As shown in Figure 4, the value of the LOO margin Bc \c is obtained from the sequence of Bc vs. a c segments for each of the decrement steps, and thus determined by their slopes 'Yc.

the KT conditions are expressed differentially as : jES where a e is the coefficient being incremented, initially zero, of a "candidate" vector outside D. Since 9i == 0 for the margin vector working set S = {Sl, .


To ensure that the distribution is valid and normalizable, we require ✓ j > 0, and ✓ jk 0.

in each example, we report the mean coverage rate of 95% confidence intervals for several coefficients averaged over 500 independent simulation runs.


Hence, for simplicity, we use the original dataset for all the processes.

almost all CE's corresponding to the results in Table 1 are very small, which are listed in Appendix D. We also illustrate CE's of our method for different N , d and r when fixing K = 5 in Fig.


Such a model requires a large amount of training data and imposes serious computational burdens.

the wide-band and narrow-band variations in speech are only loosely coupled.


These have been studied extensively in the literature [20], and can give insight into the success and limitations of spectral clustering [13].

with a small number of clusters normalized cut cannot find the small coherent segments in the image, whereas with a large number of clusters, large objects are segmented.


Constraint (2), which specifies that each variable should be assigned only one label, is known as the uniqueness constraint.

in order to specify the exact form of these SOC constraints, we need the following definitions.


What should a learning algorithm optimize on the training data in order to give classifiers having the smallest possible true risk?

let For any quasi uniform Q, the output B Q (x) of the majority vote on any example x is given by the set of majority votes B Q over quasi uniform posteriors is isomorphic to the set of linear separators with real weights.


The proof is a generalization of Theorem 2 in [17], and we provide it in the supplementary.

to make use of M -wise comparison data for Rank Centrality, we apply a sample breaking method that converts M -wise data into pairwise data.


Computed using Maxwell's equations and a spherical shell head model [12], the resulting Φ is characterized by highly correlated rows, because the small scalp surface requires that sensors be placed close together, and vastly different column norms, since the EM field strength drops off rapidly for deep brain sources.

inclusion of both W and D together can be highly disruptive.


Indeed, [28,Corollary 4.36] established the same result for higher order partial derivatives, which can be easily used in our framework as well.

then the linear functional L xi in (10) is bounded in the RKHS defined by k for any probability density p(•).


More recently, relative attributes (e.g., "more formal than these," "shinier than these") have been exploited as a richer form of feedback for interactive image retrieval [12,25,26,27,28].

in this section, we demonstrate the practical use of our system with real users.


Note that the observation to be passed on to the POSMDP to create the POSMDP observation space, O, is part of the design tradeoff -usually it is desirable to reduce the number of observations in order to reduce complexity without degrading the value of the POSMDP too much.

an Unmanned Aerial Vehicle (UAV) can be deployed to maintain WiFi network communication between the ground units.


We remark that the idea of ALOOCV is also related to that of the influence functions.

such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the outof-sample performance.


The SDE automatically incorporates the geometry and randomness induced by the statistical model, which allows us to establish the exact dynamics of SGD.

such approximation is characterized rigorously using weak convergence theory of Markov processes [17,40].


However, there is typically a large gap between the precision of distance computations in Hamming vs. product codes under the same bitrate, and ADC can be computed with similar speed ([2, 21], Section 4.4).

given n samples from an underlying K-subspace mixture model that has been clustered correctly and an independently generated query q, with probability 1 , See Appendix B for a proof.


We modify an encoder-decoder translation model by adding a latent variable as a language agnostic representation which is encouraged to learn the meaning of the sentence.

m-like step: Choose the words in y to maximize 1 S ∑ S s=1 log p(z (s) ) + log p(x|z (s) ) + log p θ (y|z (s) , x) using beam search.


In addition to the RSC condition, we assume that X has bounded column norms (specifically, n for all i = 1, . . . , p), and that the noise vector w ∈ R n has i.i.d.

to motivate the need for a unified analysis, let us provide a brief (and hence necessarily incomplete) overview of the broad range of past and on-going work on high-dimensional inference.


This provides powerful interpretative insights between the latent features in the matrix model and the words from the associated documents.

we assume that each row corresponds to a person/entity that may be present for matrix t + 1 and matrix t. It is assumed here that each column corresponds to a question (in the examples, a piece of legislation), and each question is unique.


In audio processing, convolutive NMF has been successfully used to detect motifs with temporal structure [24,25,37].

building on these schemes, NMF has been used to decompose a binned spike matrix into multiple levels of synchronous patterns which describe a hierarchical structuring of the motifs [36].


The sparse PCA problem is highly nonconvex in nature.

to ensure U (T ) enters the basin of attraction, we need Solving T gives T ≥ T min where T min is defined in (17).


We model the budgeted prediction optimization as the following Markov Decision Process.

we evaluate the effectiveness of q-inference with various thresholds to minimize inference time.


We evaluated training and test accuracy on 100 random splits of the sonar dataset from the UCI machine learning repository.

as the correct scaling is unknown, one has to either take the risk of choosing τ too small and hence failing to recover an optimal solution of ( 4), or to rely on too large τ which can result in slow convergence.


The annotators were given the samples in random order and were not told which samples came from which algorithm.

at t = 500, the closed-loop and open-loop hidden states clearly occupy distinct regions with teacher forcing, meaning that the network enters a region during sampling distinct from the region seen during teacher forcing training.


In particular, the noise term ∆ T can be deterministic or even adversarial.

∆ T is weakly correlated with signal in the sense that ∆ T (v i , I, I) 2 = O(λ min /d) for all i ≤ k: in this case our noise condition reduces to ∆ T op = O(λ min / √ k), strictly improving over SVD initialization [2] in the "undercomplete" regime k = o(d).


The LATER model (Linear Approach to Threshold with Ergodic Rate), an instance of the additive offset model, incorporates prior probability as the starting point of a linearly rising decision variable and successfully predicts changes to saccade latency when discriminating between two low contrast stimuli [10].

early in a trial, Π S has approximately the same width as in the neutral prior case, but it is shifted downwards to favor more sampling for d L (s < 0).


It extends I-POMDP's belief update to larger model space, and therefore it serves as a generalized Bayesian learning method for multi-agent systems in which other agents' beliefs, transition, observation and reward functions are unknown.

this additional resampling step is nontrivial, since empirically the samples diverge quickly due to the enormously enlarged sample space.


Unlike most prior work, we provide non-asymptotic performance guarantees which hold even for a finite number of workers and tasks.

in fact, the value b = O( √ n) seems to mark the transition between "easy" and "hard" instances of the crowdsourcing problem.


This method uses an information criterion to optimise the weights, under certain restrictions on Pr and Pr ′ (namely, Pr ′ must be known, while Pr can be either known exactly, Gaussian with unknown parameters, or approximated via kernel density estimation).

since typically we only observe examples (x, y) drawn from Pr(x, y) rather than Pr ′ (x, y), we resort to computing the empirical average To avoid overfitting, instead of minimizing R emp directly we often minimize a regularized variant where Ω[θ] is a regularizer.


# , A1 (Bounded marginal): For any such cube intersecting the Bayes decision boundary, , where " denotes the Lebesgue measure.

in this section, we investigate bounds on the rate of convergence of complexity-regularized DCTs.


As ( µ1 τp ) 2 = O(1), gradient descent takes only a logarithmic number of iterations O(log 1 ϵ ) to converge now, which does not have the quadratic dependence on λ1 λ1−λ2 any more [Shamir, 2015, 2016a, Xu et al., 2017, Xu and Gao, 2018, Xu et al., 2018.

we can also try other least-squares solvers, such as SVRG [Johnson and Zhang, 2013], accelerated SVRG [Garber et al., 2016], and coordinate descent .


The sequence consists of 59 greyscale frames, each of size 160 × 120 pixels (excluding the border).

the system has detected not to use the previous frame at this point, but to revert to using the latent appearance image f . We have proposed a method for localising an object undergoing affine transform whilst simultaneously learning its shape and appearance.


Given a parameter r > 0, for every node i ∈ V , consider the set of nodes B r (i; d n ) := {j : d n (i, j) < r}.

we present an efficient method which bridges structure estimation in latent trees with estimation in fully observed loopy graphical models.


But it cannot be generalized to the case with non-smooth regularizer.

its existing results are all based on Gradient Descent (GD) or Stochastic Gradient Descent (SGD).


[11] analyze a low communication peer-to-peer protocol that attains rates dependent on network structure.

in Figure 3, we compare the theoretical predictions of Corollary 1 with the actual behavior of dual subgradient averaging.


In the full case, the surrogate loss is jointly exp-concave, and in light of the analysis of ONS by Hazan, Agarwal, and Kale [14] such a result is not surprising.

orabona and Pál [24,25] design methods that can adapt to the norm of u.


More precisely, we consider prior distribution P with probability density P (z i , σ) to be facotorizable in its compression set dependent component and message string component (conditioned on a given compression set) such that: The above choice of the form for P I (i) is appropriate since we do not have any a priori information to distinguish one compression set from other.

with the above assumption satisfied, let, P be a non-negative reference measure on the classifier space H known as the volumic measure.


We further applied RoLR to successfully learn classifiers from corrupted training samples.

the work of S. Mannor was partially funded by the Intel Collaborative Research Institute for Computational Intelligence (ICRI-CI) and by the Israel Science Foundation (ISF under contract 920/12).


If Assumption (A) holds and is r-calibrated, then r satisfies: Proof of Theorem 3.


. . , c k } ⊂ R p to be optimal for (RKM) are The interpretation of the set inclusion above is the following: for any center c l ∈ R p , every subgradient vector in ∂Φ(x i − c l ) must be a vector associated with a vector in P F λ (x i − c l ) (Theorem 10.13 in [19]).


Our logistic regression hypernym-only model trained on the newswire corpora has a 16% relative F-score improvement over the best WordNet classifier, while the combined hypernym/coordinate model has a 40% relative F-score improvement.

for the second set of evaluations we hand-labeled a test set of 5,387 noun pairs from randomly-selected paragraphs within our corpus (with part-of-speech labels assigned by MINIPAR).


However none of these treatments neither formalise nor analyse any notion of regret in the multifidelity setting.

pick δ ∈ (0, 1) and run MF-GP-UCB with β t d log(t/δ).


We then demonstrate how statistical inference may be performed on causal parameters identified by this algorithm.

we calculated the (approximation of) the bias of each effect by subtracting the estimate from the 'ground truth.'


Moreover, we also provide a method that produces successively decreasing upper-bounds of the optimal solution, while our algorithm provides successively increasing lower-bounds.

5. stop ← true (S * is an optimal solution and γ i−1 the optimal value).


For any vector a ∈ R q and any q × q matrix W , we let a W = ( a) T W a.

it is quite hard to directly compare our GMMs and RC fairly since they are designed for different types of data.


This is because the marginal distributions of the individual attributes under both D 1 and D 2 are exactly the same.

a formal setting for capturing regression and learning with limits on the number of attribute observations is known as the Limited Attribute Observation (LAO) setting, first introduced by Ben-David and Dichterman [1].


We consider the following synthetic experiment for matrix completion.

the per-iteration running times of Garber [6] and FW depend polynomially on 1/ε, making their total running times even worse in terms of dependency on 1/ε.


Now, we construct a problem instance for which the algorithm would suffer linear regret separately for θ 2,z > 0 and θ 2,z = 0.

given the true thresholds, the algorithm would have always assigned the individual to expert j = 2 and would have a cumulative expected utility of 0.


Random DropMax also performs worse due to the inconsistency between train and test time handling of the dropout probabilities for target class.

we further perform qualitative analysis of our model to see how exactly it works and where the accuracy improvements come from.


As mentioned before, these methods achieve the rate n −α+ξ for arbitrarily small ξ > 0 in the well-specified setting: b = α − ξ in our notation.

we present our contributions in Sections 4 and 5.


The data set contains 60 000 color images with resolution 32 ⇥ 32.

consider set functions that are defined as expectations, i.e.


We evaluate both recognition and verification accuracy.

we present a scalable novel objective, multi-calss N -pair loss, for deep metric learning, which significantly improves upon the triplet loss by pushing away multiple negative examples jointly at each update.


When from the observations, a red node w ∈ V (r) is connected to at most a single green node, i.e., if v∈V (g) A vw ≤ 1, this red node is useless in the classification of green nodes.

we present an algorithm with a memory requirement which depends on the density of the graph.


Initialize directed graph G with vertices {x 1 , ..., x n } and no edges.

taking h ≈ n −1/(4+d) optimizes the above rate to d(M, M) = Õ(n −1/(4+d) ).


It is easy to verify that indeed ∥v w ∥ 2 ≤ ∥β∥ 1 and for all x ∈ X , ⟨v w , ψ(x)⟩ = p(⟨w, x⟩).

the problem is much harder in the agnostic case, namely, when L * γ > 0 and the distribution over examples can be arbitrary.


In this criterion, the loss suffered for a training example (x (t) , y (t) ) is the negative log probability of the true parse according to the model, plus a regularization term: The convexity and differentiability of conditional log-likelihood ensure that gradient-based optimization procedures (e.g., conjugate gradient or L-BFGS [6]) will not converge to suboptimal local minima of the objective function.

let X L denote an input space of all possible input sequences, and let Y L denote an output space of all possible output labels.


Algorithm  We note that in a multi-device distributed setting, some of the benefits of "Ghost BN" may already occur, since batch-normalization is often preformed on each device separately to avoid additional communication cost.


( 1) by P t and refer to it as the instantaneous primal problem to be solved on trial t. The dual optimization problem of P t is the maximization problem Each dual variable corresponds to a single constraint of the primal problem.

the loss associated with each such violation is + and the loss of the categorizer is defined as the maximum over the losses induced by the violated pairs.


It consists of examination scores of 15362 students from 139 secondary schools in London.

second, in Section 4 we characterize the spectral functions which relate to Schatten L p regularization and present the alternating minimization algorithm.


For the second-order term, it can be readily veri£ed that the Hessian of R(h) is block-diagonal with 2-by-2 blocks corresponding to h(x i ) and h(y i ) and 1-by-1 blocks for h(z i ).

speci£cally, we want to rank a set of documents according to their relevance to a given query.


In many structured prediction problems, the highest-scoring labeling is hard to compute exactly, leading to the use of approximate inference methods.

letting i * j * = arg max ij λ ij , it is easy to see that the correct MAP configuration assigns matching labels to nodes i * and j * and an arbitrary label to the third.


Form the affinity matrix A E R nx n defined by A ij = exp(-Ilsi -sjW/2( 2 ) if i # j , and A ii = O.

stacking t 's eigenvectors in columns to obtain X, we have: Actually, a subtlety needs to be addressed here.


The sublinear convergence rate obtained with this approach is up to constants identical to that in Theorem 2 for our MP variants, see [21].

to the best of our knowledge, in the context of MP-type algorithms, we are the first to combine general convex objectives with conic constraints and to derive corresponding convergence guarantees.


Mixture models provide a simple way to approximate the density of high dimensional data that lies on or near a low dimensional manifold.

as with all EM algorithms, the coordinated MFA learning procedure is susceptible to local optima.


Second, it avoids having to compute or store a complete best-response by employing sampling over chance outcomes to focus the best-response and regret updates on a small subtree of the game on each iteration.

the k-of-N game presents a difficulty due to the imbalance in the size of the two players' strategies.


An unbiased estimate of MMD 2 0 can be obtained using U -statistic where h(•) is the kernel of the U -statistic defined as h(x i , x j , y i , y Intuitively, the empirical test statistic MMD 2 u is expected to be small (close to zero) if P = Q, and large if P and Q are far apart.

1 and b grows on the order of p B, and this further simplifies our calculation.


this is a (left) censored measurement and is treated differently than a missing data point.


The marginal distribution over non-terminals, π, is drawn from a stick-breaking prior [5].

this bound cannot be maximised tractably when e is unobserved.


In each time step the learner chooses an action I t ∈ {1, . . . , K} and receives reward g It,t = µ i + η t where η t is the noise term that I assume to be sampled independently from a 1-subgaussian distribution that may depend on I t . This model subsumes both Gaussian and Bernoulli (or bounded) rewards.

the order-optimal asymptotic regret can be significantly smaller.


The fact that these kernels are very specific to the type of discrete data under consideration is a major cause of confusion to the practitioner.

let A ∈ R m×n , let q ≤ min(m, n) and let I n q = {i = (i 1 , i 2 , .


In addition, it means that we cannot use standard minimax theory for Holder classes to establish lower bounds for the estimation error over GTF classes.

let H d be the space spanned by all d-wise tensor products of falling factorial functions, i.e., for coefficients α ∈ R n (whose components we index by α i1,...,i d , for i 1 , .


Table 1: Percentages (mean and standard deviations) of correctly recognized single trials for the 2 motor imagination tasks for the 6 subjects and the average of them.

this software, known for its zero localization error, was used as a localization tool to estimate the focus of intracranial activity at the occurrence of the four ErrP peaks described in Section 3.2.


With a few exceptions, the experiments were conducted with δ = 50 and 4 computational threads.

a similar idea was proposed in a-MMSB [5], using one parameter to determine inter-role link probabilities, rather than O(K 2 ) parameters for all pairs of distinct roles, as in the original MMSB [1].


{1, 2, • • • , K} is an oracle that takes an image in its domain O and outputs one of K labels.

we test both normally-trained and adversarially-trained ResNets.


To extend the dynamics to a multi-chain scenario, we imagine an auxiliary probability distribution over K random variables.

neurons with similar stimulus preferences increased their synchrony and spike-count correlations with increasing uncertainty, consistent with the stimulus quenching response co-variability in neural data and increases in correlations at low contrast [17,16].


Our goal is to predict features of houses given a certain location in the London area.

our model is able to work on large scale datasets by using sparse approximations within stochastic variational inference.


defined as the gradient of a potential field or as a gyroscopic "steering" force ϕ(x, O) = s(x, O) × v that effectively rotates the velocity vector [22] .

as an example, consider a point-mass robot modeled as a double-integrator system with state x = (p, v) where p ∈ R d denotes position and v ∈ R d denotes velocity with d = 2 for planar workspaces and d = 3 for 3-D workspaces.


After obtaining pairwise similarity ratings from workers, and producing a Euclidean embedding, one could conceivably proceed with unsupervised clustering of the data in the Euclidean space.

iterative schemes that adaptively choose maximally informative HITs may be preferable to random sampling.


The same is true for the orthogonal distance term in eq.

ε can be specified in a problem independent way.


Since the number of subspaces L grows exponentially in n and k, an exhaustive search is, in general, computationally infeasible.

the parameters MAR and SNR represent the minimumto-average and signal-to-noise ratio, respectively.


The RT difference bewteen easy and hard items does not fully disappear in mixed blocks.

the weighting of past history should be based on the strength of the autocorrelation.


We write D E t as an abbreviation for D π E t . In a minor abuse of notation, we write s ∼ D π t to mean: draw state-action pair (s, a) ∼ D π t , and discard a.

a sample (s, a) is drawn from D π t by first drawing s 1 ∼ α(•), then following policy π for time steps 1 through t, which generates a trajectory (s 1 , a 1 , .


Furthermore, for any x = z and µ = v(x), the LHS would be n − 1 or less.

based on the inductive assumption and Eq.


The first term L adv ( Î, I) is the conditional adversarial loss defined by The second term L feature ( Î, I) is the feature matching loss [24].

extension to style manipulation Although we focused on addition and deletion of objects as manipulation tasks, we can easily extend our framework to add control over object styles by conditioning the image generator with additional style vector s by G I ( M , I, s).


The objective function for φ given by , If φ is represented as a vector concatenating all of its parameters, the gradient of g(φ) takes the form For the quadratic nonlinearity, the gradients with respect to f (h t ) take the form ∂f Gradients for the quadratic model with multiplicative interactions take a similar form.

we set the dynamics matrix A by fitting the model to a single neuron recording from V1 [4].


We evaluate the theoretical results with several case studies, and also illustrate the application of the subset selection to causal structure learning.

in general, this conjecture is not correct, and a counterexample could be constructed by having "explaining away" processes.


This implements a nonclassical receptive field [12,18] of a biological neuron as the effective receptive field is larger than that determined by feedforward connections.

in this framework, a plain seven-layer-CNN is used as a feature extractor for the input image while a recurrent neural network (RNN) is used for image sequence modeling.


In fact, at the beginning tUCB selects arms according to a UCB strategy, since no prior information about the models ⇥ is available.

in fact, if J is large, it could be preferable to run a model identification algorithm instead of umUCB in earlier episodes so as to improve the quality of the estimates μi (✓).


The requirement to have a strictly convex supervised risk function can be relaxed.

a semisupervised approach can only be called truly safe if it guarantees non-degradation of performance in this pessimistic sense.


This can be a weakness in problems with significant label noise (i.e., incorrectly labeled training examples).

the value of λ controls the trade-off between the accuracy of the approximation and the ease of optimization.


Most importantly, the network is jointly optimized towards task objectives, hence guaranteed to achieve the full performance when the former input spaces are recovered by the generator.

they claimed that catastrophic interference is a fundamental limitation of neural networks and a downside of its high generalization ability.


this poses a problem for symmetric connectivity measures, since these assess instantaneous coupling between electrodes [18].


Moreover, we note that in this scenario, the standard choice of ν = 0.5 in Theorem 2 is inferior to choosing smaller parameter values of ν = 0.1 or ν = 0.001.

the constant before σ 2 n ln 1 q k * δ approaches 8 when → ∞ (with default ν = 0.5), which is smaller than the constant of Theorem 1 which is about 30.


However, the representational properties which distinguish networks which memorize from those which generalize remain unclear.

concretely, in our setting, the underlying process is a neural network being trained on some task.


The representation of a neuron v is measured by the activation vector [Raghu et al., 2017] of the neuron v over the d inputs, For any subset X ⊆ X , we denote the vector set {z x : x ∈ X} by z X for short.

again, there are few simple matches with small sizes.


Several recent papers obtain surrogate regret bounds and efficient algorithms for this setting when the benchmark regressor class F consists of linear functions [26,24,9,22].

this result is directly comparable to the Õ(T p+1 p+2 ) bound of Cesa-Bianchi et al.


In order to learn useful, predictive representations in a fully unsupervised setting, we apply a graph-based loss function to the output representations, z u , ∀u ∈ V, and tune the weight matrices, W k , ∀k ∈ {1, ..., K}, and parameters of the aggregator functions via stochastic gradient descent.

we can derive an inductive variant of the GCN approach by replacing lines 4 and 5 in Algorithm 1 with the following: 4 We call this modified mean-based aggregator convolutional since it is a rough, linear approximation of a localized spectral convolution [17].


Also, we still do not know the lower bound of the utility using this measure.

suppose the loss function f (x, z) is G-Lipschitz , and L-smooth over x ∈ C . In DP-AccMD, let σ be as in (9) and w be a function that is 1-strongly convex with respect to || • || C . Then if we have The total gradient complexity is O .


This results in the desirable behavior of the labels varying smoothly over the graph, as sought by, e.g., spectral clustering approaches [2], diffusion kernels [5], and the Gaussian random field approach [9].

informally, a smooth eigenvector has the property that two elements of the vector have similar values if there are many large weight paths between them on the graph.


To date, almost all techniques of text classification are based on words, in which simple statistics of some ordered word combinations (such as n-grams) usually perform the best [12].

as a result, the most natural choice in data augmentation for us is to replace words or phrases with their synonyms.


When the presynaptic spike arrives at the synapse a few milliseconds before an output spike is generated, the synaptic efficiency increases.

this ensures that an up signal that decreases the weight is only generated when a presynaptic spike is active after the falling edge of a postsynaptic spike.


Part representations appear to be a natural approach to identifying people.

future work will include: tying W components for legs; evaluating arm detection; and formulating strategies to employ structure learning for detecting other objects.


Then let I m = {i r i = 1, i ≤ m} and J m = {j t j = 1, j ≤ m} and let I = I ∞ and J = J ∞ .

the rewards in Tetris are received sparsely, unlike the approximation error, which makes the value function less sensitive to the discount factor than the approximation error.


The work closest to ours is [19], which gives quadratic time lower bounds for ERM algorithms that access the kernel matrix through an evaluation oracle or a low-rank approximation.

here, the computational bottleneck is to compute a number of gradients, not necessarily to minimize the empirical loss globally.


Punctuation is ignored, but spaces are retained.

as can be seen from the description of the recursion in Definition 2, its computation takes time proportional to n I s Iii 12, as the outermost recursion is over the sequence length and for each length and each additional character in sand i a sum over the sequence i must be evaluated.


Then ξ b st (Λ), in addition to being twice the variance of the Bernoulli indicator of the edge (s, t), has the following nice interpretation: For each pair of graphs, we can ask how often they disagree on the presence of the edge: ξ b st (Λ) is the fraction of times they disagree.

we want to "overselect" instead of "underselect".


⋅ denotes the spectral norm of a matrix and ⋅ 2 is the 2 norm of a vector.

this result allows us to address most "reasonable" distributions, but still there are some "corner cases" that need to be analyzed separately.


Unfortunately, the nonstationary GP requires many more parameters than a stationary GP, particularly as the dimension grows, losing the attractive simplicity of the stationary GP model.

spline regression models have sample functions that are typically only twice differentiable.


Through further approximations, we derived an exceedingly simple algorithm, the saddle-free Newton method, which rescales gradients by the absolute value of the inverse Hessian.

if an eigenvalue is negative, the Newton step moves along the eigenvector in a direction opposite to the gradient descent step, and thus moves in the direction of θ * .


This corresponds to insulating the boundary, also known as the Neumann boundary condition.

using the group lasso penalty [18], we estimate the significance of the subnetwork by solving the following optimization problem 2 where J is the total number of subnetworks considered and X ( j) and β ( j) denote the columns of X , and entries of β corresponding to the subnetwork j, respectively.


Let h s be the s-th row of H. Since r s ± h s ≥ 0, all except the s -th elements in h s must be 0.

selecting two non-identical vectors from It has still to be shown that these U i,j are linearly independent.


So the leave-one-out hyperparameter learning will push 1/σ h to zero and 1/σ v to infinity, i.e., all points can transfer only horizontally.

the difference between LOOHL+CMN and LOOHL+Thrd, compared with the difference between 5-CV+CMN and 5-CV+Thrd, can be viewed as an approximate indicator of how well the graph is learned by LOOHL.


There is a closed lower dimensional set E ⊂ L such that the function τ * is locally constant on the complement of E. Theorem 1 implies that, with probability 1, if the model estimate m and the true model m are sufficiently close, then the actions recommended by the exactly optimal policies for both models are identical.

by bounding the amount of time allowed between successive screenings.


Using training and test set augmentation based on jittering (not employed here), they achieved the top-1 / top-5 accuracy of 62.5% / 83.0%.

finally, stacking the FVs, produced by the 1st and 2nd Fisher layers, pushes the accuracy even further.


While this rapid serial visual presentation (RSVP) paradigm complicates the task of extracting stimulus-related information from the spiketrains, it has the advantage of allowing for the testing of a large number of stimuli.

the original concepts will be embedded as a substructure in the larger lattice, with their ordering relationships preserved.


From this perspective HGMDPs appear to be a significant restriction over general POMDPs.

hence, the worst regret on any goal is 0 iff the 3-SAT problem is satisfiable.


In such cases, derivatives of the objective function with respect to the parameters are unavailable.

surprisingly, our lower bounds show that this new algorithm that uses only function comparisons achieves the same rate in terms of T as any algorithm that has access to function evaluations.


At last, this method is complicated and slow because too much calculation is involved.

we can find an expansion for w k in the form Using this expansion and the definition of m Φ i , we have Replacing the dot-product by some kernel function k(x, y) and defining l . Similarly, we have Similarly, one can simplify W T S Φ w W. First, we have w T k (Φ(x α T k S i (e j e T j − j ), I ni×ni is the n i × n i identity matrix, 1 ni is the n i -dimensional vector of 1's, and e j is the canonical basis vector of n i dimensions.


After computing elementary distances, we rescale the distances for each focal image and feature to have a standard deviation of 0.1.

we refer to all the images available for training as the training set and the set of images used to train with respect to a given focal image as its learning set.


We want to learn a function which assigns a positive value to any sequence that contains a target set of characters (in our case, two of them) regardless of their position.

ψ, and Φ are equivalent up to constants.


The difference with ADAM is in the update of v t . To gain more intuition for YOGI, let us compare its update rule with that of ADAM.

to this end, we prove the following convergence result for nonconvex setting.


For a particular diagonal line, one random vector zeros out a set of approximately d/2 entries, and the second random vector zeros out another set of d/2 entries, chosen randomly and independently of the first set.

as depicted in Figure 1 (middle), HOLEX visually first forms the full tensor product of a and b, then multiplies each row with the corresponding dimension in c, and finally sums up along each (circular) diagonal line.


On the computational front, DPMBQ costs O(n 3 ).

next, the GP is conditioned on the information in {(x i , f . Formulae for the mean function m n : Ω → R and covariance function k n : Ω × Ω → R are standard can be found in [31,Eqns.


And, by definition of πk , λk is the gain of the chosen policy πk for MDP Mk .

the rounds t = 1, . . . , T are broken into consecutive epochs as follows: the k th epoch begins at the round τ k immediately after the end of (k − 1) th epoch and ends at the first round τ such that for some state-action pair s, a, N τ s,a ≥ 2N τ k s,a .


(Right:) Fraction of samples that RMSE is smaller than 10 −7 , among 100 samples of rank-3 data matrix U V T of size 1000 × 1000, with the entries of U and V drawn from a Gaussian distribution of mean 0 and unit variance.

we see that if the topology is not locally-tree-like but with some noise, for example with some additional cliques, both trimming of the data matrix and Bethe Hessian perform much worse, reporting a wrong rank, and giving a large reconstruction error, as illustrated in Fig.


However, the task is non-trivial mainly because the two-layer sampling does not correspond to a typical empirical process: the documents for different queries are not identically distributed while the documents for the same query are not independent.

sampled from the document space D according to a conditional distribution P (d|q i ) where m i is the number of sampled documents.


We compared a nearest neighbor classifier for the global sentiment, where the representation varied from bag of words to smoothed length-normalized local sentiment representation (with and without objective sentences).

even if assumptions (3)-( 4) are incorrect, enforcing them may improve prediction by trading off increased bias with lower variance.


This can be especially problematic in the non-parametric setting, since non-Markovian state persistence in data can lead to the creation of unnecessary extra states and unrealistically, rapid switching dynamics in our model.

in Section 4 we present our results on a variety of synthetic and real-world datasets.


In the two extreme cases, we know that the "sample selecting model" constraint I v saturates when nk ⌧ mp (e.g., k = 1 and p = n), and the "model selecting sample" constraint I u saturates when nk mp (e.g., k = m and p = 1).

these observations suggest we start at the first regime mp  nk with small p and large k, and gradually switch to the second regime with mp nk by slowly increasing p and decreasing k. In earlier stages, we also should set the diversity weights and to be large, and then slowly reduce them as we move towards the second regime.


We denote T (k) as the mode-k matricization of a tensor T , which arranges the mode-k fibers to be the columns of the resulting matrix.

our theorem confirms that our algorithm is able to find such estimator with optimal rate of convergence.


Figure 1 shows an example of a BCD iteration where the blocks of columns are chosen in sequential order.

these datasets have many variables and very few samples (m n).


the distortion measure d. The bound can also be applied to a generator G ′ obtained by minimizing, e.g., some fdivergence [26] between P X and P G(Z) .

where C > 0 is an absolute constant that depends on δ, m, E[ Z 1+δ ], and • .


. . , µ (k)  Algorithm 2: TensorDecomp Remark 2.1.

previous algorithms depended inverse polynomially on the minimal separation and exponentially on the dimension for both of these quantities.


In the most general formulation, the constraints, Q : R IK ×R KJ → R NQ and R : R IK ×R KJ → R NR , are biaffine maps, that define N Q inequality and N R equality constraints jointly in a and b.

spatially, the sources are local as opposed to global.


4 This set of bootstrapped examples D L is then fed as training data into a supervised or semi-supervised algorithm Φ(D L , D U ), and MFA outputs the resulting classifier.

p (y = 1|x i = r) > P (y = 1|x i = r ) if r > r . • The monotonicity is non-trivial in that P (x i ) has positive probability for more than one feature value.


The proof follows immediately from the strict convexity of mutual information [7] and the fact that the two conditions guarantee that each Q(y|x) appears non-trivially in at least one mutual information term.

we begin by rewriting each mutual information term I R (x; y) in the criterion = min where the variational distribution Q R (y) can be chosen independently from Q(y|x) but the unique minimum is attained when We can extend the regularizer over both {Q(y|x)} and {Q R (y)} by defining The local propagation algorithm follows from optimizing each Q(y|x) based on fixed {Q R (y)} and subsequently finding each Q R (y) given fixed {Q(y|x)}.


Training of deep learning models depends on gradient descent and end-to-end differentiation.

inspired by this idea, we show the Scala implementation of this callback version of reverse-mode AD in Figure 2.


Focusing on the new comparators only, observe that their progress is nearly statistically equivalent during the first 20 iterations.

define f n min = min i=1,...,n y i , the smallest y-value seen so far, and let I(x) = max{0, f n min − Y (x)} be the improvement at x. I(x) is largest when Y (x) ∼ f n (x) has substantial distribution below f n min .


Note, that our approach is not equivalent to a variational approximation of the original posterior.

the correction term is found to be qualitatively accurate and emphasizes a discrepancy between free energy and the first two terms of the expansion Eq.


( 10) becomes an ordinary gradient descent.

then ϕ I (x) may, for example [18], be defined with the indicators of whether there are particular types of buildings near the road segment, x.


Inference is tractable if we can evaluate an MLN using these set of rules.

2 is in general of exponential size in the domain of objects.


An analysis of IT neurons that responded to the target stimulus showed that the average size of the receptive fields shrinks from approximately 56 degrees in a blank background to approximately 12 degrees with a complex scene [8].

the second object, a distractor object, was placed on the opposite side of the fovea at a fixed distance of ¢ degrees from the fovea.


Acknowledgments: This work is supported in part by ONR MURI Awards N00014-10-1-0934 and N00014-16-1-2007.

our implementation (referred to as ResNet Ours) has the following modifications which improve the performance of the original model (Table 1).


This paper does not offer novel ML algorithms, but instead seeks to increase the community's awareness of the difficult tradeoffs that must be considered in practice over the long term.

sometimes, a group of features is evaluated and found to be beneficial.


We performed a standard preprocessing on the datasets -details will be given in the full paper.

we fixed a few values for parameter b, run the selective sampling algorithm in Figure 2, and computed the fraction of labels requested over the training set.


Note that the sum of each row in the underly score matrix needs to be zero for the sake of identifiability.

we assume that there are d 1 users and d 2 items, where d 1 and d 2 are positive integers.


First, we present a simple guarantee about the rounding Algorithm 2.


we simultaneously improve the running time and approximation factor.


Takimoto and Warmuth [2000] obtained the minimax strategy for prediction in Euclidean space with squared loss.

any B t that are bounded below satisfy this condition.


It produced an average fitness within 1% of the optimum for (): between 0.1 and 0.4 and L = 32, 64,128,256 over a 100 trials, but for learning rates below 0.1 and L = 256 the average fitness fell as low as 4% below optimum.

one might think that the needle-in-the-haystack problem is hard in a special way, and results on this problem are not relevant to other problems.


Such compositional models are easier to interpret than DNNs.

denote by T (i, j) the rectangle in the image for which the presence of an object is predicted by output (i, j) of the network.


In the BXPCA, we interpret the matrix V as a lower dimensional embedding of the data which can be used for dimensionality reduction.

this is shown in figure 3d, where we show the frequency of incorrect predictions, where the error between the predicted and actual bits is greater than 0.95.


The two received signals will have some delay and some gain relative to the source, in addition to a disruption due to noise.

the authors in [1] choose a fixed sampling rate and adjust the distance between their free-standing microphones to prevent ambiguity.


[2018] is also motivated by the CLS framework.

our agent consists of three components: a standard parametric reinforcement learner with its replay buffer augmented to maintains trajectory information, a trace computation algorithm that periodically plans over subsets of data in the replay buffer, a small value buffer which stores the value estimates resulting from the planning process.


As can be seen, the latter achieves much lower d even with a small number of bases.

the proposed method achieves the same performance only using a single scale.


Moreover, we also propose a local method for multi-task regression problems.

our SMO algorithm updates a violating pair at one step by choosing the most violating pair {j, k} with j and k defined as j = arg max l∈S1∪S2 {w i a l + b l } and k = arg min l∈S2∪S3∪S4 {w i a l + b l }.


For example, from a Mondrian process on products of intervals, we can construct a Mondrian process on all of R D . Note that if the domains have infinite measure, the tree of cuts will be infinitely deep with no root and infinitely many leaves (being the infinite partition of the product space).

( 11) is the product of two stick-breaking priors.


A primary insight is that, since Algorithm 3 regularizes with the L 2 norm and penalizes with hinge-loss, omitting the positive semidefinite requirement for M and vectorizing M makes the algorithm equivalent to a oneclass, linear support vector machine with O(n 3 ) input vectors.

for maximum weight subgraph connectivity (e.g., b-matching), we use a cutting-plane method [10], iteratively finding the worst violating constraint and adding it to a working-set.


The closest work to ours is Factorie [31].

for many problems, it is possible to declare loss early as with Hamming loss (= number of incorrect predictions).


We find that the differences in MSE and 1-SSIM between the differently trained L-CAE models are smaller (5% improvement in MSE and a 4% improvement in 1-SSIM) (Figure 5 B and D).

it will be important to investigate whether the CAE can learn to generalize over different mosaic patterns.


Final object detectors are selected based on their performance on the validation set from LabelMe (see Appendix for more details).

if a group of parameters is non-zero, they will all be non-zero.


We propose an efficient way to incorporate hierarchical information into the model.

we evaluated model performance for all three models with a range of values for µ, the mean prior parameter for regression coefficients (µ ∈ {−3, −2.8, −2.6, .


Namely, for any observation signal y, and any nonzero scalar α and integer shift τ , the following equality always holds Here, s −τ [v] denotes the cyclic shift of the vector v by τ entries: Clearly, both scaling and cyclic shifts preserve the short-and-sparse structure of (a 0 , x 0 ).

note that if we could recover some shift s τ [x 0 ], we could subsequently determine s −τ [a 0 ] by solving a linear system of equations, and hence solve the deconvolution problem, up to the shift ambiguity.


This results in the update rules Note that we are less interested in the joint distribution ψ ijτ = p(i, j, τ ) than other distributions derived from it.

aarabi's method, while quite simple, is still one of the most accurate methods for localizing many simultaneous sound sources, even in reverberation.


Under a mild technical assumption, Proposition 9 suggests that losing connections monotonically increases the MSD, and individuals tend to maintain their friendships to obtain a lower MSD as a global objective.

essentially, if there is no connection between agents i and j, for < min{p ii , p jj }, corresponds to a new communication matrix adding the edge {i, j} with a weight to the network G, and subtracting from self-reliance of agents i and j.


In Figure 1(b), a link is predicted between the green and yellow atoms.

we design a graph generation procedure that can be formulated as a Markov Decision Process (MDP), which requires the state transition dynamics to satisfy the Markov property: p(s t+1 |s t , ...s 0 ) = p(s t+1 |s t ).


The Gaussian mixtures were initialized using k-means -other choices usually led to worse performance.

let us assume that the source patterns x (i) , x (j) have a high probability of being assigned to the same cluster if they lie close to a specific cluster center in some feature space.


We compare to two very recent approaches to Bayesian neural networks, namely an approach based on expectation propagation [HLA15] and an approach based on variational Bayes [BCKW15].

we first compute the posterior distribution over the model parameters, p(θ|D N ) ∝ p(θ) N i=1 p(y i |x i , θ), where D N = {(x i , y i )} N i=1 , x i ∈ X D is the i'th input (where D is the number of features), and y i ∈ Y is the i'th output.


The compactness hypothesis (CH) [5] is the basis for object recognition.

fault detection is an important problem in the machine diagnostics: failure to detect faults can lead to machine damage, while false alarms can lead to unnecessary expenses.


This is not surprising, since in this case the structured version of UCB cannot exploit the additional structure and suffers due to worse constant factors.

as is rather common we assume that the returns are sub-gaussian, which means that if X is the return sampled from some arm, then ln E exp(λ(X − EX)) ≤ λ 2 σ 2 /2.


This final representation is then passed to the answer prediction layer.

factorization-based models are known to not only be expressive and efficient, but also able to model low-rank structure well.


Structure learning faces several challenges: the number of possible structures is super-exponential in the number of variables while the required sample size might be even exponential.

state-of-the-art structure learning techniques: covariance selection [5] and graphical lasso [6], since it has been shown theoretically and experimentally that they both converge to the maximum likelihood estimator.


It would be interesting to see whether a large step size can be used for any p > 0.

staying with these goals, we propose the z update augmentation term of BADMM to be: B φ (Bz, c − Ax t+1 ), instead of the quadratic penalty term 1 2 Ax t+1 + Bz − c 2 2 in (3).


If one needs to solve problem (1) for high dimensional data, the use of standard second-order methods such as interior-point methods is precluded (see for instance [6]), since they need to solve large systems of linear equations to compute the Newton steps.

in fact, we can think of trivial examples where the replicates formulation has not a unique solution.


Attention has also been used for video generation [24], where a binary mask is learned to distinguish between dynamic and static regions in each frame of a generated video.

they generally also affect the background in unwanted ways, leading to unrealistic translations.


We use θ to denote the vector of parameters θ ij , and denote the partition function by Z(θ) to highlight its dependence on these parameters.

as in TRW, it can be shown that the solution is not dependent on the decomposition (as long as each edge appears in some structure), and the problem is equivalent to maximizing a linear function over the marginal polytope (which can be done in polynomial time for planar graphs).


We propose distances between distributions which encode invariance to additive symmetric noise, aimed at testing whether the assumed true underlying processes differ.

if X can be written in the form X = X 0 + E, where X 0 and E are independent and E is an SPD noise component, then X is decomposable.


This overcomplete case however is unnormalized and hence cannot be directly compared here.

the activity of a population of cells was recorded at a rate of 30kHz then sorted using an automated spike sorting method; from this we randomly selected five cells with which to demonstrate our method.


We propose two computationally efficient algorithms that match the query complexity lower bound within log n factor and are completely parameter free.

we estimate If there is no cluster of size at least M E x formed so far, we select a new element yet to be clustered and query it exactly once with the existing clusters (that is by selecting one arbitrary point from every cluster and querying the oracle with it and the new element), and include it in an existing cluster or create a new cluster with it based on the query answer.


Specifically, while the method based on the log derivative trick is currently the most general one, it has been observed to severely suffer from high variance problems [12,14,10] and thus it is only applicable together with sophisticated variance reduction techniques based on control variates.

given that we can reparametrize x i as described above (and all differentiability conditions mentioned above hold), the gradient from ( 11) can be equivalently written as Clearly, the above expression is an expectation of the reparametrization gradient from eq.


In this paper, we primarily target autonomous deterministic dynamics (e.g., Eq.

we modify the loss function by employing an additional term such that the original measurements y can be reconstructed from the values of g by a reconstructor h, i.e., y ≈ h(g( x)).


Obviously, x contains many outliers and has the problems of poor boundary localization and spatial fragmented predictions.

transition matrices measure the possibility of random walk between any two nodes, with our implementation they could also reflect similarities on different semantic levels.


Namely, we propose an algorithm that • provably produces an accurate estimate of the lifted target X from only n = O k log d k measurements, and • can be computed in polynomial time through efficient convex optimization methods.

then for any pair of k × k-sparse matrices X and X with disjoint supports we have Ψ XΨ T , Ψ X Ψ T ≤ 2δ 2k X F X F . Proof.


In Figure 1(b), we see that an acceptance probability q to 0.1 creates new components rather than inheriting from previous phases, leading to poor performance when the number of samples is limited.

they construct a universal Gamma process in an auxiliary space and obtain dependent DPs by normalizing it within overlapped local regions.


Now, notice that the problem of minimizing T t=m h t (X) is a PSD relaxation to the minimization problem T t=m ft (x), and for the optimal solution it holds that: where x * = arg min x∈K T t=m ft (x).

the hidden convexity of the problem allows us to bypass this issue by a simple and tight Positive Semi-Definite (PSD) relaxation.


Therefore, while switching between Φ = W ΦD and Φ = Φ may influence the initialization and possibly the update rules of a particular Type II algorithm, it does not fundamentally alter the underlying cost function.

herein we will consider the selection where Γ is a diagonal matrix of non-negative variational parameters [14,18].


This is called the MAP assignment problem in graphical models and for general graphs and arbitrary parameters is NP complete.

symmetric, that is for It is easy to see that any energy function over binary variables can be reparameterized in this form 2 .


Tangent supports array programming on both CPU and GPU through the NumPy [19] and TensorFlow Eager libraries.

the community has a strong attachment to Python and its models rely heavily on multidimensional arrays.


Other authors have reported on the range of values contained within tensors during neural network training: "the activations, gradients and parameters have very different ranges" and "gradients ranges slowly diminish during the training" [21].

additional high-precision multipliers are still needed to perform the scaling after each convolution which limits its performance.


We also believe that ideas of searching through comparisons form a bridge between many well known search techniques in metric spaces to perceptually important (non-metric spaces) situations, and could lead to innovative practical applications.

by inequality 2, we have: By property 5, there are at most O(D 3 log n) such samples at level i + 1, i.e.


Once new state vector W ′ is proposed we accept it with probability min 1, We compute P (W |λ, γ) and P (W ′ → W ) in a closed form, while we approximate the posterior P (Y |W ) by sampling L Gibbs samples while keeping W fixed.

when adding a new group k ′ we select the birth and death time of the group at random such that 1 ≤ T B k ′ ≤ T D k ′ ≤ T . For removing groups we randomly pick one of existing groups k ′′ and remove it by setting W (t) k ′′ = 0 for all t. Finally, to update the birth and death time of an existing group, we select an existing group and propose new birth and death time of the group at random.


However, a quadratic surrogate model also has quadratically many parameters which we have to estimate from a (ideally) very small data set.

the intuition of the natural gradient is that we want to obtain an update direction of the parameters of the search distribution that is most similar to the standard gradient while the KL-divergence between new and old search distributions is bounded.


If one were to suppose that people had no inherent prior biases to prefer to generalize one way or the other, it should follow that the less informative condition (i.e., random context) should reveal more individual differences.

the three cluster solution (panel a, larger γ) is more context general, and collapses category B into a single cluster.


Alternative functions could be found by solving the optimization problem, subject to some constraints, for example that f be monotone increasing, have zero Gaussian mean, and saturate for large |x|.

the following six values of z are locations of the poles at the integration endpoints and determine the salient features of the spectral density: In the Supplementary Material, we establish the relative ordering of constants 0 ≤ ζ ≤ η ≤ η , which implies that the minimum and maximum eigenvalues of H (0) are given by, The Supplementary Material also shows that the equality η = ζ only holds for linear networks, which implies that the minimum eigenvalue is nonzero for every nonlinear activation function.


Let ĥm ∈ R L and ŝ ∈ R N +L−1 denote discrete, sampled versions of the filter h m and signal s respectively.

this makes the methods computationally demanding and sometimes intractable for large filter lengths (typically in the tens of thousands for acoustic applications).


This is one natural way of adding a new point to the embedding by keeping existing embedded points fixed.

when it fails, the GPLVM tracker often freezes in latent space, like PCA.


The influence of the cross-terms (UWS T and SW T U T ) is addressed later.

then, for any real number k > 0, we have, where b is the bias term described in Section 2, and b is its estimate from the training phase.


While the HDPR is more broadly applicable, our focus in this paper is on assortative models for undirected networks, which assume that the probability of linking distinct communities is small.

the synthetic network we use for testing is generated from the standards and software outlined in [12] to produce realistic synthetic networks with overlapping communities and power-law degree distributions.


We assume that the state space is large or continuous, and function approximation must be used to compute any values of interest.

this is a constrained optimization problem.


A Banach space B is said to be uniformly Fréchet differentiable if for all f, g ∈ B, lim t∈R,t→0 exists and the limit is approached uniformly for f, g in the unit sphere of B.

it can be seen that many RKBSs (B pd p (R d ) for any 1 < p < ∞) have the same r.k (ignoring the scaling factor which can be made one for any p by choosing µ to be a probability measure).


[24] also focus strongly on nuisance management as the key challenge in defining good scene representations.

this leads to the ReLU operation (see Appendix Proposition A.3).


Our work falls in between: we leverage properties of a specific kind of parallelisation-data parallelisation-for a fairly broad class of models.

a draw A ∼ Q −p (A) is then used to initialise an uncollapsed Gibbs sampler.


To our knowledge there is no polynomial time approximation algorithm known for the general case of pairwise clustering.

ward's method is then applied to the embedded objects.


Roughly speaking, LSI holds if the logarithm of the density is strongly concave.

let (θ, x) be M -smooth for all x ∈ X , and − log π(θ) be M π -smooth.


We define a two-part loss function to evaluate the fitness of imputation.

before the generating of the sequences, these methods require the complete train dataset which is impossible in our scenario, yet our model needn't complete train datasets.


Other methods learn to predict future measurements or to follow simple text instructions [16,23,22,11]; in our case, the goal is designated using proximity to local landmarks.

the focus of our paper is to demonstrate that simpler architectures can explore and memorise very large environments using target-driven visual navigation with a goal-conditional policy.


To move from a location s towards a goal position s , we can consider a constrained gradient ascent procedure on the value landscape: 2 where π(s ) has been absorbed into the parameter α.

the presence of a reward-induced neuromodulator could allow for potentiation between the assembly and the attractor network neurons active when the animal receives a reward at a particular location.


Assume for instance that θ i = 0 for all i ≥ 3.


This is a primary source of computational savings relative to HMMs.

for AIW, we ran 15,000 burn-in samples and used 3,500 samples for predictive inference.


Moreover, for gamma-like distributions, the convolution integral tends to increase the shape parameter, which means that gamma parameter estimates produced by fitting transition durations will overestimate the amount of 'memory' in the process 7 .

for n > 4 and µ m (ξ) relatively small, the distribution has a gamma-like behavior, where new memory update transitions are suppressed near recent transitions.


Consider an Ising model with p spins, with maximum degree d and maximum coupling intensity β.

in the future, we plan to explore further theoretical and experimental power, characteristics and performance of the generalized screening estimator.


The performance of this algorithm can be affected by several parameters, including the gradient search step size, the size of the sample pool, the number of Gibbs updates, and the number of total iterations.

the proposed methods are more accurate than variational approximations.


Previous work characterizing confidence intervals for cosmological parameters either used marginalization over the other parameters, or made assumptions about the values of the parameters and/or the shape of the CMB power spectrum.

from the Equations 1 and 2, it is clear that the algorithm does not depend on data dimensionality directly.


For classification, we use one of the simplest possible models: we compute the pseudoinverse of the projected training data to calculate B (see Eq.

as most other kernel methods, KOPLS requires the computation and storage of a kernel matrix of size l × l, which limits the maximum size of the datasets where the algorithm can be applied.


We visualize some of the qualitative results of our approach in Fig.

we assess the occurring performance changes of two configurations: (i) by only adding the bounding box regression loss into the objective function ('Train'), i.e., both the segmentation net and the object localization net are trained but only the segmentation net is deployed; (ii) by training and applying the object localization net ('Apply').


The key idea is to treat stragglers as "erasures" and use ECC to retrieve the result after a subset of fast workers have finished.

(J 1 ) k×k is GΛG , (J 2 ) k×(n−k) is GΛH , and Consider an alternative way of doing linear inverse using n > k workers.


3, we use the SW-cut for (RF) 2 inference.

we derive the theoretical performance bounds of a two-class (RF) 2 , for simplicity.


To further display the advantage of reciprocal connection, we also calculate the situation when a single network receives both input cues.

to get clear understanding of the effect of reciprocal connections, we decouple the dynamics of z 1 and z 2 by studying the dynamics of their their difference, z d = z 1 − z 2 , and their summation, z s = z 1 + z 2 .


Random Features has been proposed as a kernel approximation method [2,3,10,5], where a Monte-Carlo approximation is used to approximate (3), so that the solution to (1) can be obtained by The corresponding approximation error as proved in [2,Appendix B], can be bounded by ϵ given D = Ω(1/ϵ 2 ) number of random features, which is a direct consequence of the uniform convergence of the sampling approximation (4).

a line of research has thus been devoted to kernel approximation methods that aim to preserve predictive performance, while maintaining computational tractability.


Our method achieves comparable sparsity with irregular fine-grained pruning and maintains the model accuracy to a great extent.

at each iteration during the inner loop, the only update is to swap the i-th and j-th slices in the D-th dimension of W . for S, we only need to swap the i-th and j-th rows without recomputing the tensor contraction.


Furthermore, our approach is also different from change point based algorithms [14,8] which first segment time series and then fit an invariant structure to each segment.

this is also different from estimating a nonstationary model in the conventional sense, where one interests in recovering the exact values of the varying coefficients [17,18].


While learning both words produces the best score on the new situation, explaining with high probability why the word "dax" was produced, it performs worst on the rest of the corpus.

without adding additional specialized machinery, we show how these can be explained within our model as the result of domain-general probabilistic inference mechanisms operating over the linguistic domain.


One might assume this approach would require vastly more training data than other methods with more prior structure.

adding additional machinery in the network architecture may work better.


The proposed algorithm readily applies to general convex sets.

this can be done through the application of the popular FISTA algorithm for (16), which also guarantees (14).


Moreover, unlike in LDA, it is feasible to compute the objective functions for PMMs exactly as shown below.

this algorithm successively determines an element in y to increase the posterior probability until its value does not improve.


Given these difficulties, a more practical approach is to run both π 1 and π 2 using half of the budget for each policy and combine the selected sets.

furthermore, in the adaptive setting, we cannot roll back once we run a policy.


For unresolved harmonics, it is well known that the corresponding filter responses are strongly amplitude-modulated and the response envelopes fluctuate at the fundamental frequency (F0) of target speech [8].

in section 3, systematic results and a comparison with the Wang-Brown system are given.


The results demonstrate the our methods do lead to more informative and diverse responses in comparison to existing methods.

the argmax operation is used, instead of sampling from a multinomial distribution as in the standard LSTM.


4 (right) shows that using longer rollouts, while not increasing the number of parameters, increases performance: 3 unrolling steps improves speed of learning and top performance significantly over 1 unrolling step, 5 outperforms 3, and as a test for significantly longer rollouts, 15 outperforms 5, reaching above 90% of levels solved.

we investigated several types of rollout policies (random, pretrained) and found that a particularly efficient strategy was to distill the imagination-augmented policy into a model-free policy.


We thank Bruno Olshausen, Pieter Abbeel, Sara Bolouki, Roger Grosse, Benjamin Packer, Austin Shoemaker and Joelle Skaf for helpful discussions.

then, for each combination, we defined the convergence point as the point at which the objective value reaches within 1% relative error of the observed "optimal" objective value.


1 (b), implies the following factorization Using d-separation in this DAG, we see that in cases where any values are missing, neither MCAR nor MAR assumptions hold under this model.

1 (d) with functions f R † defined as follows.


These techniques are however costly in practice and most studies either rely on a flat classifier, or a hierarchical one either deployed on the original hierarchy or a simplified version of it obtained by pruning some nodes (as [15,18]) 2 .

a node-based pruning strategy can be easily derived from the approximation bounds above.


this is a significant improvement over the passive label complexity of m. a simple auditing procedure that scans from right to left queries only a single negative point, achieving an auditing complexity of 1.


We present an update scheme called HOGWILD!

when the data access is sparse, meaning that individual SGD steps only modify a small part of the decision variable, we show that memory overwrites are rare and that they introduce barely any error into the computation when they do occur.


Non-linear non-rigid registration remains a challenge in computer vision.

we compare the performance of the CPD algorithm on 2D and 3D data against ICP and RPM algorithms, and show how CPD outperforms both methods in the presence of noise and outliers.


In greater detail, for any function f evaluated at a regular grid, for x ∈ (i/K, (i + 1)/K] and f (x) = f (1/K) for x ≤ 1/K; and the interpolation matrix is Our proposal, waveMesh, solves the following convex optimization problem where , and W ∈ R K×K is the usual DWT matrix.

the novelty of our approach is a reversal of the direction of interpolation, i.e., interpolation from fitted values on the regular grid i/K (i = 1, . . . , K), to approximated fits on the raw data x i (i = 1, . . . , n).


Our experimental results significantly extend the state of the art in autonomous helicopter flight.

we change the model such that the next state is α times the target state plus 1 − α times the next state according to the true model.


Pairs of monocular responses are generated by integrating image intensities weighted by pairs of phase quadrature RF profiles, which are the real and imaginary parts of a complex-valued Gabor function ( ): ( where and are the spatial frequency and the phase of the left and right monocular RFs, and is a zero mean Gaussian with standard deviation , which is inversely proportional to the spatial frequency bandwidth.

can be used as a confidence measure for distinguishing DIN and DOUT.


In other words, we want to use the learned policy at the states in which either the improvement is significant or the model uncertainty (error function) is small, and to use the baseline policy everywhere else.

to the best of our knowledge, such challenges have not yet been fully investigated in the literature.


Principal component analysis (PCA) is widely used for data pre-processing, data compression and dimensionality reduction.

we present a generative model for performing sparse probabilistic projections, which includes sparse principal component analysis and sparse canonical correlation analysis as special cases.


GoogLeNet is trained by polynomial LR decay and data augmentation in [41].

ternGrad achieves lower precision for larger dataset (e.g.


Step 2: keep p(w) fixed, based on the factorization assumption p({z}) = i p(z i ) and p 0 ({z}) = i p 0 (z i ), the distribution p(z) for each sample i can be obtained by solving the following problem: where Similarly, by introducing a set of Lagrangian multipliers β(y), we can get: and the dual variables β(y) can be obtained by solving the following dual problem: where P i (C) = { y β(y) = C, β(y) ≥ 0, ∀y}.

we can introduce a set of marginal dual variables and transfer the dual problem (12) to an equivalent form with a polynomial number of constraints.


We show that glm is approximately proportional to ols in random design GLMs, regardless of the predictor distribution.

if S ✓ [n], let U S denote the |S| ⇥ p matrix obtained from U by extracting the rows that are indexed by S. For a symmetric matrix M 2 R p⇥p , max (M) and min (M) denote the maximum and minimum eigenvalues, respectively.


For example, in the realizable case, i.e., when the data arise from an actual quantum state, the average L 1 loss per iteration is O( p n/T ).

an n-qubit state ⇢ induces a function f on the set of two-outcome measurements E defined as f (E) := Tr(E⇢).


Here we have overloaded the notation for a doubly convolutional layer to denote a DCNN which contains correspondingly shaped doubly convolutional layers (the DCNN in Table 1 thus corresponds to DCNN-128-4-3-2).

we have also confirmed that replacing a convolutional layer with a doubly convolutional layer consistently improves the performance, regardless of the depth of the layer.


In consequence, the assumption of uniform prior taken by SIBA is closer to the real one.

this extraction process can be characterized by vector t = t 1 , t 2 . . . t l where t k is the number of marbles of color y k extracted, with t = l k=1 t k . The probability of extracting a color distribution of marbles t, given the initial color distribution of the urn T is described by the multivariate hypergeometric distribution Consider the case in which the total number of marbles in the urn, T , is known but that the color distribution, T, is unknown.


3A shows that a large number of training episodes finally provides significant improvements.

rSNNs in the brain have been optimized through a host of preceding processes, from evolution to prior learning of related tasks, for their learning performance.


The problem of such greedy approach is target leakage: feature xi k is computed using y k , the target of x k . This leads to a conditional shift [30]: the distribution of xi |y differs for training and test examples.

for all test examples, the value of the greedy TS is p, and the obtained model predicts 0 for all of them if p < t and predicts 1 otherwise, thus having accuracy 0.5 in both cases.


In formal terms, the issue is to optimally encode a real random variable x in the number of pulses emitted by a neuron within a certain time window.

it is the simple fact that spike counts are discrete by nature, which already severely limits the possibility of graded rate coding.


These two opposing mechanisms ensure that the cell will remain at a constant activity under steady-state conditions.

with a transient change in the presynaptic frequency, h, the initial postsynaptic frequency is given by: (3) As derived from Equation 3, we see that the transient change in the neuron's spiking rate is dependent on the contrast of the input spiking rate, dfd Ii- Hence, the transient gain of the neuron is equal to the ratio of the postsynaptic spiking rate to the presynaptic input rate and it decreases with the input rate.


We consider modeling the data set D using models indexed by a complexity index k, 1 :::; k :::; kmax • For example, the models could be finite mixture probability density functions (PDFs) for vector Xi'S where model complexity is indexed by the number of components k in the mixture.

we define y = y(x) as a scalar function of x, namely a prediction at x.


Among the shallow multi-task methods, MTRL gives the best accuracies, showing that exploiting task relationship may be more effective than extracting shared feature subspace for multi-task learning.

in the tensor normal prior, the row covariance matrix Σ 1 models the relationships between features (feature covariance), the column covariance matrix Σ 2 models the relationships between classes (class covariance), and the mode-3 covariance matrix Σ 3 models the relationships between tasks in the -th layer network parameters {W 1, , .


The non-zero entries of κ are displayed in Figure 2 as functions of the parameter t. An edge contributes strongly to the kernel value, if two genotypes agree on it, but the common event (occurrence or non-occurrence of the mutation) was unlikely (Figure 2, solid and dashed line).

the application of the Fisher kernel idea to mutagenetic trees leads to a kernel that measures similarity of evolutionary escape in a way that corresponds well to virological intuition.


Clearly we see that each function contributes differently to represent the input and more information is gained from f 2 compared to the former case.

while some of these methods have produced good results on datasets such as CIFAR-10 and SVHN, none has produced low precision networks competitive with full-precision models on large-scale classification tasks, such as ImageNet.


We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded hierarchically in the network structure.

each recursive call returns a latent structure for each autonomous set.


Hence, substituting the discriminant function ( 6) into (4), we have the prediction rule Then following the principle of MED learning, we define probabilistic max-margin matrix factorization (PM 3 F) as solving the following optimization problem Note that our probabilistic formulation is strictly more general than the original M 3 F model, which is in fact a special case of PM 3 F under a standard Gaussian prior and a mean-field assumption on p(U, V ).

we use U i to denote the ith row of U , and V j likewise.


This analysis suggests that ŷpcr is not consistent when σ 2 → 0 and d → ∞ (at least for n = 2).

first, it provides an illustrative warm-up for the more complex risk bounds obtained in Section 5.


Note that our corollary 2.2 does not apply to the d-bits parity function, so it represents another type of local variation (not along a line).

we prove this lemma by induction on d. If d = 1 there are only 2 points.


We train high-capacity discriminative models that learn to map EP message inputs to EP message outputs for each message operation needed for EP inference.

f j is a stochastic function that draws a sample from ψ j (x out(j) | x in(j) ).


off-policy value estimation as called by some authors [20]).

alternatively, we can take F to be a ball of a reproducing kernel Hilbert space (RKHS), which enables a closed form representation of D(w) as we show in the following.


First, v-structures are identified and directed.

a graph of the form where " " represent a sparse connectivity which we learn, and "→" represents full connectivity.


Let h t denote a history up to stage t and s(h t ) denote the last state of history h t . We use π ht (a) to represent the probability of choosing an action a at state s(h t ), following a policy π and under a history h t . A t + 1 stage history, with h t followed by action a and state s ′ is written as (h t , a, s ′ ).

denote the uncertainty set by P = s Ps .


Further, this result requires only the expected loss = E[ t ] to have a quadratic lower bound -the individual losses t themselves need not do so.

the following Proposition shows that existence of a quadratic lower bound is actually a local condition; so long as the expected loss has a quadratic lower bound in a neighborhood of w , it must do so over the entire space W : Finally, we provide a simple motivating example of an interesting problem we can solve with an α-acutely convex loss that is not strongly convex: computing the median.


We generated synthetic networks consist of 1024 nodes and about 2500 edges using Kronecker graph model [35]: core-periphery network (CP) (parameters [0.9,0.5;0.5,0.3]), hierarchical community network (HC) (parameters [0.9,0.1;0.1,0.9]), and the Forest Fire model [36]: with forward and backward burning probability 0.2 and 0.17.

such models yield dense graphs [7] and are less appropriate for predicting unseen interactions.


The size of feature maps on each convolutional layers is reduced by average pooling for computational efficiency: where F is the number of channels and H ⇥ W is the spatial dimension.

our method improves the TNR, i.e., the fraction of detected LSUN samples, compared to ODIN: 41.2% !


Like its discrete counterpart, Theorem 3.1 provides necessary and sufficient conditions for the continuous relaxation to be tight.

while the proof of Theorem 3.1 is nontrivial, it provides a powerful tool to reason about the tightness of MAP relaxations.


We are given a training set of image and label pairs {(I t , l t )} N t=1 and the task is to predict the value of l t (e.g.

at first glance, a very simple way of using the classification RBM of the previous section in the multi-fixation setting would be to set x = x 1:K = [x 1 , .


Under the same conditions the SSEM needed 55 minutes to do the job, while the batch EM needed 186 minutes.

sparsity is interesting both with respect to fast training and predictions and ease of interpretation of the solution.


With some assumptions on S and f t , this algorithm achieves a regret of O( Although the algorithm is simple, it needs to solve a constrained optimization problem at every time step, which might be too time-consuming for online implementation when the constraints are complex.

note that the algorithm in [19] cannot be applied since the clipped constraints do not satisfy the required Slater condition.


Each of the four machines at this level executes a reactive strategy for traversing a corridor.

an instance is in a "state" if the instance's incoming history matches the suffix representing the state.


We explore a similar direction but extend this work to transparent objects.

we compare to 2 baseline methods: traditional visual words and the histogram of oriented gradients (HOG) detector [6].


The performance of this process is measured by how accurately it retrieves the phrase structure of the input string.

our two main methods, projection-based Markov Models (PMM) and constraint satisfaction with classifiers (CSCL) are shown to perform very well on the task of predicting NP and SV phrases, with CSCL at least as good as any other method tried on these tasks.


We consider all possible combinations of the regressors defined above.

when merge sort was superior, our participants chose it significantly more often than cocktail sort (p < 10 −10 ).


Our analysis has revealed that symmetry is strongly related to the attractiveness of averaged faces, but is definitely not the only factor in the equation since about half of the image-features relate to the ratings of averaged composites in a similar manner as the symmetry measure.

several regions are suggested for extracting mean hair color, mean skin color and skin texture.


While the proposed framework is flexible in simultaneously tackling data in various feature representations, the formulation itself is general in that it is established upon graph embedding.

an ensemble kernel function k (or an ensemble kernel matrix K) is then defined by the learned model from binary-class data {(x i , y i ∈ ±1)} will be of the form: Optimizing both the coefficients {α i } N i=1 and {β m } M m=1 is one particular form of the MKL problems.


During the training of Gaifman models, neighborhoods are generated for tuples of objects d ∈ D n based on the parameters r and k. We first describe the procedure for arbitrary tuples d of objects and will later explain where these tuples come from.

the feature vector v = (v 1 , ..., v |Φ| ) for tuple d, and neighborhood N ∈ N r,k (d), written as v N , is constructed as follows Deciding D |= ϕ for a structure D and a first-order formula ϕ is referred to as model checking and computing ϕ(D) is called ϕ-counting.


5 below, N must also be greater than the number of linear equations.

the rest of the paper considers targets based on a single variable.


BiCNet [19] is based on actor-critic model for continuous action, using recurrent networks to connect each individual agent's policy and value networks.

it is only a large single network for all agents, so it cannot easily scale and would perform poorly in the environment with a large number of agents.


we call such a graph a probabilistic and-or dag.


A related technique that we will consider in this paper is canonical correlation analysis [CCA; 6], a well-known statistical technique for analyzing the linear relationship between two multidimensional variables.

oCCA is employed for the orthogonal directions V that are "easy to learn" (of low prediction error) in terms of linear regression.


We first compare these models on a formal level.

the parameter values found in the likelihood optimization of the causal model are as follows: s.e.m.


Most algorithms that are being used in practice minimize a convex surrogate loss.

their technique is based on a smooth boosting algorithm applied on top of a weak learner which constructs random halfspaces and takes their majority vote.


Subjective time is the time duration which the animal perceives to have occurred, (or at least appears to perceive judging from its behavior).


Generally, network structures designed specifically for image classification are directly used as default backbone structure for other tasks including detection and segmentation, but there is seldom backbone structure designed under the consideration of unifying the advantages of networks designed for pixellevel or region-level predicting tasks, which may require very deep features with high resolution.

4 Experiments and Results For image classification, we evaluate our network on the ImageNet 2012 classification dataset [25] that consists of 1000 classes.


We work with time series data using a frame-by-frame analysis with N -point frames.

with the superscript i omitted, Yn denotes all microphone signals.


Note that Wz in RFF can be written as Rg, where R is a scaled orthogonal matrix such that each row has norm ||z|| 2 and g is distributed according to N (0, I d ).

let z = x y , and z = ||z||, then Based on the definition of ORF, w 1 , w 2 , .


Although one of the class-conditional densities in the figure is highly non-smooth, this erratic behavior occurs far from the decision boundary and thus does not affect nearest neighbor performance.

• We identify a general condition under which, as n and k grow, A n,k approaches the actual decision boundary {x | η(x) = 1/2}.


. . < γ T , start by sampling from the prior π ξ (θ), then applies successive importance sampling steps, from π ξ,γt−1 (θ|D) to π ξ,γt (θ|D), leading to importance weights proportional to: When the importance weights become too skewed, one rejuvenates the particles through a resampling step (draw particles randomly with replacement, with probability proportional to the weights) and a move step (move particles according to a certain MCMC kernel).

as any other Monte Carlo method, it may be too slow for large datasets.


Furthermore, it seems unlikely that a comparative framework could be built by independently choosing "ideal" penalty parameters λ, λ: Meinshausen and Bühlmann [8], for example, demonstrate that a seemingly reasonable oracle estimator of λ will not lead to consistent support recovery in the Lasso.

in high-dimensional settings where n p, ordinary least squares is generally inappropriate.


Let F be a set of functions mapping from X to Y, and let l : Y ⇥ Y !

in this section, we will use the properties of the local Rademacher complexity just discussed to devise a novel family of algorithms for learning kernels.


One primitive is set to have approximately the same length as a cycle of the periodic motion and the other primitive is set to be 50% larger.

6 our approach clearly outperforms all the baselines.


The pure episodic model completely fails to predict extra-list intrusions, because it restricts recall to the study list (i.e., it assigns zero predictive probability to extra-list items).

each word is assumed to be drawn from a mixture model with corpus-wide components (i.e., the topics) and document-specific mixture proportions.


the entire space H all of all possible functions mapping examples to labels.

using Theorem 4, we can write the potential φ t (s) explicitly, and then compute it using dynamic programming in O(t 3 k) time.


Let L be the corresponding labeled examples 8.

when k = 1, we recover a well-known label complexity bound for passive learning by empirical risk minimization [10].


Experimental results on real world data sets with millions of patterns demonstrated that the CVM is much faster than existing SVM implementations and can handle much larger data sets.

the RKHS norm operates on functions, while here we have vectors f and y w.r.t.


This does not imply independence however.

the following lemma is a special case of Corollary 2.7 from [17].


Note that care must be taken to ensure that the addition of this penalty term does not violate the nonnegativity of c, and to ensure that the argument of ψ −1 lies in its domain.

given a = 1, with appropriate penalty functions, our solution to (3.6) can be utilized for maximizing entropy of Bc subject to linear or non-linear constraints on c. , where h is a "link" function that models a nonlinear relationship between A and the approximant BC, we may wish to minimize D ϕ (h(BC), A).


We observe that the interpolated reconstruction loss by itself produces a reasonable model.

we also take a step forward and consider a writing style transfer task for which parallel data is available.


Experimental results demonstrate their superior performance.

let Δ = ρ 1 − ρ 2 ∈ (0, 1], and μ :=   and the number of calls to the least squares solver of In order to satisfy the CCA constraints, we perform a last normalization And we output (û, v) as our final approximate solution to (1).


The product of an arbitrary vector v by the GGN matrix, Gv = J N H L J N v, amounts to the sequential multiplication of v by three matrices.

( 7) and setting l = z, p(z|a) can be re-written as where S is the set of every possible label sequence and f z = log π∈B −1 (z) exp(b π ) is the logsum-exp function 1 , which is proportional to the probability of observing the label sequence z among all the other label sequences.


Hence, for a measurable function f : where we used the fact that i+1 (x) ≤ 1 and η is an appropriate multiple of η, e.g.

for x, y ∈ K, ρ(x, y) is the distance in the Riemannian metric whose metric tensor is the Hessian of F . the metric tensor on the tangent space at x assigns to a vector v the length and to a pair of vectors v, w, the inner product v, w x := D 2 F (x)[v, w].


We demonstrate the impact of the various normalization schemes on a large variety of data sets and show that the new normalization algorithm often induces a significant performance boost in standardized tests.

what remains to show is that the projections P 1 and P 2 can be solved efficiently (and in closed form).


Given more experience, the controller increasingly learns to make distinctions between different actions that looked the same a priori.

note that 'learning time' is measured by the number of times every state-action pair has been sampled.


For ERM problems with millions of high-dimensional examples, even quadratic time algorithms can become painfully slow (or expensive) to run.


(2015) to be a metric on the space of probability measures for any V. Both variants behave similarly for two-sample testing, with the normalized version being a semimetric having a more computationally tractable null distribution, i.e., χ 2 (J).

this is true only with optimization of the test locations.


For example, white noise images can be distinguished from natural images because of their deviation from the power law statistics, while street scenes and beach scenes can be separated from each other on the basis of differences in ensemble power spectra [2].

functional data analysis [15] provides a natural framework for modeling continuous stochastic brain processes.


In conventional CRF approaches, the potential functions are first learned, and then inference is performed based on the learned potential functions to generate the final prediction.

for example, we here describe a strategy which is analogous to the network design in [3].


From now on, assume that ICA has been performed on the transformed data z.

we observed no shift-invariance, consistent with some recent findings in the V2 area of the Macaque monkey [5].


At the same time, it should produce diverse samples covering all classes.

in this setting, only unlabeled data is available for learning.


To further exploit the semantics, we introduce a novel regularizer coupling the metrics that prefers a sparse disjoint set of features to be selected for each metric relative to its ancestor (supercategory) nodes' metrics.

more importantly, these metric learning problems are coupled together through the disjoint regularization.


Furthermore, though the kernel learning algorithm was not expoed to the test set noise, the learned kernel reflects better the structure of the feature space which makes the learned kernel more robust to noise.

5 is a scatter plot comparing the test error of each of the binary classifiers when trained with the original RBF a kernel versus the performance achieved on the same binary problem with a learned kernel.


Further, it converges to an optimal solution if the constraints are of the product set type (see [2] for details).

a set of values for the variables) of domain α.


In some applications, such as the high-stakes spectrum auctions just mentioned, this assumption is probably reasonable, as participants are typically large companies that hire consultants to optimize their decision making.

we sum uniformly over the columns of the matrix as described above) and then applying a softmax function to convert each of the resulting vectors h i into normalized distributions.


For all x ∈ I, at least one function f ∈ F is nonzero at x.

after reviewing the relevant prior work in more detail ( § 2), we give our main result ( § 3).


We find that errors are always low in regions of high confidence (low standard deviation).

moreover, since our coefficients can be related to the global depth map through convolutions, we are able to use Fourier-domain computations for efficient inference.


we find that for margin errors the following three expectations: (i) of the empirical risk, (ii) of the the true risk and (iii) of the leave-one-out risk estimator are equal to each other.


Finally, for two simple and widely studied classes of multiarmed bandit problems we demonstrate state of art performance in simulation experiments.

iDS solves a single-period optimization problem as a proxy to an intractable multi-period problem.


An immediate application of the general projection property is to reduce worst-case analyses of multivariate expectations to the univariate case.

this nonlinear optimization problem can be efficiently solved by dynamic programming, provided that the model parameters (transition kernel and reward function) are exactly known.


Lowd and Domingos [18] learned tractable hightreewidth Bayesian networks by penalizing inference complexity along with model complexity in a standard Bayesian network learner.

as in previous work [21,8], we instead use conditional mutual information, denoted by I, to partition the set of variables.


3: while ending condition not satisfied do 4: Sample 1 , 2 , .

another version of this algorithm is called Bandit Gradient Descent by Flaxman et al.


Moreover, a preliminary analysis indicates that performing accelerated gradient descent on smoothed versions of the local functions (using Moreau proximal smoothing, e.g.

we end this section with an important remark.


Intuitively, if during training an algorithm finds a box with large volume, such that all weight-vectors belonging to it attain low training error and are simple, we expect the classifier based on the center of mass to be robust to noise or fluctuations.

if w attains the supremum sup w∈Q R(w) then so does at least one vertex.


In the above form, the compiler recognizes that the z mj are drawn from a categorical distribution and θ m is drawn from a Dirichlet, and can exploit the fact that these are conjugate distributions.

augur has two distinct compilation phases.


Relation between CNNs and regular expressions without Kleene star.

the gradient is computed similarly to EINNs, while embedding is not used.


In the second, simpler model, that we are also interested in here, there is no side-information, but the agent is given a model that describes the possible relations between the arms' payoffs.

the aim of the agent is to quickly find an optimal arm in order to maximize the received rewards.


Hence, they can achieve higher objective than the maximum.

the primary goal of any KPCA algorithm is then to guarantee generalization, i.e.


While one advantage of Equation 2is that all connections are assigned a non-zero score, another benefit is derivatives with respect to model parameters are easy to determine and compute using the standard formula for the derivative of an inverse matrix.

given the sensitivity of model performance on signal processing illustrated in Figure 2, our goal is now to learn the optimal filter α by optimizing a smooth loss function.


To see why, recall that quantities max i∈[m] ψ i and (1/m) m i=1 ψ i have magnitudes on the order of √ m x and π/2 x , respectively, whereas h ≤ ρ x for some small constant 0 < ρ ≤ 1/10, to be discussed shortly.

tGGF requires at most O(log(1/ )) iterations to achieve any given solution accuracy > 0 (a.k.a., dist(z t , x) ≤ x ), with iteration cost O(mn).


Also, we need to change coordinate system of the 3D features to suit the actual projection function.

as the pose over all faces is (essentially) constant for both test and training images, the normalizing coordinate mapping T is restricted to scale and translation.


Algorithm 1 shows the online learning algorithm.

for almost all the baseline methods except ITML, their performance varied significantly as the size of the input image changed.


It can thus be solved to any given accuracy in polynomial time by general purpose interior-point methods [12].

the previous constraint can be seen as Φ(M ) k, with φ(λ) = 1 λ λ0 , which is not concave and thus does not lead to a convex constraint.


this avoids a bottleneck in sampling, as otherwise we would have to get lucky in drawing the right feature and transformation.


As a consequence of this prior specification one cannot, as opposed to Cor.

we obtained polynomially exact generalisations of standard BC in Thm.


Combining these aspects together, the R-MSN is able to help clinicians evaluate the projected outcome of a complex treatment scenario -providing timely clinical decision support and helping them customize a treatment regimen to the patient.

encoder The goal of the encoder is to learn good representations for the patient's current clinical state, and we do so with a standard LSTM that makes one-step-ahead predictions of the outcome ( Ŷt+1 ) given observations of covariates and actual treatments.