Major differences in task design complicate direct comparisons among the studies.

while it seems sub-optimal, and thus mysterious, that humans have an underestimated prior reward expectation, our simulations show that an underestimated prior mean helps to maximize long-term gain, if the observer assumes volatility when reward rates are stable, and utilizes a softmax decision policy instead of the optimal one (obtainable by dynamic programming).


This explains why uncertainty sampling sometimes achieves lower zero-one loss than random sampling, since that is the quantity it implicitly optimizes.

the dataset on the left was chosen to exhibit the wide range of convergence values of uncertainty sampling, some with lower zero-one loss than with the full dataset.


This is realized via For example, substitute([fatherOf, X, Z], The signature of and is L ⇥ N ⇥ S !

the training loss for ComplEx can be seen as an auxiliary loss for the subsymbolic representations learned by the NTP.


All operations in the Kalman filter are conjugate, and inference may be performed in closed form.

we also find that GCLDS and GCfLDS models give much better predictive likelihood than their Poisson counterparts.


The networks include nodes, n i,l , of agent i's level-l FSC.

1 with the mixture models as given in Fig.


To tackle this problem, we introduce an auxiliary function [20,9] to construct a smooth approximation of (10).

an efficient optimization method based on proximal approximation and accelerated parallel gradient method is introduced.


To do so, for each time t, we build a weighted bipartite graph where each human decision maker v j is connected to each individual (x i (t), z i (t)) with weigh: otherwise, Note that the maximum weighted bipartite matching is the optimal assignment as defined by Eq.

moreover, they also reveal that our algorithms benefit from higher diversity across the pool experts, being able to ensure fairness even if a significant percentage of judges are biased against a group of individuals sharing a sensitive attribute value (e.g., race).


The best k-group approximation problem is the discrete optimization problem arg min where the goal is to compute the projection of a vector y onto a union of subspaces each defined by a subcollection of k groups.

for the unit ball of Ω LGS-OWL , we can exploit the fact that the atoms of Ω LGS-OWL are obtained from Ω LG(k) across different k at different scales.


Once we do this, we can detect the underlying models.

in this work we tackle the harder problem of minimizing the policy regret.


The remaining results were obtained using this configuration.

a statistical model is used to get structural semantic features from low-level feature co-occurrences.


Propert y (3.1) is important since it gu arantees that the Fisher kernel performs better when t he optimal w and b are available.

this threshold is determined in the same way for FK-SVMs and TOP-SVMs.


A major roadblock to a one-to-one comparison are the auxiliary penalty parameters, λ, λ, which trade off the 1 penalty to the quadratic objective in both Eq.

( 19) can be thought of as the limiting construction of Gaussian Lasso problems in Eq.


We then perform binary classification for each noun-phrase , where w k is the weight vector corresponding to the class N P k and σ denotes the sigmoid function.

competitive results are obtained for CompCap trained using in-domain and out-of-domain data, which suggests the benefit of disentangling semantics and syntax, as the distribution of semantics often varies from dataset to dataset, but the distribution of syntax is relatively stable across datasets.


Nonnegative matrix factorization (NMF) is a popular data analysis method, the objective of which is to approximate a matrix with all nonnegative components into the product of two nonnegative matrices.

as the overall mfNMF can be solved by optimizing each individual factor in an SMS problem, we focus here on the case where the sparsity regularizer of each factor is introduced in (4), to solve max As we have mentioned, the typical choice of (•) as the matrix 1 norm is problematic in (10), as if we treat each column of X as a point on a probability simplex, as their elements are nonnegative and sum to one, then we can induce a sparse regularizer from the Dirichlet distribution.


Consider, for example, a decision making problem that is a quadratic optimization problem.

(iii) Minibatches One technique to enhance online learning is to consider multiple observations per update.


For SATURATE, we optimized a single design which achieves the maximum normalized variance reduction over all values of θ 02 between 0 and 16.

we compared designs which are robust against a large parameter range.


Although the act of recognising the tennis ball is seemingly independent of our intuition of Newtonian dynamics [31], very little of this assumption has yet been captured in the end-to-end models that presently mark the path towards artificial general intelligence.

deep neural networks can parameterize the transition and emission distributions of different variants of deep state-space models [8,16,19].


It is in fact due to discounting future rewards.

through pharmacological agents known to modulate discount rate) should increase the probability that the animal show an anticipatory response, and vice versa.


For PX-VB, we can compute the matrix rate of convergence similarly.

we first expand p(x, D) to obtain p α (x, D).


Consequently, SNNs do not face vanishing and exploding gradient problems.


Given a particular state, an action modifies the setting to a subset of the hidden variables; therefore, an action can also be defined as a setting to all the hidden variables Y =y .

even though reinforcement learning's policy requires it to be greedy with respect to the q-function, we observe that it is able to better escape the random initial configuration than the Metropolis-Hastings method.


In our experiments, iVSGPR shows better performance than the direct adoption of stochastic variational inference to solve variational sparse GPs.

a Gaussian process GP(m, k) has a dual representation in an RKHS H [12]: there exists µ ∈ H and a positive semi-definite linear operator Σ : H → H such that for any x, x ∈ X , ∃φ x , φ x ∈ H, the mean function has a realization µ in H, which is defined by the reproducing kernel k(x, x ) = ρ 2 φ T x φ x ; the covariance function can be equivalently represented by a linear operator Σ.


The analysis of this linear program is considerably more difficult than of the previous one.

in this section we also consider the length of the boundary of the identified pixels.


We show that a combinatorial procedure based on the scan statistic achieves the minimax optimal limits, however it is impractical as it requires enumerating all possible sub-matrices of a given size in a large matrix.

our present understanding of biological systems leads us to expect that subsets of genes will be co-expressed only under a small number of experimental conditions.


Marginal vectors that lie within M δ are bounded away from zero as all the components of u 0 are strictly positive.

the framework we adopt is more generally applicable to optimizing functions whose gradients tend to infinity at the boundary of the domain.


We have the optimization in (B 1 ) equals: It is clear that the largest eigenvalue of H, λ max ( H), and its corresponding eigenvector u 1 give the solution to the above problem.

all Z ∈ Ω 1 , forms the set of extreme points of Γ 1 .


For example, ALSCAL can operate on a sparse matrix by ignoring missing terms in its cost function (1).

rD algorithms operate on a dense rectangle of distances, filled in by Dijkstra's algorithm.


The sample p(s) (X | η) of iteration s from the procedure in Eq.

finally, EB-Hyp resembles ensemble methods, such as boosting and bagging, because it is a weighted sum over posteriors.


For the POET dataset, some of the target objects are quite iconic and in the center of the image.

we use the released model to extract features and train a linear SVM on top of the features.


The results of our experiments, and comparisons with Google Sets for word and movie queries are given in tables 2 and 3.

acknowledgements: Thanks to Avrim Blum and Simon Tong for useful discussions, and to Sam Roweis for some of the data.


We are interested in the multi-agent MDP: , where S is the state space and A i is the action space for agent i.

π(a|s) is the conditional probability of taking joint action a given the current state s. We define the reward function of joint policy π as an average of the local rewards: That is, R π c (s) is the expected value of the average of the rewards when the agents follow policy π at state s. Besides, any fixed policy π induces a Markov chain over S, whose transition matrix is denoted by P π .


The network was trained with a triplet loss function [23] that ensured that the embedding h produced for an image x of a specific person was closer to the embeddings for all other images of the same person than it was to any embedding of another person.

samples from the model are shown in Figure 4.


Since DIAL learns to communicate in a continuous channel, our results offer an illuminating perspective on this topic.

to our knowledge, this is the first time that either differentiable communication or reinforcement learning with deep neural networks has succeeded in learning communication protocols in complex environments involving sequences and raw images.


a(λ) ≤ Cλ β for some C > 0 and all λ > 0.

if H approximates P with exponent β then the rate in Theorem 3.1 becomes n − 4β (2+p)(1+β) which is the rate we established in Theorem 2.3 for the original SVM.


exact local computation for the sigmoid function, P(y lXI, ... ,XJ) = 1/(1 + exp[-Bo -L: j BjXj]) , requires the full exponential sum.


In this paper, we explore how these two different views of learning are related to human language acquisition.

with m verbs and k sentence structures, this results in m verb features, k sentence structure features, and mk interaction features, each of which take the value 1 when they match the sentence and 0 when they do not.


Such simple penalization has been shown to be capable of obtaining models with a high degree of disentanglement in image datasets.

we find that β-TCVAE can learn two additional interpretable properties: material of the chair, and leg rotation for swivel chairs.


We have treated density estimation of the source and target distributions, or estimating their ratios, as an orthogonal problem in this work.

the density ratio, P src (x)/P trg (x), scales the distribution's prediction certainty to increase when the ratio is large and decrease when it is small.


To show the scalability, we report the running time using 1, 2, 4, 8, 16 machines, respectively.

in terms of the amount of data (in bits) sent over the network, the communication cost of the cleaning stage grows as O(dnmT ), where d is the number of features selected by the screening stage and n is the sketch size.


For the NIR dataset, we follow the steup for the original dataset: 40 instances for training and 32 instances for test.

recently, some nonconvex alternatives, such as the bridge penalty, the nonconvex exponential penalty (EXP) [3,8], the logarithmic penalty (LOG) [19,13], the smoothly clipped absolute deviation (SCAD) penalty [6] and the minimax concave plus (MCP) penalty [20], have been demonstrated to have attractive properties theoretically and practically.


Because of this, it is sufficient for P 2 to use a Markov policy, and this can be calculated in polynomial time in the number of states and actions.

overall, the results show that PURE, MIXED and STAT perform considerably better than NAIVE and HUMAN.


their WSL appearance model treats pixels within the target region independently, and therefore does not have notion of the "thing" being tracked.


L 2 λ distances: Classical work on nonparametric statistics has typically focused on the problem of smooth density estimation under L 2 λ loss, corresponding the adversarial loss d [49,47].

second, since the risk R I (P, X) depends on the unknown true distribution P , we cannot calculate it in practice.


By now, it has been shown that CMOL circuits can combine high performance with high defect tolerance (which is necessary for any circuit using nanodevices) for several digital applications.

this work has been supported in part by the AFOSR, MARCO (via FENA Center), and NSF.


( 7), starting at the stage when the pair entered the race, and ending with the stage when the pair either dropped out or wins the stage.

this model assumes that each point on the tree is associated with a D dimensional multinomial vector, and each entry of this vector on each branch of the tree evolves independently (thus independent-sites), forward in time, and with mutations occurring at rate λ d on entry d. When a mutation occurs, a new value for the entry is drawn from a distribution φ d , independently of the previous value at that entry (thus parentindependent).


The dataset was split into training (80%) and test (20%) sets, and two scenarios were considered: Scenario TRAIN -the opponent's model is learned from the training set only.

we find it interesting to consider the classical loss as well, thereby presenting the complementary view.


For any δ such that 0 < δ < 1, with probability at least 1 − δ, for any k ∈ {1, . . . , K} e(f, ĥk ) ≤ 2 While the use of data-dependent complexity measures can be expected to yield more accurate bounds and thus better decisions about the number k * of piles to use, it is not without its costs in comparison to the more standard data-independent approaches.

here our target model f is any function from an input class X into some bounded subset of R. (Frequently we will have X ⊆ R d , but this is not required.)


In most cases, this evolution can be written as a dynamical system, where is a potentially nonlinear learning rule that determines how synaptic weights change as a function of previous spiking.

in order to model the dynamics of the time-varying synaptic weights, we turn to a rich literature on synaptic plasticity and learning rules.


In the local model, each individual applies a differentially private algorithm locally to their data and shares only the output of the algorithm-called a report-with a server that aggregates users' reports.

this produces an ( , δ)-locally differentially private algorithm; however, it is non-interactive.


When the minority classes form compact clusters and the majority class distribution is locally smooth, the method will select examples both on the boundary and in the interior of the minority classes, and is proved to be effective theoretically.

if we select a point at random from B 2 , the probability that this point is from the minority class is at least In subsection 2.2, we have discussed rare category detection for the binary case.


( 1), we can see that the MAP problem reduces to finding a truth assignment that maximizes the sum of weights of satisfied clauses.

a collection of sets C is a partition of a set X if and only if each set in C is nonempty, pairwise disjoint and the union of all sets equals X.


The flexibility in the choice of message passing algorithm makes it easy to consider several instantiations of the framework and use the one best suited to a particular problem.

quantities about x s such as expected values under the pseudomarginal can be computed using the samples x (i) s . for any given variable node x s , the incoming messages to x s given in (4) are defined in terms of the importance weights and sampled values of the neighboring variables.


However it is possible to also view them in a more principled manner.

for the documents in D i , the estimates for γ t d,i should be better than they might be in the documents D \ D i .


Previous sampling methods for regression ensure that the variance can be directly related to the function error, whereas here such sampling methods give 2 error, the bounding of which in terms of function error can be expensive.

when the number of zero entries in a row is small, we can always choose that row completely and not do sampling on it.


. . , A K . We take a one-versus-all approach, training one forest for each unseen class.

while our training "exemplars" are the true attribute signatures for each unseen class, the test images will have only approximate estimates of the attributes they contain.


the literature on the reject option is quite extensive and mainly discusses rejection mechanisms for various hypothesis classes and learning algorithms, such as SVM, boosting, and nearest-neighbors [8,13,3].


We then prove individual regret bounds for any sub-Gaussian distributions (similarly to Bubeck et al.

theorem 3 The policy of Figure 3 has regret bounded as R n ≤ i:∆i>0 ∆ i + 80+log(∆i/ε) ∆i , uniformly in n. The proof of this result is fairly technical and it is deferred to the supplementary material.


Such threshold-triggered dynamics generates discrete, all-or-none responses of synaptic current, which is non-differentiable.

it is generally hard to guarantee convergence of these bottom-up approaches, which do not consider the complex effects network dynamics nor the task information in designing of the learning rule.


One end of each spring is attached to a frictionless horizontal or vertical rail that is 39 pixels from the center of the image.

some of the finer details of the reconstruction may be slightly wrong and need to be fixed up by an iterative local search that adjusts the motor program to reduce the reconstruction error.


Let X ⇢ R d be a domain such that we have an extension operator E of the form described in front of Theorem 1, P X be the uniform distribution on X and f 2 L 1 (X).

[12] shows that the rate n /( +p) is often asymptotically optimal in a minmax sense.


In order to solve the relaxed convex optimization problem (8) efficiently at each round of the CCCP, we have designed a stochastic subgradient descent algorithm, using the Pegasos framework developed in [18].

moreover, current MIL and MIML algorithms usually rely on a 'key' instance in the bag [1] or they transform each bag into single instance representation [25], while our algorithm makes an explicit effort to label every instance in a bag and to consider all of them during learning.


It can therefore provide a learning signal if the generated data has collapsed.

see Appendix A for details of our algorithm and the DMGAN objectives.


based upon sampled images, and show that for certain types of super-resolution problems, this sample-based prior gives a significant improvement over other common multiple-image super-resolution techniques.

the Huber parameters are more likely to lie close to their own optimal values than our sample-based prior parameters are.


Next, we compute the marginal decrease r t i of the selected coordinate i and use it as feedback to adapt our coordinate selection strategy using a bandit framework.

figure 4b depicts the per epoch clock time for " = 0.5 and different values of E. Note that the clock time is not a function of ".


Recurrent neural networks (RNNs) live at the heart of many sequence modeling problems.


One hopes that the manifold structure could be preserved in the much lower dimensional Euclidean space.

a framework of semi-supervised learning based on differential operators can be formulated as follows: where C ∞ (M) denotes smooth functions on M, R 0 : R × R → R is the loss function and R 1 (f ) : C ∞ (M) → R is a regularization functional.


In the majority of our experiments, mixture models (with many mixture components) appear to outperform RBMs and logistic PCA.

we integrate out the Bernoulli parameters µ and the cluster distribution parameters π, and we sample the cluster assignment variables z.


The Bethe Hessian systematically outperforms B and does almost as well as BP, which is a more complicated algorithm, that we have run here assuming the knowledge of "oracle parameters": the number of communities, their sizes, and the matrix p ab [5,4].

we will therefore, somewhat improperly, call Hessian the matrix at the paramagnetic point: A more general expression of the Bethe Hessian in the case of weighted interactions atanh(w ij /r) (with weights rescaled to be in [0, 1]) is given by eq.


This is accomplished by matrix factorization techniques such as independent component analysis [13], nonnegative matrix factorization [12] and (hierarchical) dictionary learning [4,3].

the experiments in section 4.1 suggest that it may also be worthwhile to investigate the use of more parametric forms for the impulse response instead of the completely unbiased variant used here.


The diversity functions we propose are monotone submodular functions by construction.

(9b) by summing the intersections with each B k (y ) separately.


We devise our video recognition architecture accordingly, dividing it into two streams, as shown in Fig.

we measure the effect of: using multiple (L = {5, 10}) stacked optical flows; trajectory stacking; mean displacement subtraction; using the bi-directional optical flow.


Without sub-sampling, Algorithm 1 is equivalent to Algorithm 2 of [8].

from the right plot of Figure 1 we see that the test residual keeps dropping at a constant rate after 50 basis vectors have been added.


Like many No Free Lunch theorems, the result of the previous section is not surprising given there are no assumptions about the planning algorithm.

there have been many suggested philosophical avenues for finding such a reward (such as reflective equilibrium [Rawls, 1971]), but all have been underdefined and disputed.


( 4), ( 5), ( 6) by sampling few points from the standard normal distribution.

unfortunately, methods such as SGD or Adagrad converge slowly for some difficult-to-train models, such as untied-weights auto-encoders or recurrent neural networks.


In this paper, we show that it can be well solved with deep learning and using both face identification and verification signals as supervision.

these models are much limited by their linear nature or shallow structures, while inter-and intra-personal variations are complex, highly nonlinear, and observed in high-dimensional image space.


As negative test images we take all remaining images from the other categories.

learning object parts is formulated as two instances of the problem of finding maximal cliques in weighted graphs that satisfy hard constraints, and solved with the proposed Particle Filter inference framework.


The theoretical and experimental results based on benchmarks are still highly consistent.

more specifically, let X ∈ R d and Y ∈ {±1} (d ∈ N) be the input and output random variables and equipped with an underlying joint density p(x, y).


an experimental evaluation compares AGS to state of the art algorithms for MMAP [14] and illustrates its potential in solving hard inference problems.


When the signal of interest is known without uncertainty, the frequency representation can be obtained by means of the Fourier transform [6].

the connection between temporal and frequency representations of GPs has aided the design of the GPs to have specific (prior) harmonic content in both parametric [25][26][27][28][29] and non-parametric [22,23] ways.


Significant plasticity in sensory cortical representations can be driven in mature animals either by behavioural tasks that pair sensory stimuli with reinforcement, or by electrophysiological experiments that pair sensory input with direct stimulation of neuromodulatory nuclei, but usually not by sensory stimuli presented alone.

a mechanistic description alone neglects the information-processing aspects of the brain's function.


. . , π k generated from the very start: where the initial (stationary) policy π 1,1 is chosen arbitrarily.

a value function v if T π v = T v, the set of such greedy policies is written G(v).


Analyzing the most strongly correlated 75 pairs of neurons during the 180 minute recording (2-fold cross-validation) we find that the GBLM and Adaptive Filtering both increase model accuracy (Fig 4A).

both the GBLM and Adaptive Filtering only increase the log likelihood relative to a homogeneous Poisson process by 3-4% for the parameters used here at the largest recording length.


The experiment on detecting persons wearing sunglasses within a collection of rather heterogeneous face images effectively demonstrates that the proposed method is able to detect atypical objects without prior assumptions on the expected number of outliers.

in order to derive an objective characterization of atypical objects it is, thus, necessary to select a suitable model in advance.


[17] proposed to use a specific stimulus decoding algorithm to classify trials that give accurate sensory information, and then quantify the increase in behavioral performance in the trials where the sensory decoding is correct.

our intersection information measure I II (S; R; C) can also be used as a metric to discover and index brain areas that perform the key computations needed for perceptual discrimination, and thus turn sensory information into choice.


The OLS-UCB algorithm with parameter λ > 0 and f (t) = log t + (m + 2) log log t + m 2 log(1 + e λ ) enjoys for all times T ≥ 1 the regret bound where x stands for the smallest positive integer bigger than or equal to x.

let G t = {A * µ ≥ A * μt + E t (A * )} be the event that the estimate of the optimal action is below its true mean by a big margin.


Next, we shall consider the problem of extending this approach to infinite-dimensional discrete distributions.

the multiplicities representation significantly reduces the time and space complexity of our computations for most datasets, as we need only compute sums and products involving the number symbols with distinct frequencies (at most n max ), rather than the total number of symbols K. In practice, we compute all expressions not explicitly involving ⇡ using the multiplicities representation.


The following sections provide details of each of the steps.

unlike other methods that handle overlapped spikes (e.g., [10]), our method jointly learns waveforms and spikes within a unified framework.


Other systems in the computer graphics literature convert sketches to procedural representations, e.g.

we evaluated, but did not train, our system on 100 real hand-drawn figures; see Fig.


In Section 2, we review properties of k-submodular functions.

especially when b = 18, the number of entropy evaluations is reduced by 31%.


Conversely, if x j is relevant, then we expect that changing the bandwidth h j for that variable should cause a large change in the estimator.

(2001) focuses on variable selection in multi-index models rather than on bandwidth estimation.


For fading, we considered a family of trial-dependent functions that specify the distance of the chosen exemplar to the category boundary (left panel of Figure 4).

post-hoc power computation revealed that with 50 subjects and the variability inherent in the data, the odds of observing a reliable 2% difference in the mean is only .10.


They then showed how to solve the offpolicy evaluation problem by incorporating the causal bounds into the decision-making procedure.

the reward is determined by values of: (1) the UCs governing the MUCT; (2) a set of unobserved variables (other than the UCs) where each affects an endogenous variable in the MUCT; and (3) the IB.


Nevertheless, we may obtain some evidence through Monte Carlo simulation.

the signal energy is given by Substituting into the definition (3), the SNR is given by The minimum-to-average ratio of x is defined as Since x 2 /k is the average of {|x j | 2 | j ∈ I true }, MAR ∈ (0, 1] with the upper limit occurring when all the nonzero entries of x have the same magnitude.


The CVAE is composed of multiple MLPs, such as recognition network q φ (z|x, y), (conditional) prior network p θ (z|x), and generation network p θ (y|x, z).

the parameters of the VAE can be estimated efficiently in the stochastic gradient variational Bayes (SGVB) [16] framework, where the variational lower bound of the log-likelihood is used as a surrogate objective function.


The parameter β is a normalization constant which depends on the power of the noise, σ 2 N , and the power of the amplitudes, The update for A which minimizes this cost function is similar to update (5) with some modifications.

we found that the quadratic expression of a Gaussian process competed with the L α sparseness term.


Again this will be pursued for the journal version.

for each choice of probability distribution q on experts, there is an algorithm that guarantees for each expert k. (2) it is not immediately obvious how this can be achieved.


For each function type, subjects completed 10 training trials followed by 30 testing trials.

it remains to be addressed how our findings scale up to higher dimensions and benchmark optimization problems.


The first measure we use is the total number of points in all S i across all iterations, an implementation-independent measure.

in the second and third figures, we compare the performance of the dynamic program against our method, with different percentages of points flipped/corrupted.


To gain some insight, we illustrate our idea with a specific example.

if we require the marginals to be consistent only locally, we obtain a tractable approximation [34].


The approximation is significantly tighter than the existing work [9], which allows us to achieve stronger guarantees while providing better empirical performance.

this is a much weaker definition than having a non-zero breakdown point: a breakdown of requires that bounded response be guaranteed when any fraction of the data is perturbed arbitrarily.


since there is a recurrent relationship between consecutive layers, the controller can be naturally designed as a LSTM network.


The following exposition can be readily extended to the general case by setting δ(x, y The aim of learning is to find a hypothesis h ∈ H that has minimum risk.

we study the self-normalized estimator [12] which is superior to the vanilla estimator when fluctuations in the weights dominate the variance [19].


Unfortunately, finding the correct parameters turns out to be a difficult problem which cannot be solved in closed form.

the difference between the entropy of the independent model and the multi-information yields the joint entropy of the respective distribution.


We then explored the feature space that was learned by the latent feature model and the response space that was learned by the likelihood by systematically traversing the reconstructions obtained from different points in these spaces.

principal component analysis was implemented in scikit-learn [51].


2 Lower Bound on Sample Requirements: The above result states that roughly samples are required for structural consistency under any estimation method.

the LDA models are learnt using the lda package 5 .


They project the original label space into a low dimensional label space.

we can answer the second question: the globally optimal CC exists only when the minimization of the upper bound is achieved over this CC.


Finally, RECT obtains results comparable to LR even without generalizing.

when the sum of rewards and the constraints are defined in terms of different policies, this naturally induces a "belief state" that is similar to the augmenting set of outcomes B previously described.


The results are shown in Figure 2 (c) where the performance of RLS significantly drops as the number of missing data is increased.

the main advantage of using sparse coding is that state-of-the-art results can be achieved with a simple linear classifier as reported in [24].


For instance, (2.4) allows i a i = 1 for γ ∈]0, 2 3L ].

the spectral analysis of M becomes much more complicated to get for s ≥ 2, where the analysis of at least cubic equations are involved.


This suggests that our method shares similarities with functional gradient boosting (FGB), a leading method for constructing regression forests, run in the log space [16].

in the CV health model, the differences were significant at p =1e-9 for all training set sizes.


One option is to take the state-wise minimum of values from multiple random executions of Algorithm 1, which preserves the transitive feasibility of the value function.

we present a new formulation of value function approximation that provably minimizes a bound on the policy loss.


The kernel CCA procedure identifies a set of projections from both languages into a common semantic space.

the spectrum of the problem (9) has paired positive and negative values between W V and V . Cross-linguistic retrieval with KCCA.


The policy is normally parameterized by users and is controlled by tuning θ.

no tractable algorithm for the NSG learning has been proposed to date.


Also it was noted early on, that the final classifier achieved by adversarial training is again vulnerable to adversarial samples [7].

interestingly, it has recently been shown that there exist universal adversarial changes which when applied lead, for every image, to a wrong classification with high probability [17].


Let A t denote the set of possible assignments at time t where each assignment is a string (a 1 , ..., a t ) of binary variables

we use the same data as described in section (3.1) but without providing category membership for any of the training data.


Future work should also consider whether the categorical principles we described (C1 through C5) are better characterized as probabilistic expectations.

more formally, the independence principle specifies how the prior for the multiple object case is related to the prior p( v 1 ) on velocity fields for a single object (Equation 1): (2) We now develop a prior p( v) that incorporates probabilistic expectations about the motion of physical objects.


An exponential filter predicts that ARR− will always create a stronger expectation for an R on the current trial than AAR− will, because the former includes an additional past repetition.

if the environment does not change, γ t = γ t−1 .


Hence, if d Q is close to 1/2, Var(W Q ) must be small as well.

in this paper, however, we restrict ourselves to the more common case where the set H of classifiers is defined without reference to the training data.


this work was supported in part by the NSF Grants IIS-0534929, IIS-0812118 in the Robust Intelligence Cluster and by the DOE Grant DE-FG52-06NA27508.


In this n p setting, coordinate-wise CONCORD algorithm is especially fast due to its computational complexity O(np 2 ).

the Gaussian graphical model estimation or inverse covariance estimation has seen tremendous advances in the past few years.


There are strong theoretical guarantees for online learning, and it usually uses regret or the number of mistakes to measure the performance of the learning procedure.

though most studies consider data stream with fixed features, in real practice the features may be evolvable.


One might argue that feature mis-specification is not a critical issue in light of effective methods for subset selection.

our view is that even this enormous set will result in model biases that might be ameliorated by generalizations of DR.


It can be shown that the solution of the L 0 regularization problem in (1) achieves good prediction accuracy if the target function can be approximated by a sparse w. It can also solve the feature selection problem under extra identifiability assumptions.

the performance of the algorithms are reported in Figure 5.


First, it provides a consistent improvement over linear SVM.

also, training Random Recursive SVM is carried out in a feed-forward way, where each step involves a convex optimization problem that can be efficiently solved.


be the weighted sum corresponding to node ND.

([9] always visits the children in left-right order, which in our experiments also gave significantly worse performance than our version.)


The data is presented in n-gram format, where n ranges from 1 to 5.

the local nature and the need for anchors to be picked by hand or by nearest neighbor search make the local anchoring method unsuitable for detecting corpus-level shifts.


Once a CAP TCHA is broken (i.e., computer programs can successfully pass the test), bots can impersonate humans and gain access to services that they should not.

training several different machine learning algorithms on different types of audio CAP TCHAs allowed us to analyze the strengths and weaknesses of the algorithms so that we could suggest a design for a more robust audio CAPTCHA.


Our method shows that tools from machine learning and Bayesian statistics allow us to leverage multiple resolutions of information to make accurate predictions with well-characterized uncertainties.

note on priors For photometric weight and redshift inference, we use a flat prior on z n ∈ [0, 8], and empirically derived priors for m n and w n , from the sample of spectroscopically measured sources.


Experimental design consists of selecting which experiments to run or measurements to observe in order to estimate some variable of interest.

this same factor is obtained for α ≥ 1/3-supermodular functions.


Throughout the paper, H is set at H = min(L, M ) (i.e., the matrix BΘ ⊤ can express any multinomial distribution).

investigation on related models, e.g., Poisson MF [9], would help us fully explain this phenomenon.


Note that planning is performed entirely in the latent state without access to any observations except for the depiction of the current state.

we parametrize the transformation matrices and offset as vec where vec denotes vectorization and therefore vec To circumvent estimating the full matrix A t of size n z × n z , we can choose it to be a perturbation of the identity matrix A t = (I + v t r T t ) which reduces the parameters to be estimated for A t to 2n z .


1, given that the distribution has a given variance, the variance of variance is controlled by n and the fourth moment of the distribution.

for β = 0 the distance between the peaks of the distribution is non-consequential.


For the renewal process in which ISIs are drawn from a given distribution function, it is proven that the Fano factor is related to the ISI variability with F ≈ C 2 V [4].

for the inference of λ(t) from {t i }, we use a prior distribution of x(t), such that the large gradient of x(t) is controlled by where the hyperparameter γ controls the roughness of the latent process x(t): with the small γ, the model requires a constant latent process, and vice versa.


[GMMM+03] defines a divide-and-conquer strategy to combine multiple bi-criterion approximation algorithms for the k-medoid problem to yield a one-pass streaming approximation algorithm for k-median.

although many clustering algorithms have been designed with the k-means objective in mind, very few have approximation guarantees with respect to this objective.


The pathwise derivative estimator is known to have much lower variance than the score function estimator in many applications, and indeed was used by [23] with Gaussian dropout.

this happens despite the fact that the 2nd and   3rd hidden layers are of the same shape and prior length scale setting.


In this paper we showed that for a general class of convex online learning problems, there always exists a distance generating function Ψ such that Mirror Descent using this function achieves a near-optimal regret guarantee.

this includes the class F Lip which is the class of all functions with subgradients in X , and since F lin (X ) ⊂ F Lip (X ) we get the first equality.


The q-OCSVM method groups leaves associated with the 8 areas into 3 clusters, which perfectly corresponds to the hierarchical structure of the labels.

for all methods, the F -measure is bounded by 0.8 as long as the number of modes is greater than 3, correctly suggesting the presence of 3 modes for the data.


We set σ 2 implicitly via the signal to noise ration (SNR) as SNR = var(y)/σ 2 , where var(y) is the variance of y.

we applied the projection approach as additional post-processing for the two Bayesian model baselines.


The quality of our prices and value functions will depend on whether it is valid to assume a single price for each resource: if the prices stay constant then our approximate plan will translate perfectly to the physical world.

enemy positions are sampled from the particle filters at the beginning of each rollout and each policy is evaluated over several possible enemy position combinations to determine the performance of a policy.


Recalling that α ≥ 0, we have that sign(v j • x) = f (x) if and only if angle from v to x lies in (π/2, π/2 + α).

. . , (x m , y m )} of labeled examples, the number of examples misclassified by the hypothesis sign(v • x) is a nonconvex function of v, and thus it can be difficult to find a v that minimizes this error (see [12,18] for theoretical results that support this intuition in various settings).


In the following parts of the paper, we define the likelihood ratio distance between x and y as the square root of the negative logarithm of the similarity: ) It is worth pointing out that, for arbitrary distributions p(x), d(x, y) is not necessarily a distance metric as the triangular inequality may not hold.

table 2 shows the 99% FPR on the data without jitter effects 2 .


Accepting that performance-communication tradeoffs are inherent to distributed algorithms, we proceed with the goal of minimizing the loss in performance relative to J(γ * ).

the observation process Y satisfies p(y|x) = n∈V p(y n |x).


In this paper, we propose and evaluate the first model and learning algorithm for scene understanding that exploits rich relational information derived from the full-scene 3D point cloud for object labeling.

y l i only take values {0, 0.5, 1} at the solution) [10].


The figures show that the robustly regularized risk provides a different type of protection against overfitting than standard regularization or constraint techniques do: while other regularizers underperform in heavily constrained settings, the robustly regularized estimator b ✓ rob n achieves low classification error for all values of ⇢.

:= argmin ✓ R(✓) = 0, which satisfies R(✓ ? )


For data y ∈ R n , isotonic regression seeks to minimize 1 2 y − β 2 2 subject to the condition that the β i are non-decreasing.

the gradient and second differential of L(β | y, X) amount to As an example, when ψ(θ) = θ 2 /2 and c 2 (τ ) = τ 2 , the density (1) is the Gaussian likelihood, and GLM regression under the identity link coincides with standard linear regression.


For the worst case of HF, the conjugate gradient (CG) algorithm requires at most d iterations to terminate, meaning that it requires d evaluations of H θ v product.

( 6) is appealing since it does not need to store the dense matrix and provides an unbiased H θ v estimator with a small sample size.


We consider undirected, weighted graphs G = (V, E) with n vertices.

denoting by H ij the expected hitting time, by C ij the commute distance between two vertices v i and v j and by d i the degree of vertex v i we prove that the hitting times and commute distances can be approximated (up to the constant vol(G) that denotes the volume of the graph) by The intuitive reason for this behavior is that if the graph is large, the random walk "gets lost" in the sheer size of the graph.


This causes the neural network to encode derivatives of the target function in its own derivatives.

many of the ground truth functions we care about in practice have an unknown analytic form, e.g.


Even with large batches, each new instance still requires collapsing the uncertainty around the instance-specific parameters in order to quickly perform well on the task.

the HiP-MDP paradigm introduced a low-dimensional latent task parameterization w b that, combined with a state and action, completely describes the system's dynamics T (s |s, a, w b ).


In general, there is no value a v that maximizes θ v (a v , a −v ) independently of the opponent's choice of a −v .

as a consequence of Theorem 2, we can identify the unique Nash equilibrium of the game with cost functions θ +1 and θ −1 , if it exists, by finding the minimax solution of the game with joint cost function θ 0 .


Bayesian matrix completion [25]), where the ability of scale-up will be appealing.

gMC scales undesirably to large datasets, which are becoming common.


The USPS dataset 2 consists of 7291 training and 2007 test images from ten classes of handwritten digits.

the impact of regularization on the performance of the classifier is only minor.


We take 1) and add random effects as follows: (4) Each group j has its own component mean u jk for the kth component and these group-level parameters come from a common prior distribution N (µ k , τ 2 k ).

given a template mixture of two components with parameters θ a and θ b , in hierarchical DPs a mixture model for each group can have m a and m b exact copies (commonly known as tables in the Chinese restaurant process representation) of each of the two components in the template-thus, there is no notion of random variation in component parameters across groups.


In general, it is impossible to find a perfectly unbiased estimator for a continuously varied stimulus, using a finite number of weights.

these studies indicate that the above conclusions apply to a broad class of populations in which information is encoded in the second order statistics of the responses.


[29,30,24,38,5,4,31,35], are not directly useful for the analysis of the nonconvex and nonsmooth optimization problem stated above.

note that the first assumption is needed; otherwise the function may not be global because it could take a smaller value at a non local min outside X (possible when S is unbounded).


As AI systems become more powerful and autonomous, these failures will become more frequent and grave as RL agents exceed human performance, operate at time-scales that forbid constant oversight, and are given increasingly complex tasks -from driving cars to planning cities to eventually evaluating policies or helping run companies.

let V π R (s) be the expected return of reward function R from state s, given that the agent follows policy π.


Despite the importance of map synchronization, the algorithmic advancements on this problem remain limited.

to simplify the discussion, we fix m = 10, n = 200 and vary the observation graph G and p to evaluate NormSpecSync and existing algorithms.


While we prove that the learning bounded vertex cover Bayesian network structures can be done in polynomial time, the unavoidable dependence on k in the degree the polynomial makes the algorithm of our main theorem infeasible for practical usage when the vertex cover number k increases.

we report the score for the optimal DAG without structure constraints, and for the optimal DAGs with bounded tree-width and bounded vertex cover when the bound k changes, as well as the running time required for finding the optimal DAG in each case.


Suppose that Then there exists a factorization of 2 R m⇥k is an orthonormal matrix, and satisfies kU The proof of Lemma 4.6 is provided in Appendix B.5.

the proof of Theorem 3.4 for alternating gradient descent and gradient descent, and related lemmas are provided in the appendix.


Prediction of escape According to Table 3, the sharpnesses of both starting points are larger than 19.0.

when B ⌧ n the largest non-uniformity allowed is roughly p B/⌘.


In Async-HDP, a processor can add new topics to its collection during the inference step.

during the Gibbs sampling step, each processor locally samples the z p topic assignments.


The second general approach relies on auxiliary action labels, available in real or simulated robotic environments.

our generations compare favorably with leading approaches, despite being a simple model, e.g.


Throughout the rest of this section, we impose an additional assumption that the distribution D is finitely supported: IIxl12 :s M almost everywhere with respect to the measure D. From Section 3.1, we know that for any sufficiently small positive number A, Ilw.w.

for problems that are numerical in natural, the potential parameter space can be significantly reduced by using the first order condition of the optimal solution.


For comparison purposes we plot the MMD test from [9], in which a kernel method was proposed for solving the two-sample problem.

we first compare the divergence between a uniform distribution between 0 and 1 in d-dimension and a zero-mean Gaussian distribution with identity covariance matrix.


A state-ofthe-art approach is the low rank model [16,12] where one can first conduct matrix completion on adjacency matrix and then use the sign of completed matrix for relationship prediction.

many semi-supervised clustering algorithms are thus proposed by taking both item features  and constraints into consideration [13,25,37].


Interestingly, the truncation procedure in the gradient stage turns out to be useful in avoiding spurious stationary points in the context of nonconvex optimization.

even though the truncated spectral initialization improves upon the "plain vallina" spectral initialization, its performance still suffers when the number of measurements is relatively small and its advantage (over the untruncated version) narrows as the number of measurements grows.


And, by all measures, the orthogonal bases outperform their coupled counterparts with the same β, except for HYBRID and DECOUPLED.

it is invariant to reparametrization and can normalize the problem to be well conditioned [20].


We take the notion that ACh influences the balance of bottom-up and top-down one step further, suggesting that in the hierarchical cortex consisting of several processing stages, ACh could mediate this balance at any stage.

as long as there is some input, even if it is unspecific noise, hallucinations can be formed, but losing the input completely might require too much of a bias shift.


This implies that HSGD enjoys the merits of both SGD and FGD.

comparatively, HSGD-lin outputs more accurate solutions with linearly increasing batch size, which is consistent with Theorem 4.


The Plackett-Luce (PL) model, the Mallows model, and their variants have been, by far, the most studied models in this literature.

this implies that there are r 0 products from G which are less preferred than a k . With this notation, we can write .


This is intractable for large state spaces.

we also assigned the cost of 1 to actions detecting whether a rock is good or bad.


Furthermore, the limited amount of training data (e.g., Middlebury [3] or Sintel [5]) may not fully demonstrate the capability of learning-based optical flow algorithms.

we train the network for a total of 600k iterations.


Hence, AdaBoost "boosts" the weak learning algorithm to achieve a stronger classifier.

our low-dimensional study provides insight into AdaBoost's large scale dynamical behavior.


In this paper, we demonstrate how abstract, intuitive properties of clustering functions can be used to taxonomize a set of popular clustering algorithmic paradigms.

clustering is an ill defined problem -given a data set, it is not clear what a "correct" clustering for that set is.


The faces presented the largest computational challenges.

gRIFT defines prior distributions on its parameters.


For Z 0 ✓ Z, we now define g The constructions have the following properties that guarantees the effectiveness of the recursive steps of RAC.

we introduce two conditions on the objective function, the marginal likelihood rate bound (MLRB) and the marginal likelihood bound (MLB).


On the other hand, for some of α A , the second assumption does not necessarily hold because we do not know the optimal α A beforehand.


It is worth noting that oracle complexity measures only the number of queries to the oracle-for instance, the number of (approximate) function or gradient evaluations.

convex optimization is the task of minimizing a convex function f over a convex set S ⊆ R d . Assuming that the minimum is achieved, it corresponds to computing an element x * f that achieves the minimum-that is, x * f ∈ arg min x∈S f (x).


In such cases, the goal should be to synthesize plans that are robust with respect to any known incompleteness of the domain.

a typical plan to take an image using an instrument, e.g.


Unlike existing work which creates dependencies across multiple DPMG through exact or perturbed sharing of mixture components or through sharing of the entire mixture model, proposed I 2 GMM model associates each cluster with a distinct atom of the higher level DP through centering of the base distribution of the corresponding DPMG at that atom.

there are a total of seventeen Gaussian components, four clusters, and 17,000 instances (1000 instances per component) in this data set.


One possible construction algorithm is an extension of Kruskal's algorithm for the MST where we pick edges without replacement and restart for every new tree.

for T = 1 this gives the MST of the unperturbed data set; for T → ∞ it gives a stochastic graph where e ij is the probability (in the Laplace sense) of that edge under the noise model.


By substituting this step with a suitable nonparametric regression procedure, [2,3,4] come up with a corresponding non-parametric algorithm.

the SALP formulation (1), is, as discussed earlier, the parametric counterpart to the RSALP.


As before, each column of matrix A and B, represent components that project the data in space and time respectively.

changes in oscillatory activity are termed event related synchronization or desynchronization (ERS/ERD).


2 Another disadvantage of the algorithm is that the expansion of the look-ahead tree is uniform; it does not adapt to the MDP.

when there is structure in the rewards (like in the previous case), then κ = 1 and we obtain a rate Õ(1/� 2 ).


In this DBM, 2 /3 of the first RBM's prior over the first hidden layer has been replaced by the prior defined by the second-layer RBM.

the disadvantage of the pretraining procedure for Deep Belief Networks is that the top-layer RBM is forced to do most of the modelling work.


Brain image analyses have widely relied on univariate voxel-wise analyses, such as voxel-based morphometry (VBM) for structural MRI [1].

the most important point is that the proposed approach makes the results more consistent with the anatomy, making their interpretation more meaningful.


To produce an explicit correspondence field between the sets, we use the pyramid construct to divide-and-conquer the optimal matching computation.

the expense of the VG pyramid matching remains steady and low, even for high dimensions, since data-dependent pyramids better divide the matching labor into the natural segments in the feature space.


Some recent work suggested that combining different CF models may improve the prediction accuracy.

the family H included 200 randomly sampled features (a new sample was taken for each of the iterations in the stagewise algorithms).


The PAC learnability result shows that there is no information-theoretical obstacle to influence function learning under incomplete observations.

we compare our algorithm to the following approaches: (1) CIC fits the parameters of a CIC model, using the NetRate algorithm [7] with exponential delay distribution.


We compute this with a simple, greedy but fast algorithm: The resulting pairs of matching locations are closer than d m , which should be set approximately to the radius of a vesicle.

it offers adjustable model complexity depending on the training data, thus providing good generalization performance.


Assume for a moment that Figure 1: The figure on the left shows the sequence of states along an optimal path beginning at a single-cluster configuration and ending at the MAP configuration (F1 scores for each state are shown).

the reward function used is the residual improvement based on the performance metric F when the system transitions between states s and s : this reward can viewed as learning to minimize the geodesic distance between a current state and the MAP configuration on the proposal manifold.


The scalar (inner) product of two vectors x and y in the n-dimensional real space ℜ n will be denoted by x ′ y and the 2-norm of x will be denoted by x .

first, notice that (by negation) the feasibility constraints in (1) can also be defined as: a solution w is feasible iff there exist no pair of samples from the two classes such that f w ( ) orders them incorrectly.


We assume that the α-walk-summability condition in assumption (A2a) holds.

these conditions are NP-hard to verify for general graphical models.


Next, we extract from the above table a specific comparison among SHAZOO, WTA, and LABPROP.

predicting with the label of the connection node closest to i t in resistance distance is reminiscent of the nearest-neighbor prediction of WTA on weighted line graphs [6].


Computing the cost function or its gradient requires finding the maximin edges for all pixel pairs.

we would like a way of characterizing whether two pixels are connected in the thresholded affinity graph.


In the first style of evaluation, we compared the performance of our classifiers against the Known Hypernym versus Known Non-Hypernym labels assigned by 1 The corpus contains articles from the Associated Press, Wall Street Journal, and Los Angeles Times, drawn from the TIPSTER 1, 2, 3, and TREC 5 corpora [7].

there has been significant recent interest in finding methods for automatically learning taxonomic relations and constructing semantic hierarchies.


Then the selections in steps (S2) and (S3) are done in time O(1).

regret bounds for these algorithms do not scale as well with the number of arms: even if the tree widths are given, then letting ∆ min min x∈X: ∆(x)>0 ∆(x), the regret bound is proportional to |X δ |/∆ min (where X δ is as in Definition 1.1), whereas the regret bound in Theorem 2.3 is (essentially) in terms of the covering numbers N cov δ/8 (X δ ).


Even though we have simplified the state space by partitioning by user, the state space for a single user remains sufficiently complex to preclude standard table-based representation of value functions (also, each user's state space is effectively infinite, as there are real-valued state features).

the Living Room is a central public place, frequented both by many regulars, and by users new to LambdaMOO.


This means an advantage of the Bayesian learning.

indeed, we give the asymptotic form of the stochastic complexity as F (n) λ log n where n is the sample size, by comparing the coefficient λ with that of the true Bayesian learning, we discuss the accuracy of the VB approach.


In this experiment we attempt to model and predict the performance of students learning from an interactive computer-based tutor.

it uses the same history information as Feat-HMM but reduces the number of parameters to O(b) at the expense of inductive bias.


For each k ∈ [N ], the distribution P t,k over labeled examples that is given to the k-th run of the weak learner is as follows: a draw from P t,k is made by drawing (x, f (x)) from P and accepting (x, f (x)) as the output of the draw from P t,k with probability p x = α t,k (h 1,1 (x), .

in the t-th stage of boosting the weak learner is run N times in parallel.


The breakdown point of an estimator is the smallest fraction of bad observations that can cause the estimator to take arbitrarily aberrant values, i.e., the smallest fraction of outliers needed to completely break an estimator.

to obtain the sample complexity of our formulation we need to bound the difference that a single sample can make to the loss.


The asymptotic correctness of this practical methods is implied by the identifiability of the model, which is theoretically analyzed in the following section.

change the value f (x) to ŷ′ in order to achieve the highest score increase.


Though there has been significant work on PAC RL algorithms for the infinite horizon setting, there has been relatively little work on the finite horizon scenario.

a key idea is that in order to obtain accurate estimates of the value function of a policy from a starting state, it is sufficient to have only a loose estimate of the parameters of (s, a)-pairs that are unlikely to be visited under this policy.


( 11) is equivalent to adding zero-mean, fixed-variance Gaussian noise to the network weights during training.

if the weights have a prior probability P (w|α) that depends on some parameters α, the posterior can be written Pr(w|D, α).


When the variability in the data is due, in part, to small transformations such as translations, scales and rotations, factor analyzer learns a linearized transformation manifold which is often sufficient ( [4], [11]).

2) requires summing over all possible transformations and is very expensive.


To classify the green nodes, we will use the matrix A (g) = (A vw ) v,w∈V (g) , as well as the graph of indirect edges.

we focus here on scenarios where the network size can be extremely large (online social and biological networks can, already today, easily exceed several hundreds of millions of nodes), so that the adjacency matrix A of the corresponding graph can become difficult to manipulate and store.


1 shows that root leverage weights yield lower predictive loss than leverage based weights when the model is correctly specified.

since the hat matrix H is idempotent and symmetric, the squared norm H i• 2 = e T i H T He i = e T i He i = H ii .


when there exists h ∈ H with L (h) = 0 and so L * = 0.

|φ| ≤ b < ∞) and the relevant measure of complexity is the VC-subgraph dimension.


It is noticeable that they used pre-defined logic to generate questions with information gain criteria to make novel (i.e., not shown in the training dataset) and human-like questions.

the green mask highlights the correct object.


Richard E. Turner is supported by Google as well as EPSRC grants EP/M0269571 and EP/L000776/1.

although heuristics could be introduced to break up the clumps, this result suggests that using small α values for online inference and learning might be more appropriate (this recommendation differs from the batch setting where intermediate settings of α around 0.5 are best [13]).


Moreover, the activities in various levels of the hierarchy resemble electrophysiologically recorded activities in the visual cortical neurons during attentional modulation and perceptual discrimination, lending farther credence to the particular encoding and computational mechanisms that we have proposed.

this spans a broad spectrum, from distributional codes that can also encode restricted aspects of uncertainty [1] to more exotic interpretations of codes as representing complex distributions [1,2,3,4,5].


Also, the predictive scores for OVE and OVE-SGD are similar to SOFT, although they tend to be slightly worse.

this stochastic optimization procedure cannot deal with large values of K because the normalizing constant in the softmax couples all scores functions so that the log likelihood cannot be expressed as a sum across class labels.


From a top-down view, the model can be considered as a stochastic feedforward network (Tang and Salakhutdinov, 2013), where the input matrix in Φ (T ) , the output matrix is Φ (1) , and the stochastic units are drawn from the Dirichlet distribution.

for example, one commonly-used prior for TP and WD is a Dirichlet distribution, as in Latent Dirichlet Allocation (LDA) (Blei et al., 2003).


[15], we formulate the Spatial-Model as an MRF-like model over the distribution of spatial locations for each body part.

for datasets that cover a larger range of the possible poses (for instance the LSP [17] dataset), we would expect these distributions to be less tightly constrained, and therefore this simple Spatial-Model will be less effective.


If we encode x as a binary indicator vector z(x) over the bins, z(x) z(y) = 1 if x and y fall in the same bin and zero otherwise, so Now consider shift-invariant kernels that can be written as convex combinations of hat kernels on a compact subset of R × R: k(x, y) = ∞ 0 k hat (x, y; δ)p(δ) dδ.

we have presented randomized features whose inner products uniformly approximate many popular kernels.


Except for [32,33] discussed above, most of these works study the single-agent setting.

the agents aim to collectively maximize the global sum of local rewards.


The synapse's effect on the soma is also described below in terms of the current (I SYN ) its output voltage produces in a pMOS transistor whose source is at Vdd.

the synapse circuit is excitatory to the neuron.


The multiple kernel learning problem was first formulated as a semi-definite programming (SDP) problem by [5].

for the proposed level method, the values of p change smoothly through iterations.


there is a single audio signal source (of the speaker) but several interfering motion fields in the video sequence.


The amount by which the dual increases serves as a new and natural notion of progress.

we can now apply our algorithmic framework from Sec.


Using the categorization paradigm, Zotov et al.

the phenomenon is not inconsistent with the model.


Therefore, if eventually θ 1 is the true parameter vector satisfying C 1 and C 3 , then θ 2 satisfies these conditions as well.

for every subset of indices J ⊂ {1, . . . , N }, we denote by A J the M ×N matrix obtained from A by replacing the columns that have an index outside J by zero.


For "A", we use all captions (including reference MLE captions) that did not have minor or major errors, and GT for the rest.

β = 1 for perfect (or GT), 0.8 for acceptable, and 0.6 for grammar/fluency issues only.


In the multi-class setting that we focus on in this work, Li et al.

this indicates that the GLC is robust to the use of uncalibrated networks for estimating C, and that improving its performance may be difficult without directly improving the performance of the neural network used to estimate p(y | x).


This cannot be achieved with 2-part codes or practical network compression.

inefficiency of Variational Models for Deep Networks.


This gives more accurate and flexible approximations than the mean-field approach.

the ELBO convergence for SLANG shows that the optimization procedure does not necessarily converge to a local minimum.


In our context, we employ a random vector h d (w) of length p to reduce the variance of the sampled gradient, where A is a p × p matrix and h(w) E d [h d (w)].

stochastic gradient algorithms can run many more iterations in a limited time budget.


We demonstrate on image classification benchmarks that the deepest layers (convolutional and dense) of common networks can be replaced by significantly smaller learned structures, while maintaining classification accuracy-state-of-the-art on tested benchmarks.

the algorithm is called recursively and independently for the k ancestor sets (line 8), and then for the descendant set, treating the ancestor sets as exogenous (line 9).


Hence, we generalize the loss suggested by Bartlett and Wegkamp (2008) to arbitrary asymmetric misclassification and rejection costs.


Then the model complexity of function class F Θ is upper bounded by: Then, by Lemma 1 and 2, one could carefully construct a feasible solution set (by setting M and N ) such that both Rℓ (f * ) and E Ω R(F Θ ) are controlled to be reasonably small.

such social network can be modeled as a signed network where trust/distrust are modeled as positive/negative edges between entities [24], and the problem is to predict unknown relationship between any two users given the network.


Full details about the data can be found in [5].

the GEM based K-kNNG anomaly detection scheme proposed in [4] is computationally difficult.


We begin with a general but relatively naive lower bound that depends only on the geometric structure of the parameter space, as captured by its metric entropy.

lemma 1 shows that minimax lower lower bound can be derived by showing that, for some t > 0 to be chosen, it is difficult to identify V within a radius of t. The following extension of Fano's inequality [8] can be used to control this type of error probability: Lemma 2 Let V → X → V be a Markov chain, where V is uniform on V. For any t ∈ R, we have Lemma 2 allows flexibility in the application of the minimax bounds from Lemma 1.


Third, among nonlinear methods SVM tended to perform better than the two neural network architectures.

here we propose a model that makes a first step toward neural control of novel artificial motor systems.


We do this with a support vector machine.

we show four evaluation runs for our system; there is no evidence of substantial variance in detect rate.


In the realizable setting, [26,10,9,56] give efficient algorithms that have optimal label complexity of Õ(d ln 1 � ) under some distributional assumptions.

to achieve computational efficiency, it adaptively chooses a sequence of hinge loss minimization problems to optimize as opposed to directly optimizing the 0-1 loss.


For our sublinear time algorithms we need more efficient access to the matrix, specifically the following two variants: (1) We say that we are given A with column adjacency arrays if we are given arrays B 1 , .

the proof of this lemma, as well as most other proofs in this extended abstract, can be found in the full version of the paper.


The advantage of Fisher linear discriminant is that it is simple and easy to implement.

first, we perform signal processing based on the generalized cross correlation transform called Phase Transform (PHAT) also called Cross Power Spectrum Phase (CPSP).


The need for highly structured output functions in an RNN has been previously noted.

it is important to note that any approach based on having stochastic latent state is orthogonal to having a structured output function, and that these two can be used together to form a single model.


To mitigate this issue, alternative metrics have been studied in the literature, a large portion of which are special cases of f -divergence (e.g., Csiszár & Shields, 2004): where f : R + → R is any convex function.

we use Adam (Kingma & Ba, 2015) with a constant learning rate of 0.0003 for optimization.


Then, we compare whole-network acceleration with the best-performing masks to baselines such as decrease of input images size and an increase of strides.

our experiments show that this method can reduce the evaluation time of modern CNN architectures proposed in the literature by a factor of 2× -4× with a small decrease in accuracy.


This is satisfied if η ≥ 1 2 + 1 2β in the worst-case, and under the assumption that node delays are i.i.d., it is satisfied in expectation if η ≥ 1 √ β .

as in the first experiment, distributed coded L-BFGS is solved by having the master node encoding the data locally, and distributing the encoded data to the worker nodes (Appendix D of [12] discusses how to implement this step more efficiently).


If violations occur, we propose to project the proposed gradient g to the closest gradient g (in squared 2 norm) satisfying all the constraints (7).

unfortunately, it has been very hard to scale up these methods to lots of modules and tasks, given the combinatorial number of compositions of modules.


The similarity between (6) and the usual Bregman divergence ∆ ψ in (2) is apparent.

indeed, by interpreting p and q as probability distributions over {0, 1} n we have: = p({0})q({0}) where • is true, and 0 otherwise.


Similarly, for SVP we evaluate the three values 5 × 10 −5 , 10 −4 , 2 × 10 −4 for the step size, and select 10 −4 as the largest for which SVP converges.

let {v s , λ s } r s=1 be the top r Finally, we show that conditioning on A1 and A2 is valid since these events have high probability as long as m is sufficiently large.


2 implies that free energy upper bounds the negative log likelihood.

iterative inference models [32] directly account for these priors, instead performing inference optimization by iteratively encoding approximate posterior estimates and gradients: The gradients, ∇ λ q F, can be estimated through black box methods [35] or the reparameterization trick [27,37] when applicable.


Hyperparameters We can also place conjugate priors on the hyperparameters α and σ w and perform posterior inference on them.

let y ij ≡ Y (i, j) = 1 if we observe a link from entity i to entity j in that relation and y ij = 0 if we observe that there is not a link.


Figure 1 shows a generic action potential and the associated ionic currents, comparing the latter to the minimal currents required.

after reviewing the ionic basis of action potentials, we first sketch how to compute the minimal energy cost for an arbitrary spike shape, and then solve for the optimal action potential shape with a given height.


In subsection 2.2 we derive exact bounds in closed form for histogram descriptors (e.g.

in image retrieval the user can search a large image database for a query object specified by an image window [20].


6 Our goal is tag prediction: we select 1000 descriptive tags along with two random sets of 10,000 images each, associated with these tags, for training and testing.

we train a linear model by minimizing W p p + ↵KL on the training set, where ↵ controls the relative weight of KL.


See Appendix C.1 of the supplement for more discussion.

they are not jointly convex in the optimization variables (i.e.


If a pool is tested negative, then all samples in the pool are negative.

in fact, we will show in this paper that increasing the number of tests improves the accuracy of our PFS scheme.


First, it does not eliminate from consideration correlations that can be explained by direct edges among the observables.

to summarize our approach: In the first phase we analyze the network learned using conventional structure search to find semi-cliques that indicate potential locations of hidden variables.


This condition could potentially be relaxed so long as there is enough intersection where we can learn η.

experimental data does not suffer from confounding but is usually limited in both scope and scale.


1 proves that the losses attained on each iteration form a monotonically nonincreasing sequence of positive numbers, that must therefore converge.

we exploit this property to generate supervision for the label ranking problem at hand.


We allow for an arbitrary cost metric to measure the distortion between the true and the computed function values.

hence, the accuracy gets exponentially worse in k. if those k-parties are allowed to collaborate, then they can compute the XOR in advance and only transmit the privatized version of the XOR, achieving accuracy of λ/(1+λ) = 0.5+(1/4)ε 2 + O(ε 3 ).


If e = (i, j) is an edge in K m,n (where K m,n is the complete bipartite graph with m blue and n red vertices), we will also write A e instead of A ij and for any (m ⇥ n) matrix A.

for some path P in K m,n we obtain In the following, we will consider the following parametric estimator as a candidate for estimating a e : Notations 3.5.


Since models with larger empirical reward are preferred, ideally one hopes to maximize empirical reward during training.

these approaches offer improvements to standard maximum likelihood estimation, but they are fundamentally limited by not incorporating a task reward.


Put another way, fixing i, we can view 'T/i,r as a distribution, iii, over the labels r. This distribution should give a high probability to the correct label Yi.

otherwise, we suffer loss which is linearly proportional to the difference between the confidence of the correct label and the maximum among the confidences of the other labels.


Second, the resulting estimator v is not unbiased, so the statistical assumptions (4.1) for a stochastic oracle do not hold.

as a result, a fundamental question that arises is a) whether the agents' sequence of actions stabilizes to a rationally admissible state under no-regret learning; and b) if it does, whether convergence is affected by the information available to the agents.


Nonlinear models for censored data have also been studied, including decision trees (Segal, 1988;Molinaro et al., 2004), Random Forests (Hothorn et al., 2006) and Support Vector Machines (Pölsterl et al., 2016).

linear models for censored outputs have been extensively studied under the name accelerated failure time (AFT) models (Wei, 1992).


with Bernoulli distribution of unknown mean.

cOMBEXP has much lower complexity than COMBAND and achieves the same regret.


The overall separation for a given input statistics (determined by ū, r, and b) is then given by s * .

because of the physical background, this theory focused on the autonomous dynamics of the system, i.e.


Each page is labeled with the Yahoo's second level sub-categories from which the page is hyperlinked.

the margin represents the distance from the image of the training sample x i to the boundary between the correct label L i and wrong label λ. MML optimizes the linear map W so that the smallest margin between all training samples and all possible labels becomes maximal, along with a penalty C for the case that samples penetrate into the margin.


Modeling real-valued data The model above can be readily extended to model real-valued sequence data, by substituting (4) with p(v t |h t , v t−1 ) = N (µ t , diag(σ 2 t )), where and µ mt and σ 2 mt are elements of µ t and σ 2 t , respectively.

2 Model Formulation Deep dynamic generative models are considered, based on the Sigmoid Belief Network (SBN) [16].


In the next section, we resolve the second issue by establishing the connection between problem (5) and the minimum HGR correlation principle [1].

next, we state a result from [1] which sheds light on the computation of p x,0 and p x,1 .


This clarifies the relation between CCA and our method: Both methods aim to minimize the average distance between X and Y embeddings.

his method is in fact the discrete analogue of the more widely known Canonical correlation analysis (CCA) [10].


weights drawn from a normal distribution N (0, σ 2 ) with zero mean and standard deviation (STD) σ.

is taken over all inputs u 1 (•), u 2 (•) from the ensemble defined above, all initial conditions of the network and all circuits C. a good separation of the n bits, i.e.


Assuming a probability model p(X, Y, Z), where X are the data, Y are the target labels, and Z are the nuisance parameters, we consider the problem of learning a predictive model f (X) for Y conditional on the observed values of X that is robust to uncertainty in the unknown value of Z.

we reuse the datasets used in (Baldi et al., 2016a).


For generating k independent hashes we just use different random seeds which are kept fixed for the entire dataset.

the number of non-zeros is around half million.


Concretely, given a desired quantile level q ∈ (0, 1), how can we automatically infer (a bound on) the suitable density threshold α q ?

here, we are given α > 0, and wish to produce c : (1) instances with low density are deemed to be anomalous.


For a fair comparison, to ensure the same training/testing partitions for all algorithms across all datasets, we report the results by using either widely used open-source software packages or the code made public available by the original authors.

these transformed covariates ln(1 + e β k xi ), which can also be concatenated with x i , will be further used to train another iSHM pair.


First, we must choose an order r ∈ {1, 2...n}; this is equivalent to selecting the degree of a polynomial used to perform standard interpolation on the hypercube.

in other words, for any vertex v 1 in G 1 and any vertex v 2 in G 2 , there exists a vertex (v 1 , v 2 ) in G. Additionally, the edge set of G is such that, for any edge the set of hypercube graphs (or, identically, the set of Hamming cubes) can be derived using the Cartesian product operator.


In the first experiment, we chose d = P = Q = 10 and r 1 = r 2 = r 3 = 3.

when each task is parametrized by a weight vector over features, the goal would be to learn a features × aspects × customers tensor.


The forget gate units h f t and the input gate units h i t in Equation ( 2) are drawn from Gaussian distributions depending on their corresponding weights and biases Y f , W f , Y i , W i , b f , and b i : The output h t depends on the output gate h o t which has its own weights and biases Y o , W o , and b o : (3) In the RRN, information of the processed sequence is contained in the cell states s t and the output states h t , both of which are column vectors of length K W . Note that RRN can be seen as a generalized and Bayesian version of LSTM [1].

we call this denoising recurrent autoencoder (DRAE).


The magnitude of Γ st is a scalar multiple of the correlation of X s and X t conditioned on X \{s,t} , and encodes the strength of the edge (s, t).

our main result concerns a connection between the inverses of generalized inverse covariance matrices associated with the model ( 4) and the structure of the graph.


the Markov chain was initialized randomly except that all clusters were assigned to the top-most region (spanning the 13 years).

the nature of the dependencies between the DPs differ; for instance, their model cannot be interpreted as a mixture of DPs like ours.


In this section, we compare the performance of the approximation methods presented above on 5 artificially generated time-series.

only posteriors for which the count variables take value 1 are required 8 .


This choice is often crucial for an MBRL algorithm, as even small bias can significantly influence the quality of the corresponding controller [Atkeson andSantamaría, 1997, Abbeel et al., 2006].

most works that use NNs focus on deterministic models, consequently suffering from overfitting in the early stages of learning.


(Equivalently, we can imagine a dummy top layer HMM, which is always in state 1: 3 B .

the parameters of such shared sub-models only need to be learned once.


Results are summarized in Table 2, which are averages over 5 runs with different random splits of the training data.

in order to further understand ∆-GAN, we write (2) as conditional GAN ( 5) The objective of ∆-GAN is a combination of the objectives of conditional GAN and BiGAN.


Thus the problem can be converted to a two sample test between a subset of the original samples and the other subset which is permuted -Binary classifiers were then harnessed for this two-sample testing; for details see [19].

let L(g(u), `) be our loss function for a classifying function g 2 G, for a sample u , (x, y, z) with true label `.


Even though the individual observations x uj t , j = 0, 1, . . . , d − 1 are highly dependent, the range of O Hu , the emission matrix of the HMM describing the path H u , is contained in the product of the ranges of O uj , where O uj is the emission matrix at node u j (Lemma 4 in the Appendix).

in biological applications, the main outputs of interest are the learned observation matrices of the HMM and a segmentation of the genome into regions which can be used for further studies.


The NAI's end applications are in predicting hearing impairment intelligibility and using statistical decision theory to describe the auditory systems feature extractors -tasks which the STI cannot do, but are available to the NAI.

there is correlation between the different frequency bands of speech [11], which tends to make the STI over-predict intelligibility.


The optimal policy can be computed by an efficient algorithm called value iteration [22].

θ c could be interpreted as cooperativeness of the group on average.


Finally, to perform such a program, the replica trick is used [6].

indeed, sensor networks can be considered as a promising technology with a wide range of potential future markets [1].


If Im B 6 ⇢ Im A, which is notably the case if rk B > rk A, then r A B 2 (A, B) no longer exists.

the WORDNET dataset [Miller, 1995] (higher=better).


The edges E of the graph connect nodes at each level of the hierarchy to nodes in the neighboring levels.

the hierarchical structure of our model is partly motivated by known properties of cortical organization.


Correlations between the states in our dataset may reduce the effective dataset size, harming learning.

in each step of EXIT, Imitation Learning is restarted from scratch.


The best regret bounds are achieved for step sizes of the form ηk −1/2 and η log(m)k −1/2 respectively [28]; we also tuned η to generate the best empirical results.

we discover that regret matching with simple initialization can offer competitive training performance compared to state-of-the-art deep learning heuristics while providing sparser solutions.


Our model also has n • n d more parameters to compute the feedbackward vectors than the bidirectional-RNN.

assume, for now, that each word vector a ∈ R n is obtained by sampling each element from a uniform distribution: a i ∼ U(−0.001, 0.001).


See supplementary material for a more detailed comparison of the two bounds.

often the search problem is considered in the domain of point data: given a database of vectors listing some attributes of the data objects, which points are nearest to a novel query vector?


Neurons tend to fire regularly but without conserving the exact timing of spikes in response to constant or quasi constant input current.


We first consider the case where the conditional labelling includes vertices on both sides of v it .

given a labelling u ∈ IR n of G = (V, E) we define the cut size of u by if u ∈ {−1, 1} n we say that a cut occurs on edge (i, j) if u i = u j and Φ G (u) measures the number of cuts.


Would it still be possible to optimize the function efficiently?

for any query in which i x i ≤ n 1/2 , the likelihood of the oracle returning f is exponentially small in n δ .


These efficiency results are nontrivial; a crucial step in obtaining them is to exploit special properties of squared Euclidean distance.

although many features of our cost function are familiar from the simpler k-means setting, there is one which is worth pointing out.


By regarding each element objective as a single task, the hypothesis adaptation procedure can be decomposed into the adaptation of the element hypothesis for each element objective, and the adaptation of a global hypothesis for the weighted total objective.

to minimize the loss function Sample η t ∼ N (0, I K ).


The number of axons connecting a pair of regions is often significantly smaller than the number of neurons encoding the representation within each region [10].

our results can explain experiments in which retinal projections were redirected neonatally to the auditory thalamus and the rerouting produced visually responsive cells in auditory thalamus and cortex, with properties that are typical of cells in visual cortex [12].


accurately setting these parameters is critical to performance.


It would be interesting to see how A varies with Λ, particularly when λ i 's become small which allows the flow to propagate sufficiently (Fig.

we randomly sample 20 instances as labeled data and make sure there is at least one label for each class.


Traditional supervised learning is evidently a degenerated version of multi-instance learning as well as a degenerated version of multi-label learning, while traditional supervised learning, multi-instance learning and multi-label learning are all degenerated versions of MIML.

an image usually contains multiple patches each of which can be described by a feature vector, and the image can belong to multiple categories since its semantics can be recognized in different ways.


weighted finite automata (WFA) and weighted finite-state transducers (WFST) are fundamental concepts and representations widely used in computer science (Mohri, 2009).


Perhaps, when we attempt to train the residual network using gradient-based methods, we might hit some poor local minimum, with a worse error than what can be obtained with a shallower network?

2 for a precise definition) can't be more than poly( ) worse than any fixed linear predictor.


Recall that the algorithm specifies α := λ 3 and generates a sequence of evenly-spaced indicies b t i := nα(i For every i ∈ 0..  10), ( 11) and Lemma 1, there exists some N 1 such that for all n ≥ N 1 we have, Since λ ≤ λ min , we have α ∈ (0, λ min /3].

l t (π k ) := max (Equality occurs when π k for some k ∈ 1..κ is exactly at the start or at the end of a segment.)


The subsampling of the frequent words improves the training speed several times and makes the word representations significantly more accurate.

if "Volga River" appears frequently in the same sentence together with the words "Russian" and "river", the sum of these two word vectors will result in such a feature vector that is close to the vector of "Volga River".


As a result, reconstruction fidelity as a function of λ has a maximum at the sweet spot of sparsity for CS (decreasing the value of λ leads to sparser representations).

neither ACS nor practical applications of BCS are fully blind learning algorithms, as both rely on further constraints [4] inferred from the original data.


The trajectories of the principle angle over 20 independent simulations with block size h = 4 are shown in Figure 1a.

conventional optimization research usually focuses on proving that SGD converges to first order optimal stationary solutions (Nemirovski et al., 2009).


These are realizations of external errors where the iterative Alg.

we found a threshold phenomenon for reliable operation, which manifests the tradeoff between the amount of internal noise and the amount of external noise that the system can handle.


Some examples of covariates includes accessibility, distance to water, mean of land surface temperature and stable night lights.

our problem is made more complicated by the aggregation of labels, as standard lower bounds to the marginal likelihood used in [17] are also intractable in our model.


This results in parameter updates of the form: (θ t+1 , φ t+1 ) ← (θ t , φ t ) + Γ t (g t θ , g t φ ), where Γ is a diagonal preconditioning matrix that adaptively scales the gradients for faster minimization.

in the objective function (8), the label predictive distribution q φ (y|x) contributes only to the second term relating to the unlabelled data, which is an undesirable property if we wish to use this distribution as a classifier.


Policy convergence can be established under various restrictions (see the extended version for further details).

while the greedy value function approach is often considered to possess practical advantages in terms of convergence speed and representational flexibility, its behavior in the proximity of an optimum is currently not well understood.


If one makes further restrictions (on Y), then minimax results can be derived, such as in Takimoto and Warmuth [2000], Barron et al.

also, interestingly, while f is an arbitrary function in H, this regret term depends on K only at the sequence points x ≤T .


This similarity asks for further investigation on the difference between 2 -regularized methods and random projections in terms of prediction performance and computational complexity.

in fact, the more the features in F, the higher the chance for some of them to be correlated under ρ, thus leading to an ill-conditioned matrix G. since d < D, the probability that d independent random combinations of ϕ i lead to highly correlated features ψ j is relatively small.


Whereas the associations between kernels and neural networks was known [31], previously proposed networks used random synaptic weights with no learning.

once more, we index a receptive field solution by the rotation group element, g 0 , where the response is maximum: with , µ being determined by ↵ through self-consistency equations.


As suggested in [1], one can also learn parameters so as to optimize a "lagged criterion" that directly measures simulation accuracy-i.e., predictive accuracy of the model over long time scales.

the XCell Tempest train and test flights were 800 and 540 seconds long, the Bergen Industrial Twin train and test flights were each 110 seconds long.


This initialization meant that our recursive approach bore some similarity to recurrent ConvNets, in which the first and second stage networks are constrained to be identical [20].

note however that ZNN is more general, as the sparsity of filters need not depend on max-filtering, but can be controlled independently.


In Section 5 we discuss some possible variants and generalizations of the full architecture.

this training strategy seems to be slightly less stable than our general strategy, since the standard deviation of the accuracy over the ten training/testing sets is slightly higher (data not shown).


Under basic assumptions, KRR achieves an error R( f λn ) = O(n −1/2 ), for λ n = n −1/2 , which is optimal in a minimax sense and can be improved only under more stringent assumptions [17,18].

when approximate leverage scores are used M , smaller than n γ/2 √ n is always enough for optimal generalization.


Next, we define the following diagonal matrix From Assumption 2, lim N →∞ P r[ n h n,j = 0] = 0, ∀j.

the NVIL algorithm has complexity O(M JN train ) for computing gradients in both the generative model and recognition network.


Separate experiments showed that 2 × 2 matrices were sufficient for learning either the mod 3 or the mod 4 version of our modular arithmetic task, so the mod 12 version can clearly be done using a pair of 2 × 2 matrices for each number or relation.

we tried matrices of various sizes and discovered that 4 × 4 matrices gave the best generalization when some of the cases are held-out.


Our algorithms are quite practical, and variants of them can be implemented to run fast in practice.

by a union bound, the probability that some call to HESSIANSOLVE fails is upper bounded by O( √ m log(npw p max /δ))/n 3 = O(1/n).


Let be the set of all possible paths through the network.


In our current study, we fitted a global time of day curve at 5 minute resolution to data obtained from randomized serving scheme through a periodic (weekly) adaptive regression spline.

we must also explore the underlying pool constantly to identify promising alternatives, quickly discarding poor performers.


An interesting property of VPN is that its planning ability is used to compute the bootstrapped target as well as choose options during Q-learning.

given an n-step trajectory x 1 , o 1 , r 1 , γ 1 , x 2 , o 2 , r 2 , γ 2 , ..., x n+1 generated by the -greedy policy, k-step predictions are defined as follows: Intuitively, s k t is the VPN's k-step prediction of the abstract-state at time t predicted from x t−k following options o t−k , ..., o t−1 in the trajectory as illustrated in Figure 3.


In 1996 a major advance was achieved when Olshausen and Field showed that simple-cell-like receptive fields emerge when sparse coding is applied to natural image data [3].

linear simple cell models are commonly used in studies concerning the connections between visual input statistics and simple cell receptive fields [3,4].


The result shows that search can be guided: response times become faster as either the target color or target orientation becomes sparse, because a relatively unique feature serves as a reliable cue to the target.

third, EGS suggests a novel perspective on attentional control, and executive control more generally.


This task better models real data than the sorting task above, because each generated token must follow the grammar and is therefore conditioned on all previous tokens.

this makes sense in many translation spaces as there are a finite number of reasonable ways to transform a sentence in one language to a correct one in the other.


Catastrophic forgetting: learning new tasks may hurt the performance of the learner at previously solved tasks.

we are interested in the "more human-like" setting where i) the number of tasks is large, ii) the number of training examples per task is small, iii) the learner observes the examples concerning each task only once, and iv) we report metrics that measure both transfer and forgetting.


One prior that can be differentiated this way is KL-regularization.

for sparse coding we use KL-divergence for both the loss and the regularization functions, as minimizing the KL-divergence between the empirical probability distribution of the document given by each input vector x and f (B, w) is equivalent to maximizing the "constrained Poisson distribution" used to model documents in [21] (details given in appendix D).


In addition to comparing graph-based transfer against feature-based transfer, we further conducted a series of ablation studies.

inspired by linguistic theories of constituent phrase structure [7], these works restrict their latent parses to be binary trees.


Matrix Completion: Low rank matrix completion has an extensive literature; a few examples include [22; 6; 21; 28] among several others.

with very few tied preference values, this setting best fits the case of total ordered observations (case A in Section 4.1).


The consistency loss [13] penalizes the network if it predicts the same unlabeled data inconsistently given different noise , e.g., dropout masks, as R U = E x∼p(x) ||p c (y|x, ) − p c (y|x, )|| 2 , where || • || 2 is the square of the l 2 -norm.

we consider two alternative losses on the unlabeled data.


Unfortunately, little prior work has empirically compared the design decisions involved in choosing the particular propagation method.

while Bayesian models such as GPs perform well in low-data regimes, they do not scale favorably with dimensionality and often use kernels ill-suited for discontinuous dynamics [Calandra et al., 2016], which is typical of robots interacting through contacts.


In this section, we train a standard convolutional neural network 3 to imitate an MCTS expert.

the improved plans from the better expert quickly manifest in a stronger apprentice.


A branch and bound algorithm has two main ingredients: Branching : the region X is recursively split into smaller subregions.

but note that the constraint (2) is then not straightforward to enforce.


This is the sole reason interdependency was required in the first place.

since users are scattered in space, the physical reality dictates that different arms have different expected channel gains for different players.


Then the learner models the data, taking into account the labeled examples as well as the remainder of the data, which we assume to be much larger in volume.

the mixture density of the region we chose for the group of anomalies is not sufficiently low for them to rank high on the hint list.


Let G w (x) := {y ∈ Y : f w (x, y) > 0} for f w (x, y) = w, ψ(x, y) .

whenever only a feasibly small subset of variables has to be considered, we can solve the problem using a general purpose QP solver, or a slightly modified SVM solver.