are specific to a small number of training examples have a small prior probability, and will be discouraged from propagating forward.

in the first set of experiments, we test CNNs on the CIFAR-10, CIFAR-100 and tiny Imagenet datasets.


This cost function was motivated by the scenario, where a human expert tries to constrain the RL agent to adhere to human advice that the agent should stay in the center.

the baseline fails to show a meaningful policy except when ĉ = 200 since the Monte-Carlo cost returns at early stage mostly violate the cost constraint, resulting in random behavior.


We address this problem by adding a regularization term that prefers dictionaries with small number of primitives, as well as primitives of short length.

we thus formulate the problem of learning motion dictionaries as the one of solving the following optimization problem min where δ train , λ and η are parameters of our model.


S is said to be a minimal separator if S is a minimal (α, β)-separator for some non adjacent a, b ∈ V . If T = (K, S) is a junction-tree for G (see [7]), then the nodes K of T correspond to the maximalcliques of G, while the links S correspond to minimal separators of G (We reserve the terms vertices/edges for elements of G, and nodes/links for the elements of T ).

when the size of all the minimal separators are bounded, we may use these decompositions to easily solve problems that are hard in general.


While it is pretty easy to quickly estimate any subband likelihood or marginal distribution when working with Gaussian or multi-Gaussian densities [7], straigh implementation of ( 2) is not always tractable since it requires the use (and training) of L neural networks to estimate all the posteriors P(q3IS~,E>.e).

ideally, we want to design a particular HMM able to accommodate multiple time-scale characteristics so that we can capture phonetic properties, as well as syllable structures and {long term) invariants that are more robust to noise.


The above sufficiency conditions seem to be somewhat well-known; for example, most of the sufficiency statement appeared (albeit in somewhat less precise form) in [1].

(Note that this model is not the same as a Volterra series model; these two classes of systems have very different uniform approximation properties.)


Data augmentation has also been explored.

dCNN-32-6-3-2 produces a DCNN with the exact same shape and number of parameters of those of the reference CNN; DCNN-16-6-3-1, DCNN-4-10-3-1 are two ConcatDCNN instances from Section 2.2, which produce larger sized models with same or less amount of parameters.


Mode collapse can be accurately measured on synthetic datasets, since the true distribution and its modes are known.

the learning principle for VEEGAN will be to train F θ to achieve both of these objectives simultaneously.


We give the first (", )differentially private algorithm for robust PCA.

we limit our study to what is possible in the non-interactive variant of local differential privacy.


In fact, the global convergence of Algorithm 1 only happens for some special cases.

after t iterations, we have ŵt − w t ≤ t 0 .


Moreover, our study further demonstrates the relevance of DBMs as cortical models [11,12].

there is a bias apparent in the model towards one of the interpretations (different for different images).


sample pairs (x 1 , x 2 ) from P X × P X , and use Z(x 1 , x 2 ) as the label of x 1 − x 2 , where Z is the feedback from comparison oracle.

for example, A 2 algorithm can be adapted to Algorithm 1 straightforwardly by keeping U as the sample space and V as the version space.


MAESN learns a latent space that can be used to inject temporally correlated, coherent stochasticity into the policy to explore effectively at meta-test time.

since the KL-divergence loss (Eqn 3) encourages the pre-update parameters to be close to the prior, all of the variational parameters ω i are driven to the prior at convergence (Fig 5a).


By selecting the best chromosomes, and doing crossovers among them, better solutions are found.

(2) Does the genetic algorithm of Genetic-Gated RL models have advantages over a simple multi-policy model?


We have shown that a technique based on 1 -regularization, in which the neighborhood of any given node is estimated by performing logistic regression subject to an 1 -constraint, can be used for consistent model selection in discrete graphical models.


They showed that a carefully chosen prior will lead to asymptotic emptying of the redundant components.

theorem 1 formalizes the rate of concentration with increasing sample size n. One of the main assumptions required in theorem 1 is that the posterior rate of convergence relative to the L 1 metric is δ n = n −1/2 (log n) q with q ≥ 0.


Of the twelve pairs of images we tested, RMP failed to converge on 11/12 within 20 minutes, whereas COMPOSE failed to converge on only two of the twelve.

we also need to find all the max-marginals.


Under the first-order approximation of Equation 3, the simulation result is exact (Fig.

the threshold θ i is dependent on the weights, perhaps implying a lack of generality.


. . , i m with probability B ψi 1 ...ψi m . If A n is a random affinity tensor of the hypergraph, our aim is to find Z n or ψ from A n . Notice that if A n ∈ R n×...×n contains the expected values of the entries in A n , then one can write the entries in A n as The subscript n in the above terms emphasizes their dependence on the number of nodes.

if one considers m correct matches then certain properties are preserved.


Gaussian mixtures, where mixing distribution is not static but evolves according to (1).

in MSM-LDA, we can also update the hyperparameter α sequentially from the history.


It has not been shown how the representations in these models could be learned from natural images.

this visualization will be useful for understanding what the phase shifting components D in the second layer have learned.


Denoting the linear regression coefficient of log(v) versus log(κ) by β and the linear regression coefficient of log(α) versus log(κ) by ξ, it can be easily shown that (5) entails: Hence, if log(α) and log(κ) are statistically uncorrelated, the linear regression coefficient between them, which we termed ξ, would be 0, and thus from (6) the linear regression coefficient of log(v) versus log(κ), which we named β, would be exactly − 1 3 .

note that both for the planar and spatial shapes, the noise-level that drives the non-power-law signal to conform to the power-law is in the order of magnitude of the average displacement between consecutive samples.


The decay over the root mean squared gradients is set to 0.95.

assume we have a length-T binary visible sequence, the tth time step of which is denoted v t ∈ {0, 1} M . The TSBN describes the joint probability as where and each h t ∈ {0, 1} J represents the hidden state corresponding to time step t. For t = 1, . . . , T , each conditional distribution in (2) is expressed as where h 0 and v 0 , needed for the prior model p(h 1 ) and p(v 1 |h 1 ), are defined as zero vectors, respectively, for conciseness.


To perform estimation, we need a recipe for obtaining the permutations π.

acknowledgments: Markus Weimer is funded by the German Research Foundation as part of the Research Training Group 1223: "Feedback-Based Quality Management in eLearning".


Once again according to the correspondence between graphs and ratings, we will get that 2 → 1 should be contained in graph G, which contradicts with G 2 .

for the weighted pairwise surrogate loss, we get its sufficient condition of statistical consistency as shown in Theorem 5.


Ordinary differential equations (ODEs) can provide an useful framework for modelling the dynamics in these biological networks [1,2,13,8].

gibbs sampling can be extremely slow for densely discretized functions, as in the regression problem of Figure 1, where the posterior GP process is highly correlated.


Q-sampler for the Candidate Question Set In the main experiments, we compare two Q-samplers which select the question from the training data.

at 5-q, AQM-gen1Q performs slightly worse than AQM-countQ-depA (72.89% → 70.74%).


In which case it is important to return a solution in the original space.

let σ k+1 be the kth largest singular value of G t . Setting the projection dimension as Due to the randomized approximation we incur an additional 2τ √ β opt compared with the regret of ADA-FULL (eq.


We vary the the condition number of the data covariance (⌃) as well as the number of measurements (n).

let w ⇤ = arg min w,kw G k0k ⇤ f (w) and let f satisfy RSC/RSS with constants ↵ k 0 , L k 0 , respectively (see Definition 2.1).


Since this entailed finding the precise constants underlying earlier theorems, and a correspondingly more delicate analysis, we follow Negahban and Wainwright [8] and focus on the case where there are two-tasks (i.e.

certain rows of Θ would have many non-zero entries, corresponding to features shared by several tasks ("shared" rows), while certain rows would be elementwise sparse, corresponding to those features which are relevant for some tasks but not all ("non-shared rows"), while certain rows would have all zero entries, corresponding to those features that are not relevant to any task.


It is therefore natural to look at higher order derivatives and search for a second-order stationary points.

this work was supported by DARPA Lagrange and ONR BRC Program.


We review the related works in Section 5 and conclude in Section 6.

we get where κ(F ) is the condition number of the matrix F , R is an upper bound on the RKHS norm of object feature maps ψ(x) H . We define Q max as an upper bound on k c=1 q c H (can be seen as the generalization of the inequality k c=1 q c ≤ 1 for probabilities).


The results were corrected   for multiple comparisons using FDR correction with α = 0.05.

in the frequency domain, this temporal localization can be implemented by inducing correlations between the Fourier coefficients of neighboring frequencies.


For general multivariate regression, the only available method we are aware of is rodeo [11].

this is mainly an artifact of our analysis instead of a drawback of the additive forward regression algorithm.


the mechanism by which this is accomplished is not well understood.


Unfortunately, a direct deconvolution does not exist in general for linear transformations represented as EFF, since it involves summations over patches.

in (ii) during the final non-blind deblurring procedure we employ a sparsity prior for x by choosing p = 1/2.


We define the orthogonal projection operator Π : We consider the transfer problem in which M tasks {M m } M m=1 are available and the objective is to learn the solution for the target task M 1 transferring samples from the source tasks {M m } M m=2 .

we propose a method that adapts λ at each iteration so as to minimize the transfer error E λ .


The objectvie πi ni = πj mj at the right-hand side of ( 9) is a sufficient condition of the objective i∈Pj πi ni = π j at the left-hand side of (9).

m i = |P i |, n i = |S i | imply the in-degree and out-degree of the node i. Matrix A denotes the corresponding adjacency matrix where each entry a ij ∈ [0, ∞) is the weight of link (i, j).


Then, one can adopt the principle of separating the presence of an entity and its instantiation parameters into capsule length and orientation, respectively.

in stochastic gradient method, since only a small change is made to update W l in each training iteration, thus it is often sufficient to use this recursion to make an one-step update on the normalization matrix from the last iteration.


The proofs of parts (i) and (ii) overlap to a large extent.

this is in contrast to the design from Ens + , where even p/n = 10 can be handled.


For, example most blobs are surrounded with a thick ring of very small nonzero values.

for CanICA, the hard-thresholded version has been (a) Qualitative comparison of the estimated dictionaries.


Finally, we extend the filter to handle heavy-tailed noise.

we use a dynamic tracking model, the Kalman filter [10].


For both models, A i (t) and σ i (t) are unobserved.

the results are based on 260,000 samples and were obtained in approximately twelve hours on a standard workstation.


The theoretical analysis is done in a non-parametric limit, i.e., we assume a model with infinite capacity.

given a fixed encoder E, the optimal discriminator outputs q * D (s | h) = p(s | h) and the optimal predictor corresponds to q * M (y | h) = p(y | h).


This proves that σ (D) and σ (D) are independent when D is drawn from X(n, 1 / 2 ).

the best current approaches are based on Markov Chain Monte Carlo methods, which have some practical limitations.


Over the past few years, there has been much research on this question in the machine learning community, with just a few examples including [24,2,1,5,4,10,20,19,25,13].

their results relied on with-replacement sampling, and are applicable only for much smaller condition numbers.


Note that self-loops are avoided by setting w {i,i} = 0.

we have proposed an alternative form of exchangeability for random graphs, which we call edge exchangeability, in which the distribution of a graph sequence is invariant to the order of the edges.


One standard approach to convex relaxation would be a combination of group L 1 (the first constraint) and L 1 (the second constraint) penalties.

o(N P + P D + P D log D) is the computational complexity of partition-wise linear models where P is the number of active partitions.


For now, suppose we are given a reward R : P → R which takes in a distribution P and returns a real value indicating how preferable P is.

we first rank the individual features based on their classification accuracy, and only consider the top 80 features (using 80 features achieves essentially the same accuracy as using 184 features).


The goal of the subject is then to infer the unknown weights in order to predict reinforcement.

it would be useful to develop less extreme models in which subjects either rely on sampling with more particles, or on some combination of sampling and exact inference.


(C4) Probability of support: The probability of i being in the support of x * is uniform over all i ∈ {1, 2, . . . , r}.

in contrast to previous theoretical analyses for this problem, we replace a condition on the operator norm (that is, the largest magnitude singular value) of the true underlying dictionary A * with a condition on the matrix infinity norm (that is, the largest magnitude term).


3 If the bound B is not known beforehand then one can use a doubling trick.

we present the SI-BO algorithm, which leverages recent low-rank matrix recovery techniques to learn the underlying subspace of the unknown function and applies Gaussian Process Upper Confidence sampling for optimization of the function.


The features of the data are 14 dimensional and consist of partially informative and partially random features.

we restrict ourselves to a Boltzmann machine that has individual and pairwise features only and corresponds to an undirected graphical model G F = {V F , E F } where each node V F corresponds to an individual feature and the edges in E F between the nodes correspond to the pairwise features.


Hence, the algorithm will converge to a local optimum, which depends on the initialization conditions.

both boosting and SVM follow a two-step procedure: (i) mapping data to some intermediate space, and (ii) determine the boundaries that separate the classes.


Error propagation might occur when the model replicates an incorrect previous logical form, which hurts performance.

take A5 for example: it has a semantic category num, a function symbol count, and a semantic category set as the only argument.


The error measure d (e) is given by subject to certain constraints, such as positivity of the messages and potentials.

additionally, graph simplification by edge removal may be regarded as a coarse form of message approximation.


The sequentially trained iSHM pairs can be stacked into PBDN, a feedforward deep network that gradually enhances its modeling capacity as the network depth increases, achieving high accuracy while having low computational complexity for out-of-sample prediction.

the infinite support hyperplane machine (iSHM), which interacts countably infinite non-negative weighted hyperplanes via a noisy-OR mechanism, is employed as the building unit to greedily construct a capacity-regularized parsimonious Bayesian deep network (PBDN).


This gives us a natural way to set p since p = 1 k , where k is the expected skill length.

they are consequently more complex and computationally intensive than the much simpler changepoint detection method we use, and they have not been used in the context of skill acquisition.


In practice, a nonlinear output layer together with its matching loss function [11], such as the softmax function with cross-entropy loss, is widely used.

( 13) immediately gives a convex approximation of the Hessian for CTC as removing the linear team −f z from L c (F ) in Eq.


The main difference is that for the stochastic bandit problem, the goal is to maximize the sum of obtained rewards, whereas ours is to maximize the performance of the final classifier.

results on only four tasks are presented in a companion article [20].


In this setting the notion of adversarial regret is adopted [Auer et al., 2002b, Hazan andKale, 2011], where the regret is measured against the best possible fixed action that could have been taken in hindsight.

mAB formulation has been studied extensively, and was leveraged to formulate many real-world problems.


Assuming that Z has low (k, q)-rank means that the noiseless response is a sum of a small number of terms, each involving only a small number of features from either of the input vectors.

the Truncated Power iteration (TPI) algorithm of [20] can easily be modified to compute Ω * k,q which corresponds to a generalization of the rank 1 sparse PCA in which in general a = b and k = q.


If M t is small and the energy estimate is poor, then minimising the energy estimate exactly is a waste of computation, as as soon as the mini-batch is augmented the proxy energy loss function will change.

let us denote by M t (j) the indices of samples in M t assigned to cluster j.


Moreover, the size of the optimal neighborhood of a data point, which can be different for different points, provides an estimate of the dimension of the manifold to which the point belongs.

this requires a linear combination of more than 2 data points.


However, these methods all require a large amount of extra computational cost, and some of them also result in loss of accuracy on normal examples.

note that the output F (z) has L − 1 equal non-maximal elements for any points on the low-dimensional manifold S ŷ = ( i,j =ŷ db ij ) dd ŷ .


On one hand, this result establishes that it is indeed possible to have polynomial (or almost linear) time approximation algorithm for arbitrary pair-wise MRF with polynomial growth.

through extensive simulations, we show that our algorithm finds extremely good approximate solutions for various kinds of MRFs with geometry.


we must instate additional assumptions on the data if we hope to compute nonnegative matrix factorizations in practice.


The KBR approach nonetheless has a weakness common to other nonparametric methods: if a new data point appears far from the training sample, the reliability of the output will be low.

we now demonstrate the consistency of the KBR estimator in Eq.


Our analysis gives tight bounds on the precision-variance trade-off induced by QSGD.

4-bit QSGD with 8192 bucket size (not shown) loses 0.57% for top-5 accuracy, and 0.68% for top-1, versus full precision on AlexNet when trained for the same number of epochs.


We report empirical evidence against such a connection and in favor of an alternative explanation.

he also notes that little progress has been made on this topic in the past decade.


We assume that the vector X = {X s | s ∈ V } has a distribution that is Markov with respect to the graph G, so that its distribution can be represented in the form Here A(θ) := log x∈X N exp s∈V θ s (x s ) + (s,t)∈E θ st (x s , x t ) is the cumulant generating function that normalizes the distribution, and θ s (•) and θ st (•, •) are potential functions.

1  Consider the problem of joint learning (parameter estimation) and prediction in a Markov random field (MRF): in the learning phase, an initial collection of data is used to estimate parameters, and the fitted model is then used to perform prediction (e.g., smoothing, interpolation, denoising) on a new noisy observation.


There is also an alternative, more direct motivation for diffeomorphic mappings in the context of dimensionality reduction, however.

diffeomap seems to produce a result which is superior to that of the GP-LVM (Lawrence, 2004), for example, but may be inferior to that of the SNE (Hinton & Roweis, 2003).


The drawback of second-order methods is that they have to store and invert the t × t covariance matrix between all SV included in the predictor.

1 can be refined in the specific case of squared loss as follows.


Note the effect of 9 in preventing the ACh level from dropping to h . Figure 3C shows that the ACh-based approximate posterior values w x ¤ z { are much closer to the true values than for the purely bottom-up model, particularly for values of w yx ¤ ¡ z ¡ { near h and l , where most data lie.

the ACh signal of figure 4A was calculated assuming knowledge of the true posterior, which is unreasonable.


Pick any finite edge-set Q ⊂ S × S. Let Z denote the number of edges of Q ǫ cut by a point x chosen at random from P. Since the edges have length at least ǫ, this x has at least an ǫ chance of cutting any of them, whereby EZ ≥ ǫ|Q ǫ |.

the expanded role of P in our model makes it substantially different, although a few intuitions do carry over -for instance, Corollary 3 generalizes the notion of teaching dimension [8].


Obviously, this set of n -1 vectors is a rich  ) Note the visual similarity of the shape contexts for 0 and 0, which were computed for relatively similar points on the two shapes.

experimental experiences show that the algorithmic performance is independent of the details.


1, the pivotal quantity criterion is imposed with respect to p(X|Z) where Y is marginalized out.

(Pan et al., 2011;Gong et al., 2013;Baktashmotlagh et al., 2013;Zemel et al., 2013;Ganin and Lempitsky, 2014;Ajakan et al., 2014;Edwards and Storkey, 2015;Louizos et al., 2015) are all based on the minimization of some form of divergence between the two distributions of f (X)|Z = 0 and f (X)|Z = 1.


With the ability to train Koopman models that account for control inputs, we now consider a modified version the two-dimensional cylinder test case that allows for a scalar control input to affect the fluid flow.

viewed in this light, we note that the controller obtained through MPC is quite interpretable, and is functionally similar to a proportional controller performing feedback based on y-velocity measurements with a gain of 0.4.


Our results offer the best of both worlds: O(K log T ) bounds without restrictive assumptions.

we ran independent experiments with varying horizons and recorded the accumulated regret: the markers on the curves corresponding to these algorithms represent these numbers.


The paradigm of Hebbian learning has recently received a novel interpretation with the discovery of synaptic plasticity that depends on the relative timing of pre and post synaptic spikes.

in the case of inhomogeneous Poisson spike trains where input neurons fire independently, the covariance ~o spikes should have an effect only when a rare pattern ~'f/ is presented.


We show that this holds even when the rules output winning alternatives.

for α 1 , α 2 > 0, if noise models P 1 and P 2 are PPM-α 1 and PM-α 2 , respectively, then their composition The lemma's proof is relegated to Appendix D. Let us explain the process of generating votes for the uniform team and for the diverse team.


This amounts to determining all bits such that sign(r T G t1 u) = sign(r T G t u), or equivalently, (r T G t1 u)(r T G t u) ≤ 0.

to experiment with this scenario, we randomly mix online additions of 50,000 constraints with 10,000 queries, and measure performance by the recall value for 300 retrieved nearest neighbor examples.


We use these bins to define our ranking constraints: all the datapoints with target value falling in the same bin were grouped together.

we test tested our approach in a set of nine publicly available datasets 1 shown in Tab.


In this paper, we balance this negative result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference.

also for approximate methods, however, the benefits of lifting will decrease with the amount of symmetry-breaking evidence (e.g., Kersting et al.


This alternative is intuitively subject to a trade-off between the increased sample size and how different the aggregated users are.

for concreteness here we adopt the latter approach, since it serves well in the following section on density estimation.


1 the K-means initialization and the final solution.

specifically: Here Z i,k , i = 1 . . . N, k = 1 . . . K are binary variables indicating if site y i belongs to global component x k . The N × N matrices B [1] .


We observe that this ratio stays almost the same for RL with different decoders.

we assume that the vehicle is located at the depot at time 0, so the first input to the decoder is an embedding of the depot location.


to apply the EM method, we consider the complete data to be the sample histograms s and the pmfs that generated them (s, v 1 , v 2 , .


Indeed, this is in a sense the core sampling problem that has always plagued active learning: the labeled sample T might not be i.i.d.

in this case, the algorithm adds x n , with this inferred label, to S. Otherwise, the algorithm requests the label y n and adds (x n , y n ) to T . S contains examples with inferred labels consistent with h * , and T contains examples with their requested labels.


We use liblinear for SVM implementation; error penalty C is selected using cross-validation.

we use uncertainty sampling where we consider the entropy of the posterior over label vector as the selection criterion for BML-CS-Active method.


We also thank Leslie Smith for advice and assistance in model building.

juvenile barn owl could recover its sensory map alignment by shifting its auditory map.


For any p ∈ (0, 1), one can specify b t so that with probability 1−p, the total regret of Q-learning with UCB-Bernstein (see Algorithm 2) is at most O( Theorem 3 shows that for Q-learning with UCB-B exploration, the leading term in regret (which scales as T ) improves by a factor of √ H over UCB-H exploration, at the price of using a more complicated exploration bonus design.

the key observation is that, although in the worst case the value function is at most H for any state-action pair, if we sum up the "total variance of the value function" for an entire episode, we obtain a factor of only O(H 2 ) as opposed to the naive O(H 3 ) bound (see Lemma C.5).


• In Section 5, we show that MMD GAN is computationally more efficient than GMMN, which can be trained with much smaller batch size.

we observe that it is not necessary in practice.


Further, we provide a parametrized version of the bounds that can adjust the trade-off between the efficiency and the accuracy of the bounds.

finally, a graph whose score is the median from all 100 scores is chosen for Figure 2a.


The library then gives the typical rotamers for each side-chain and their prior probabilities.

this leads only to a modest increase in prediction accuracy.


Overall, Group-OMP performs consistently better than all the comparison methods, with respect to all measures considered .

we compare the performance of these methods in terms of the accuracy of variable selection, variable group selection and prediction.


Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space.

using ψ, and noting that the program involved by the SVR algorithm is convex, the estimation of the preimages does not have to deal with any problem of local minima.


The results in this paper are a generalization of the results of Zhang and Yu [24] to the online setting.

5: Define end for Predict y t = y N t . Obtain loss function `t and su↵er loss `t(y t ).


As covariance function, a Gaussian kernel is frequently used [1]  where σ 2 s denotes the signal variance and W are the widths of the Gaussian kernel.

after determining w k for all k local models in the partitioning space, the input point will be assigned to the nearest local model, i.e., the local model with the maximal value of distance measure w k .  Figure 2 shows the normalized mean squared error (nMSE) of the evaluation on the test set for each of the three evaluated scenarios, i.e., the simulated SARCOS arm in (a), the real SARCOS arm in (b) and the Barrett arm in (c).


To compile an SDD for the hierarchical, simple routes of G, we first compile an SDD representing the simple routes over each region.

hence, graph G B is an abstraction of graph G, while each graph G bi is a subset of G. Moreover, one can think of each subgraph G bi as a local map (for region i) together with a particular set of edges that connects it to other regions.


Like CTPF, the underlying MF algorithm has a per-iteration complexity that is linear in the number of non-zero observations.

like fLDA, both papers tie latent spaces without corrective terms.


In addition, ResNets introduce shortcut operations which also provides considerable versatile features since receptive fields of neurons in different layer are various as discussed in [18].

in addition, Versatile v2-ResNet-50 with the same amount feature maps achieved a 8.2% top-5 accuracy, which is slightly higher than that of the baseline models.


Subsequently, our reinforcement learning algorithm takes over and learns how to move the ball into the cup reliably.

the state of the system is described in joint angles and velocities of the robot and the Cartesian coordinates of the ball.


Although we have access to an analytic closed form of the (marginal likelihood) objective, this function is (i) expensive to evaluate and (ii) highly multimodal.

we define the d-KG factor for a given set of q candidate points z (1:q) as d-KG(z where E n [•] is the expectation taken with respect to the posterior distribution after n evaluations, and the distribution of μ(n+q) 1 (•) under this posterior marginalizes over the observations y(z (1:q) ), ∇y(z (1:q) ) = y(z (i) ), ∇y(z (i) ) : i = 1, . . . , q upon which it depends.


with continuous features, the nonlinearity of the reward was further exacerbated, making it difficult for linear methods to represent it even on the training environment.


despite the availability of a large amount of video data, visual frame prediction remains a challenging task because of the high-dimensionality of video frames.


In linear discriminative prediction we select the y that has the greatest value for the inner product Φ(x, y), w . Linear discrimination has been widely studied in the binary and multiclass setting [6,4].

the dual is a quadratic Dual problem: max ᾱ F (ᾱ), where min w,¯ Relationship between optimal values: w * = C i,y α * i,y Φ i,y where w * is the arg min of the primal problem, and ᾱ * is the arg max of the dual problem.


In each image, the bounding box of a bird is given.

spatial pyramid matching may not be the best choice for fine-grained object recognition, since falsely aligned object parts can lead to inaccurate comparisons, as shown in Figure 1.


For a review of properties of Bregman divergences, see Chapter 11.2 in [11], or Appendix A in [2].


While one can expect that mixtures of splines (Bar-Joseph et al., 2002) or functions with universal approximation capabilities can be fitted to any mean behavior, the restricted class of functions that we proposed (based on the simplified dynamics of the mRNA changes implied by the differential equation in Equation ( 4)) is likely to fail if the true dynamics does not match the assumptions.

there are two main reasons to use the proposed restricted class of functional forms: (1) to be able to interpret the resulting mean curves in terms of the synthesis / decay rates at each of the regimes as well as the switching times; (2) to naturally incorporate alignment by real-values shifts along the time axis.


We could easily get two classifiers to predict the type and relation of a noun phrase: predictR(X,R) and predictT(X,T), which are simple classifiers as described in Section 2.1 using their own features.

we also define every document to be "near" itself, so near(d i , d i ) is always true.


The Hadamard-Rademacher process in two dimensions: explores a state-space of 16 orthogonal matrices, is ergodic with respect to the uniform distribution on this set, has period 2, the diameter of the Cayley graph of its state space is 3, and the chain is fully mixed after 3 time steps.

aW acknowledges support by the Alan Turing Institute under the EPSRC grant EP/N510129/1, and by the Leverhulme Trust via the CFI.


The SAG-LS method was initialized with L 0 = 1 .

incremental Aggregated Gradient: Finally, Blatt et al.


In parallel, recent work in neurophysiology shows that the basal ganglia can be modeled by an actor-critic version of temporal difference (TD) learning [4][5] [6], a well-known reinforcement learning algorithm.

the signal generated by dopaminergic (DA) neurons resembles the effective reinforcement signal of temporal difference (TD) learning algorithms [5][8].


Our aim is to illustrate the combination of neural networks and intuitionistic modal reasoning.

dually, if A is active in every ω j then A must be activated in ω i (this is done with the use of feedback connections and a hidden neuron that computes a logical and, as detailed in the algorithm below).


[2] showed that SVM-like algorithms optimizing the AUC have good generalization guarantees, and [11] showed that maximizing the margin of the pairs, defined by the quantity g(x) − g(x ), leads to the minimization of the generalization error.

to derive the bounds, we consider φ, the 1-Lipschitz function defined by φ Given a training example z, we denote by z l its label and z f its feature representation.


When the statistical model M is regular, or the true distribution Po (x) is at a regular point , the mle-based p(x, 0) and the Bayes predictive distribution are asymptotically equivalent, and are Fisher efficient under reasonable regularity conditions, where d is the dimension number of parameter vector (j.

by substituting t(w) in ( 14) the log likelihood function becomes t=l the mle w is given by the maximizer of L(w), w = argmaxwy2(w).


We define point-wise cost function c : , which measures the cost on a position k by comparing G S (x x x, k) and the gold-standard tag y y y (k) , and we introduce the point-wise loss as Then, we define sample-wise cost function C : Y n × Y n → R + , which is the cost function with respect to a whole sample, and we introduce the sample-wise loss as Given G and a training set S, what we are most interested in is the generalization risk in structured prediction (i.e., expected average loss) [18,7]: Since the distribution D is unknown, we have to estimate R(G S ) by using the empirical risk: To state our theoretical results, we must describe several quantities and assumptions following prior work [2,12].


For DPP-MC, the running time includes the automated λ tuning.

some common techniques to determine k include performing a density-based analysis of the data [9], or selecting k that minimizes the Bayesian information criterion (BIC) [10].


We propose a scalable algorithm for inference, which can be parallelized for use on very large data sets.

inference for GRUMs has been generalized in [4], Azari et al.


(For instance, see Section 6.1 in [11] for a thorough discussion.)

ground truth keypoint matching is provided in the dataset.


Different IBP draws could result in different number of nonzero columns in B x and B y .

we accept the proposal with an acceptance probability given by a = min{1, p(rest|η * ) p(rest|η) }.


One way to achieve this is to use the fact that y|X ∼ N (0, Σ).

further analysis of the data indicates that learning on this task is hard as there is a lot of variability that cannot be explained by the 1-out-of-13 encoding used for the input features.


Following an energy-based framework, the energy of a triplet is equal to d(h + , t) for some dissimilarity measure d, which we take to be either the L 1 or the L 2 -norm.

its complexity may make it quite hard to learn, resulting in worse performance.


The distance is evaluated by cosine similarity based on the vectorial representations learned by DMTE.

most text embedding models do not embed the semantic relatedness between different texts.


( 2) and update unmixing matrix with the learning rule in Eq.

with heavy noise, the recognition rates of MLP sharply decrease, and the error backpropagation can hardly provide valuable information to the leA network.


This error bound is tight with respect to static PMW, which incurs additive error O(( log N log k ✏n ) 1/3 ) for only k total queries.

we instantiate BBSCHEDULER with the SmallDB algorithm as an illustrative example.


There also has been an early attempt on transfer in planning problems, for two specific classical (deterministic) domains of TSP and Sokoban [Groshev et al., 2018].

a 'good' state embedding space is a space in which similar states are close together and dissimilar states are far apart (similarly for state-action pair embeddings).


In addition to our random projection (RP)-based test, we implemented the methods of BS [6], SD [7], and CQ [9], all of which are designed specifically for problem (1) in the high-dimensional setting.

we seek sufficient conditions in Theorems 2 and 3 for ensuring that the ARE is small.


Algorithm 1 SCD method for (5) We propose the use of a stochastic coordinate descent (SCD) algorithm [12] to solve (5).

set Packing es + o(s) [1] MAP-inference [19], Natural language [9].


A common formulation of this task is the estimation of the conditional probability p(y x) from data through learning associations between y and underlying factors of variation of x.

data samples (x) can be abstractly represented as a set of underlying factors of variation F = {f i }.


Experimental Settings: Posterior inference for the truncated models (i.e., EPM, CEPM, and DEPM) were performed using standard (non-collapsed) Gibbs sampler.

as the Gibbs sampler for φ and ψ can be derived straightforwardly, the posterior inference for all parameters and hyperparameters of the DEPM also can be performed via closedform Gibbs sampler (detailed in Appendix C).


The basic effect, replicated across several different experiments, is that there are strong individual differences in how people solve the problem.

in panel (d), the numbers are 17.5% and 73.9%.


We see that the average value of ε lies approximately in the range (0.01, 0.1).

fix i = j and consider a pair of clusters C i , C j with means µ i , µ j and define the following notations.


In order to reduce the data sparseness problem for using rich syntactic information in the context, we study the use of RFs in the structured language model (SLM) [5].

we applied this new probability estimation technique to the Structured Language Model, in which there are three model components that can be estimated independently.


The 18 conditions come from using c = ±1 and c = ±0.3, with the degraded condition (|c| = 0.3) only being run for the case of low load, as in figure 1D.

to take account of the possibility of erroneous, early, responses, there is also a probability of 0.01 per step of stopping the accumulation and reporting whichever sign of target has a higher probability (guessing randomly if this probability is 0.5).


The contingency awareness approach [4] improved performance of the SARSA algorithm by augmenting the feature sets with a learned representation of the parts of the screen that are under the agent's control.

finally, recall that the UCTtoClassification-Interleaved agent was designed so that its input distribution during training is more likely to match its input distribution during evaluation and we hypothesized that this would improve performance relative to UCTtoClassification.


Denote ALGWC as the algorithm for the worst-case problem (i.e.

problem 2 becomes the submodular multiway partition (SMP) for which one can obtain a relaxation based 2-approximation [5] in the homogeneous case.


The statement of the theorem is written in a conditional form, because nonvanishing errors e(x) prevent us from making a stronger statement.

our proof exploits properties of Moreau-envelopes [28; pp.


We next examined how well the proposals explore the region assignment of clusters.

for any measure µ over Θ ⊗ Y define the restricted projection µ t by Note that µ t is a measure over Θ for each t ∈ T. Now let α be a base measure over the product space Θ ⊗ Y and consider a gamma process over Θ ⊗ Y.


Those with knowledge of the theory of stochastic linear bandits will recognise some similarity.

the controller should learn which VPS benefit the most from which resource types and allocate accordingly.


This assumption holds well for face-scenes, but if neighboring objects may vary in scale a single m-detection map will not suffice.

but these criterions are shared by other complex "scenes".


The hierarchical Dirichlet process (HDP) [Teh et al., 2005] has been proposed to borrow statistical strengths across multiple groups by sharing mixture components.

bMDL automatically avoids "negative transfer" with which many TL/MTL methods are dealing.


By the assignment rule, we have A t xt ∈ ∂σ t (ŷ t ), and the dual variable update can be viewed as ŷt+1 ∈ argmin y t s=1 A s xs , y − ψ * (y).

the algorithm is stated and analyzed for a twice differentiable, separable ψ(u).


We annealed the learning rate linearly from its initial value to 0 over the course of training.

rAM with 4 glimpses gets slightly better performance than the convolutional network and outperforms it further for 6 and 8 glimpses, reaching 1.2% error.


Hence, they inevitably suffer from the semantic gap, which is defined in [8] as the lack of coincidence between low level visual features and high level semantic interpretation of an image.

we picked the top two relevant images as positive samples and top two irrelevant images as negative samples.


Put more generally, similarity depends on what "small changes" are in a given application, and implies that similarity is domain specific.

intuitively, slow convergence is not always the case, for example when the support of the distributions lies in a lower dimensional manifold of the space.


The mean reward of an arm a is denoted by µ a and the maximal reward is µ ⇤ = max 1aK µ a .

given information JG, Y K, the algorithm POMISs (Alg.


Hence, in our analysis we need to separate out the eigenvectors that correspond to well spaced eigenvalues from the others.

. . , u d be the eigenvectors of G. We define the j-th eigenvalue separation ∆ j by For any ∆ > 0 define also Our results are expressed in terms of the effective rank ( 6) of G at horizon T . in order to account for the error in estimating the eigenvalues of G, we define the effective rank ρ t with respect to the following slight variant of the function kappa, Let M (i) be the estimated gradient outer product constructed at the end of phase i, and let µ and u 1 (i), .


The voxels used in the reconstructions were selected as follows: For each test trial, n voxels with smallest residuals (on training set) were selected.

we observed a significant negative correlation (r = -0.3067) between stimulus complexity and reconstruction accuracy.


This is especially true for subbands at different scales, which exhibit strong dependencies.

joint distributions: In addition to one-dimensional marginal statistics, the FoGSM model is capable of capturing the joint behavior of wavelet coefficients.


We note that it is provably impossible to achieve such a guarantee in sublinear time for arbitrary matrices A, and our proof exploits special properties of distance matrices.

are there sublinear time algorithms achieving (1.2)?


Note the different scaling of the rightmost plot.

unlike the Gibbs samplers mentioned above, SMC-based methods often do not scale well with dimension.


This attack, however, requires that poisons fill at least 12.5% (and up to 100%) of every minibatch, which may be unrealistic in practice.

to better understand what causes the attacks to be successful, we plot the angular deviation between the decision boundary (i.e.


The results in column Min are computed by constrainedly minimizing V-ROUGE via the methods of [11], and the results in column Max are computed by maximizing V-ROUGE using the greedy algorithm.

for every image, the resulting bag-of-words representation is normalized to the unit 1 -norm.


While we develop a more general treatment, the main focus in the paper is on the Poisson likelihood for count data, which is motivated by the applications in spatial statistics.

we propose new bounds and tractable approximations, leading to improved prediction accuracy and scalability to large datasets, while explicitly taking uncertainty into account.


Even our approach requires a similar optimization process.

each T i is trained only on the samples from domain i and F is the shared network trained on all p source domains.


In such downstream models, latent topic assignments are sufficient statistics for the prediction model and it is easy to define the max-margin constraints based on existing max-margin methods (e.g., SVM).

by using a normal prior on ψ, the scene model can capture the mutual correlations between different objects, similar to the correlated topic models (CTMs) [3].


Proof: First we note that convergence is guaranteed by the strict convexity of the primal problem [6].

various methods [22,13,16,12,1] enforce consistency structure during inference by imposing constraints on the feasible instances.


Incremental update algorithms [2] attempt to overcome this problem but cannot guarantee a bound on the number of operations required per iteration.

at time , the algorithm receives an input 0 F , makes its prediction % 10 ' , receives the correct outcome t , and updates its hypothesis into " I according to (5).


Our model builds on the proposals of several previous researchers.

the problem of planning can then be stated as follows: Given a goal state g, an initial state s, and number of time steps T , what is the sequence of actions â1:T that maximizes the probability of reaching the goal state?


We will refer to this as the naive group lasso approach.

. . , X k n k ∈ R p are independent and identically distributed from a N (0, Σ k ) distribution, for k = 1, . . . , K. Letting S k denote the empirical covariance matrix for the kth class, one can maximize the penalized log likelihood maximize where , λ 1 and λ 2 are nonnegative tuning parameters, and ) is a penalty applied to each off-diagonal element of Θ 1 , .


For any strategy profile a, a i denotes the strategy of the i th player, and a −i the strategies of the other players.

we define aggregator functions f t G (a, i) f (a I t G (i) ) that return the aggregate at level t with respect to player i.


In [30], the authors propose a mutual-exclusivity loss function that forces the set of predictions for a multiclass dataset to be mutually-exclusive.

we create five labeled datasets from available training samples.


Suri and Schultz's model can even produce one form of sensory preconditioning.

we then present a model of conditioning based on a constrained hidden Markov model, using quasi-Bayes estimation to adjust the model parameters online.


The regularized permutahedron-based convex formulation is a convex QP with O(m) variables and constraints, where m is the number of comparators in its sorting network, while the Birkhoff-based one is a convex QP with O(n 2 ) variables.

in this paper, we use a relaxation based on these polytopes, which we call "sorting network polytopes."


Although model-free methods avoid the need to model system dynamics, they typically require policies with carefully designed, low-dimensional parameterizations [4].

in our evaluation, we demonstrate this capability by training a policy for inserting a peg into hole when the precise position of the hole is unknown at test time.


Next, we use the same policy and place the agent in a stochastic world.

both parties will be happy with this agreement in expectation.


approximately 1 second of 1) the original sources, 2) the MAP source estimates and 3) the resynthesized sources (from the estimated model parameters).

for non-stationary sources, on the other hand, the autocorrelation functions vary through time and it is not possible to choose a single common whitening filter for each source.


We will now describe these priors in more detail.

in addition to scaling to more factors, f-LDA is more predictive than simpler multi-dimensional models.


Our goal is to minimize the expected risk, which averages the loss over some true data generating distribution p * (Z).

they are only feasible when the number of hyperparameters is very small, whereas our approach can optimize many hyperparameters.


Note, that other loss functions than the squared loss could be used.

with the proximal maps we have presented so far, the PDHG algorithm has the following form.


Our bilinear model with f (x, α, θ) = x T Wα + b does not admit a straightforward probabilistic interpretation.

discrimination helps especially when the size of the training set is large.


The squared Euclidean distance between two instances x i and x i is ∑ j∈N (x ij − x i j ) 2 , while the weighted squared Euclidean distance is written as where w := [w 1 . . . w ] ∈ [0, 1] is an -dimensional vector of non-negative weights and ε i,i := We develop a feature weighting algorithm within the framework of regularized empirical risk minimization, i.e., minimizing the linear combination of a loss term and a regularization term.

the number of neighbors k ∈ {1, 3, 5} was selected based on the classification performance on the validation set.


Similarly, we can fix m = 5 and track optimal r V 's behavior when r U changes.

we show that no DR maps can achieve perfect precision and perfect recall simultaneously.


It is important to realize that although the mapping is one-to-one, we still need to satisfy the constraint in equation 4 because a volume element dx will change under the mapping.

and let Σ = U SU T be an eigenvalue decomposition.


Such a model is always log-supermodular decomposable.

checking that the maximum value attained on any M -cover is bounded by the maximum value over the base graph to the M , in and of itself, appears to be a daunting task.


As a result, some algorithms avoid using unlabeled examples directly in model training and instead focus on "changes of representation" that find a more informative representation from unlabeled data and use it to encode the labeled examples [4,1,11].

in this section we introduce a framework to transfer knowledge from unlabeled text.


Note that, in order to execute this algorithm each machine must be sufficiently powerful to obtain the gradient of the Moreau envelope of its local function, which is indeed the case in our framework.

for non-quadratic losses, the round complexity bounds are somewhat worse, and there are no guarantees for strongly convex and smooth functions which are not self-concordant.


The data was parameterised into 39-dimensional feature vectors including 12 MFCCs and a log energy term with corresponding delta and acceleration parameters.

in this paper, a simpler normalisation method is employed.