Note that presence of constraints and oracle inexactness do not allow to directly apply the results of [16].

pageRank [18], HITS [11], and their variants [8,9,19] are originally based on a discrete-time Markov random walk on a link graph.


The swapping is done so that the product of singular values of the matrix formed by the selected columns is increased with each swapping.

the "two stage" algorithm described in [2] requires only 2 passes if the leverage values are known.


It is impossible to make a trust relationship with the workers.

non-adaptive schemes can be arbitrarily worse (see Theorem 2.4).


Adding (3) into the minimization problem (2) encourages solutions where w i ⇡ w j when E w ij is large.

such methods will first involve computing the eigen decompositions of the graph Laplacians, and then storing the large, dense matrices A, B.


S(0) = 1, an excitatory synapse subsequently issues an Excitatory Post-Synaptic Current (EPSC) that drives the post-synaptic neuron.

the model used differential equations to characterize a typical cat soleus spindle.


One such example is the seismic event detection [9], where we would like to detect the onset of the event precisely in retrospect to better understand earthquakes or as quickly as possible from the streaming data.

there is an optimal block size for each case.


Then for γ > 0 and a fixed probability of error δ ∈ (0, 1), we have P G = Ĝ ≥ 1−δ, provided that m ∈ O( 1 γ 2 ln n + ln r δ ) interventional samples are used per δ-noisy path query in Algorithm 5.

we consider an experiment as the actual setting of values to the variables.


For SELU parameters α = α 01 and λ = λ 01 , we show in the next theorem that if (ω, τ ) is close to (0, 1), then g still has an attracting and stable fixed point that is close to (0, 1).

we have introduced self-normalizing neural networks for which we have proved that neuron activations are pushed towards zero mean and unit variance when propagated through the network.


Our first main contribution is to characterize a rich class of structured sparse regularizers that allow efficient computation of their polar operator.

the algorithm is quite simple: Line 3 Algorithm 1 Generalized conditional gradient (GCG) for optimizing (1).


Similarly, the collection of weight trajectories {{W n →n (t)}} n ,n , which we will collectively refer to as W (t), model the time-varying synaptic weights.

neither of these approaches accommodate the breadth of synaptic plasticity rules present in the literature.


To establish an upper bound on performance, we plot the Oracle policy, obtained by re-ordering the actions at the end of each detection episode in the order of AP gains they produced.

our goal is to learn a dynamic, or closed-loop, policy, which would exploit the signal in scene and inter-object context for a maximally efficient path through the actions.


The toy example is intended only as a demonstration of the core idea underlying our hypothesis: that different choices of word order map the same probabilistic structure of the world (P ) onto different information profiles.

in these languages, the order in which words are spoken conveys a great deal of the sentence's meaning.


This is explained by the fact that in Causal InfoGAN, Q is only trained on generated observations, and can overfit to generated images.

to evaluate planning performance, we hand-coded an oracle function that evaluates whether an observation trajectory is feasible or not (e.g., does not cross obstacles, correctly reports ∅ when a trajectory does not exist).


Bag-of-words document representations are often used in text, image and video processing.

4 extends the technique to learn the dictionary by alternating optimization.


Many other methods have been compared against a similar benchmark [6,8].

projection in KL-divergence is intractable here because the evaluation of the gradient ∇ θ KL(ψ∥θ) requires the marginals of distribution ψ.


This massive data access requires an enormous amount of network bandwidth.

we compare the parameter server with two special-purpose second general parameter servers, named System A and B, developed by a large Internet company.


In this case, the outputs of  alternating estimation algorithms should deteriorate through the iteration loop since they estimate their components based on imperfect estimates of each other.

we presented an automated cell extraction algorithm for calcium imaging which uses a novel robust estimator.


We provide the first experimental comparison of verification methods.

it ignores another natural branching strategy, namely, splitting the input domain.


The notion we propose is "oblivious", in that it is based only on the joint distribution, or joint statistics, of the true target Y , the predictions Ŷ , and the protected attribute A.

as machine learning increasingly affects decisions in domains protected by anti-discrimination law, there is much interest in algorithmically measuring and ensuring fairness in machine learning.


Along with this synthetic setup, we also fit a Bayesian LR model to the Australian Credit and Heart regression datasets from the UCI database, for additional runtime comparisons.


It is clearly visible that ( 7) is also a forward Chapman-Kolmogorov equation.

this is probably due to the fact that the lower bound (20) ignores the contributions of the variance of the x µ term in the free energy, which is due to the variance of the jump process, and hence removes the penalty for having intermediate jump posteriors.


In a setting where losses are allowed to drift, we characterize -in a nearly complete manner-the power of adaptive adversaries with bounded memories and switching costs.

with this notation, the loss at time t is simply written as � t (X t ).


Note that, modulo constants, the bound only differs by the additive term L/T ↵ .

t = 1, then sublinear regret is not possible.


It is natural to consider using this method to improve a supervised classifier by smoothing its classifying result.

note that the first assumption is local, whereas the second one is global.


When the coach directs a team, instead of managing a whole scene, she focuses attention selectively on the key position and gives some directional but not specific instructions to the players near the location.

deep Deterministic Policy Gradient (DDPG).


Presumably, the indirect pathway involving the flocculus is computationally powerful because of a huge number of intermediate granule cells, but its memory is of short-term nature.

in this case, we must implement supervised learning of v for learning to occur.


The two-level model explored in this paper assumed stationary objects, resulting in simplified dynamics for the two levels in our recurrent network.

the hierarchical model offers a new Bayesian interpretation of attentional modulation in V2 and V4.


Each categorical input attribute was converted into n binary attributes by a 1-of-n encoding (where n is the attribute's arity).The post-processed versions of these datasets are at http://www.cs.cmu.edu/∼awm/kns 1.

each experiment required R k-NN classification queries (where R is the number of records in the dataset) and each query involved the k-NN among 0.9R records.


Through a series of invertible transformations, an arbitrarily complex posterior can be constructed.


In this paper we introduce the use of optimal transport methods in variational Bayesian inference.

for example, the distribution of natural images is thought to span a sub-manifold of the original pixel space [15].


Thus instead of setting the threshold as 0 always, our theory suggests setting η k proportional to the noise level √ noise .

let 0 < δ < 1/2, and Ω ∼ Uniform(d) be the index of the row sampling ⊆ [m].


Let us notice that the "signed margin", pus, is not derivable at point O.

the paper begins with a brief presentation of MarginBoost (section 2).


Using the law of total probability, we have the following equation for the filtering distribution: We can think of the integral in (5) as a sum over a distribution of experts, where each expert corresponds to a single pose history, u 1:t−1 .

for each expert we could then use Kalman filtering equations to infer the posterior distribution of texture given the observed images.


Recent advances that exploit the capacity and flexibility in this approach have expanded what kinds of models can be trained.

* For clarity of presentation, we will often omit dependence on parameters φ of the generative model, so that p(x, h) = p(x, h; φ) Variational methods have surpassed traditional methods such as Markov chain Monte Carlo [MCMC,15] and mean-field coordinate ascent [25] as the de-facto standard approach for training directed graphical models.


The solution quality is given as the sum of regrets for the players in milli-big-blinds.

there has been a vexing gap between the theory and practice of equilibriumfinding algorithms.


Unlike the well-separated, synthetic dataset, the Sub-Clusters method that only uses local splits and merges does not converge to a good solution here.

instead, we approximate the Hastings ratio by substituting the two original topic parameters, θ b and θ c , for the proposed sub-topics.


For example, suppose we know that f con is Gaussian with known covariance matrix and unknown mean.

one of these disadvantages is the apparent difficulty in making NDEs robust, which is desirable when the data follow not the density of interest, but rather a contaminated version thereof.


Indeed, after n observations and with the proper step-sizes, averaged SGD achieves the rate of O(1/µn) in the strongly-convex case [5,4], while it achieves only O(1/ √ n) in the nonstrongly-convex case [5], with matching lower-bounds [8].

a crucial point is that for machine learning scenarios where f n is a loss associated to a single data point, its complexity is only twice the complexity of a regular stochastic approximation step, since, with f n (θ) = ℓ(y n , x n , θ ), f ′′ n (θ) is a rank-one matrix.


Note that Theorem 2 does not in any way indicate what is the best non-factorial reweighting scheme in practice (for example, in our limited experience with empirical simulations, the selection α → 0 is not necessarily always optimal).

for example, with α small, the penalty g SBL (x) is more highly concave favoring sparsity, while in the limit at α becomes large, it acts like a standard 1 norm, still favoring sparsity but not exceedingly so (the same phenomena occurs when using the penalty ( 11)).


This is similar in spirit to our approach.

denotes the proximal function of f , which is defined by with the minimum located at xf (q, y).


Any optimization method can be envisioned to minimize J ν .

from the basic properties of the Bellman operator, for any policy π we have that T * v π ≥ v π . Consequently, the ν-weighted 1 -norm of the residual is indeed the expected Bellman residual: there is naturally no bias problem for minimizing a residual here, contrary to other residual approaches [1].


In the remaining of this section, we review some important algorithmic issues 3 .

we show empirically that the number of kernels in the conic combination is not a monotonic function of the amount of regularization.


random variables of finite variance will be distributed normally.

the answer is in the computational overhead required for the different approaches, since these more general models require inference by Monte Carlo methods.


In general, it is not easy to quantify the difference to the lower bound of Lai and Robbins lim inf Even for Gaussian distributions, there is no general closed-form formula for T * (µ) and w * (µ) except when K = 2.

denoting d(µ, µ ) = KL(ν µ , ν µ ) the Kullback-Leibler divergence between two distributions parameterised by µ and µ , they provide results which can be adapted to obtain the following bound.


The last operation is a task-specific 1 × 1 convolution to yield a width K t adapted to the task t. When learning from multiple auxiliary tasks, the first two layers of the encoder are shared to have a common encoder trunk with task-specific heads, further reducing computation.

design of this component has not been fully explored and further experiments should yield better results.


Here, we assume m ≤ n/(2 It is straightforward to verify the conditions of Theorem 1.

the estimators in (2.4) and (2.5), as well as the results of Theorems 1, 2, 3, can be easily adapted to the case of partially observed graphs.


The following corollary is straightforward.

when G and/or H may be degenerate at some points), by assigning the mean rank to ties [4].


If that is the case, )) is a posterior index for the infinite-dimensional projective limit model.

a probability is assigned to the I-dimensional set A I by applying the J-dimensional measure P J X to the cylinder with base A I .


That is, in the case of c → ∞, the objective in (1) is a monotonically decreasing function of a.

the vertical blue and red lines denote an "ambiguous region" around the decision boundary; objects to the left of the blue line have the label "not graspable;" those to the right of the red line are labeled as "graspable," and objects between these lines could have labels in mixed order.


This experiment does not satisfy ε-differential privacy for any fixed value of ε, since there is no fixed maximum number of rounds for which the experiment will run (for a fixed number of rounds, a simple composition theorem, Theorem 2.5, shows that the ε-guarantees in a sequence of computations "add up.")

our empirical results show that the active, ex-post privacy approach massively outperforms inverting the theory curve, and also improves on a baseline "ε-doubling" approach.


Then, we can treat the input bag-of-words as a |x|-trials multinomial sample from that distribution and use as the reconstruction loss its negative log-likelihood: We now must ensure that the decoder can compute p( x = x i |φ(x)) efficiently from φ(x).

first, the encoder representation will now involve a sum of the representation of all words, reflecting the relative frequency of each word: Moreover, decoder training will assume that, from the decoder's output, we can obtain a probability distribution p( x|φ(x)) over any word x observed at the reconstruction output layer.


Often, the distributions used in these models are difficult to sample from, being defined over large state spaces or having unknown normalization constants.

these differences were statistically significant, with a one-tailed Student's t-test for independent samples giving t(38) = 7.36, p < 0.001 and t(38) = 2.01, p < 0.05 for µ and σ respectively.


No other constraint on the distance or distance ratio is enforced.

these descriptors have not gained popularity in practical applications despite good performance in the patch verification task.


(2013) and Paige & Wood (2016) presented a heuristic algorithm for constructing such stochastic inverses.

constraint-based approaches (Pearl, 2009;Spirtes et al., 2000) find the optimal structures in the large sample limit by testing conditional independence (CI) between pairs of variables.


Moreover, we note that although P-TAP2 demonstrates improvements with respect to the P-MF, the P-TAP3 does not yield significantly better results than P-TAP2.

calculating F is computationally intractable since the number of possible states to sum over scales combinatorially with the number of units in the model.


The PCL algorithm maintains a separate model for the policy and the state value approximation.

although such methods have demonstrated improvements over on-policy actor-critic approaches, they have not resolved the theoretical difficulty associated with off-policy learning under function approximation.


As expected in such hard cases, RDP needs much more time than Greedy.

in these experiments, RDP outperforms both a baseline greedy algorithm and an SAA+MIP algorithm, which is a state-of-art technique for stochastic network design.


An element of the independence model is called a product distribution.

using this description, we estimate the maximal Kullback-Leibler divergence between an arbitrary probability distribution and the best approximation within RBM n,m .


Their algorithm is however asymptotically biased and does not converge to the optimum.

figure 3 (bottom) compares non-uniform sampling versions of S-MISO (see Appendix A) and SGD (see Appendix D) with their uniform sampling counterparts as well as N-SAGA.


The configuration of three landmarks was chosen especially to illustrate the affine distortion that may arise if the landmarks lie close to a subspace (in this case, a line).

because they are not explicit goals but only convenient byproducts, they are not in fact reliable features of the local approach.


[14] relied on pre-segmented and labelled images to estimate joint distributions over words and objects, while Socher [15] learned a latent meaning space covering images and words learned on non-parallel data.

figure 2 displays several examples of these similarity curves along with the overlaid recognition text.


We can now state our main result on sparsistency.

our first result shows that the lasso is sparsistent under compression, meaning that the correct sparse set of relevant variables is identified asymptotically.


Alternatively, S i+1 can be computed approximately and we found that (5) is fast (O((|Ω| + m + n)r 2 )) and gives the same convergence speed.

based on this, a similar lower bound of grad s F can be derived.


Furthermore, an estimated CTM can be used to explore otherwise unstructured observed documents.

lDA cannot predict the remaining words as well until a large portion of the document as been observed so that all of its topics are represented.


Images were presented upright inverted on alternating runs, with each inverted run preserving the image and category order used in the preceding upright run.

to our knowledge this is the first application to both voxel selection and functional connectivity based on multivariate activity patterns.


For metrics, since Prim R-CNN predicts possible sets of bounding boxes, there is no longer a direct correspondence between predicted primitives and ground truth primitives.

we show quantitative results of finetuning on SUN RGB-D in Table 4 and qualitative results of finetuning in Figure 6.


For example, if we believe that the receptive field is well-approximated by a Gabor function, then our method constructs stimuli that optimally constrain the Gabor parameters (orientation, spatial frequency, etc.)

the problem of incorporating this strong prior knowledge into an existing algorithm for optimizing neurophysiology experiments [8].


Specifically, to enable GAIL to produce diverse solutions, we condition the discriminator on the embeddings generated by the VAE encoder and integrate out the GAIL objective with respect to the variational posterior q (z|x 1:T ).

we first demonstrate the effectiveness of our VAE architecture and investigate the nature of the learned embedding space on a reaching task with a simulated Jaco arm.


Although different sampling techniques could be used in principle [15], our goal is to model correlations between each variable X uv and some neighboring region G uv in G. Such a neighborhood should be large enough to make ∆λ 2 (u, v, G uv ) sufficiently informative with respect to the overall network, but also small enough to keep the spectral decomposition of G uv computationally tractable.

the proposition follows straightforwardly from Lemma 1, given that We now proceed to define FRFs.


The results reported here for our experiments are without checkpoint averaging; Adam+Noam: refers to the special custom learning rate schedule used in [35]; Avg: refers to checkpoint averaging used for the reporting of En-De BLEU scores.

for YOGI, we restrict to tuning just two scalar hyperparametersthe learning rate and β 2 .


A commonality of existing algorithms for Ensemble Clustering [3,2,9] is that they employ a graph construction, as a first step.

minimizing the function 2 is a reasonable substitute to minimizing the sum of the L 1 -norms in the IP model 1.


In the worst case the full dimensionality d appears (upper-bound), and more arm-set specific quantities, such as the norm of the arms L and of the directions Y * , appear in the lower-bound.

x Y and G do not adjust to the empirical gaps and consider all directions as equally important.


Q-Learning can be directly applied to multi-agent settings by having each agent i learn an independently optimal function Q i [34].

figure 4: The reward of MADDPG against traditional RL approaches on cooperative communication after 25000 episodes.


Locally Linear Embedding (LLE, [3]) and Laplacian Eigenmaps (LE, [4]) can be viewed as Laplacian operator based methods which mainly consider the local neighborhood structure of the manifold.

for any vector a ∈ R m , we have P i a ∈ T xi M and (a − P i a) ⊥ P i a.


To maintain bounded staleness while minimizing wait times on read row() operations, SSPtable uses the following cache protocol: Let every table-row in a thread or process cache be endowed with a clock r thread or r proc respectively.

in SSP, workers can make updates to a parameter 1 ✓, where the updates follow an associative, commutative form ✓ ✓ + .


This is due to examples where the random draws of lead to function values ¡ © $ that are consistent with much longer length scale than the true function; the mean prediction becomes somewhat inaccurate, but worse still, the inferred variance becomes very small (because a very slowly varying function is inferred), leading to very poor performance compared to SMC.

a point in a sparse region is far more informative about the shape of the function for BMC than points in already densely sampled areas.


These limitations of VAEs are becoming increasingly understood.

there was no desire to simultaneously design an inference network q φ (z|x).


At present, evaluation is not automatic and does not scale.

to illustrate the method, we re-evaluate the performance of agents on Atari [2].


For the matrix factorization task using U oI CU R , reconstruction accuracy was the Frobenius norm of the difference between the data matrix A and the low-rank approximation matrix A constructed from A(:, c), the reduced column matrix of A: A − A F , where c is the set of k selected columns.

neither should be too large, and their relative values express the balance between feature compression and expansion.


Similar to Subsection 3.1, a naive way to apply the MC method to a network is as follows: Let 0 ⇡ := {|( B⇡ ) m,n |, ( ⌦⇡ ) m,m ; 1  m  n  p}, and for any pair of domains ].

for variable E and any set S, if , then S is not the parent set of E. Similarly, the authors of [WSBU18] consider the case that a (i) 6 = a (j) and either E . under this assumption, in this case for variable X 2 {C, E} and set , then S is the parent set of X.


See more detailed derivation and proofs in the SM.

this way, T is represented uniquely as a set of clades T C . distributions over the tree space can be specified as distributions over the space of sets of clades.


9 For the experiments here, n = 869, 641, 588, or roughly 900 million, x, y pairs.

when using an approximate counter we continue to see reasonable results, with some error introduced due to the use of probabilistic counting.


Let @ n A be a sequence of probability measures in @XA.

in practice, the discriminator class is usually implemented by a feedforward neural network, and it is known that a fixed neural network has limited capacity (e.g., it cannot implement the set of all the bounded continuous function).


The intuition of incorporating the triggering probability p D,S i to modulate the 1-norm condition is that, when an arm i is unlikely triggered by action S (small p D,S i ), the importance of arm i also diminishes in that a large change in µ i only causes a small change in the expected reward r S (µ).

in the disjunctive form the player stops when the first 1 is revealed and she gains reward of 1, or she reaches the end and gains reward 0.


Our results are comparable to and sometimes better than those of previous methods.

the posterior distribution of all parameters are usually highly peaked.


We show that our DCRF is differentiable with respect to depth and surface normals, and allows back-propagation to the depth and normal CNNs during training.

we formulate the problem as DCRF which embeds surface affinity and depth normal compatibility into the regularization.


We defined a space of simple graphics programs that control a turtle [11] and whose primitives include rotations, forward movement, rescaling of shapes, etc.

our objective is to synthesize a program that maps a stem to a tuple of inflections.


Kernel eigenvoice adaptation will have to deal with several parameter spaces.

usually, only a few eigenvoices (e.g., M < 10) are employed so that a little amount of adaptation speech (e.g., a few seconds) will be required.


We performed extensive experimental analysis to understand the proposed M-Walk algorithm, including (i) the contributions of different components, (ii) its ability to overcome sparse rewards, (iii) hyperparameter analysis, (iv) its strengths and weaknesses compared to traditional KBC methods, and (v) its running time.

compared to the policy gradient method (PG-Walk), and Q-learning method (Q-Walk) methods under the same model architecture, M-Walk with MCTS is able to generate trajectories with more positive rewards, and this continues to improve as training progresses.


Barn owl is a nocturnal predator with strong able auditory and visual localization system.

the simulation is to emulate a virtual barn owl at the center of a fixed, head-centered reference system with the origin centered on the perch as in Fig.


To investigate the correlation between communication and attention, we further visualize the communication among ATOC agent at certain timestep and its corresponding heatmap of attention in Figure 5.

the communication of DIAL is rather simple, just selecting predefined messages.


This interpretation provides an insight into the non-optimal stationary points of the convex max-product, i.e., points for which it is not able to generate consistent beliefs b α (x α ) when it iterates over i = 1, . . . , n. The representation of the subdifferential as the amount of disagreement between the marginalization constraints provides a simple procedure to verify dual optimality, as well as to construct primal optimal solutions.

it uses a double loop scheme where every update involves executing a convex sum-product algorithm.


1 partitions the 2N -dimensional nonlinear dynamical system into N scalar systems associated with each membrane voltage v k i and an additional N scalar systems associated with each calcium concentration level z k i .

using two-photon microscopy, imaging can also be localized to specific depths and cortical layers [5].


Line 7 continues to update scalar coefficient δ m+j , which is equivalent to update the direction p with respect to the base vector b m+j or corresponding y j .

each machine has up to 12 concurrent vertices.


A factored, n-agent Dec-POMDP is a Dec-POMDP such that the system state can be factored into n + 1 distinct components, so that S = S 0 × S 1 × • • • × S n , and no state-variable appears in any S i , S j , i = j.

there exists a functional mapping, J : In a Dec-MDP, then, the sum total of the individual agent observations provides a complete picture of the state of the environment.


The authors of [17] have also claimed: "it would be interesting to try to find basis vectors for all experiment vectors, using actual experiment vectors and not artificial bases that offer little insight."

we call it the fast CUR algorithm because it has lower time complexity compared with SVD.


The randomized cluster structures were relatively balanced and hierarchical.

we cast the problem as a problem of estimation and the goal is to recover the unknown docum ent weights or relevance assessments.


For each octant, we average over the octant's included orientations and fit the result to a power-law.

armed with a better understanding of the statistics of real scenes, we are better prepared to develop successful depth inference algorithms.


The proposed formulation also allows to handle non-uniform blur with a straightforward extension.

this might be caused by the loss of information during its two-step process.


The chosen exploration rate ensures that we are able to obtain concentration results for the number of times any link is sampled.

this basic model fails to capture an essential feature of service in many settings: in a queueing system, jobs wait until they complete service.


Tracking task is transformed into foreground and background binary classification problem in this framework.

in this paper, a novel approach to integrate multiple similarity measures is proposed.


The results reported for SCM-PB refer to the Bayes classifier only.

the radius ρ i for each i ∈ i will be chosen stochastically according to the posterior Q.


We begin by using a result from [2] that classical mean-shift (using a flat kernel) is equivalent to finding the local maxima of the following density estimate: In standard mean-shift, d is the Euclidean distance function, b is a constant that controls the kernel bandwidth, and z(b) is a normalization constant.

there is still much room for improvement in weaklysupervised element discovery algorithms.


Apart from being a non-convex problem, the matrix factorization studied in the present paper is further complicated by the {0, 1}-constraints imposed on the left factor T , which yields a combinatorial optimization problem that appears to be computationally intractable except for tiny dimensions m and r even in case the right factor A were already known.

algorithm 4 is impractical as a stand-alone scheme, because without proper initialization, it may take many iterations to converge, with each single iteration being more expensive than Algorithm 3.


These bounds suggest that probit loss converges more rapidly.

we assume a source probability distribution over labeled data, i.e., a distribution over pairs (x, y), where we write E x,y [f (x, y)] for the expectation of f (x, y).


Nevertheless, we show that the proposed algorithm for factored bandits can be applied to utility-based dueling bandits.

in many specific cases mentioned in the previous section, κ is typically small or even 1.


Furthermore, and quite importantly, our proposed recipe is complete.

our experiments on simulated data and a streaming Wikipedia analysis demonstrate that the proposed SGRHMC sampler inherits the benefits of Riemann HMC, with the scalability of stochastic gradient methods.


Our experimental results have demonstrated that McRank (including multiple classification and multiple ordinal classification) outperforms both the regression-based ranker and the pair-based Lamb-daRank.

for example, suppose within a query, the URLs are all labeled level 1 or higher.


Presumably as such, they have not yet been widely adopted in critical problem domains, such as diagnosing deadly diseases [13] and making million-dollar trading decisions [14].

when it comes to ultra high-dimensional data, getting generalizable insights could still be a challenge.


This suggests that some discriminative information may have already been lost after the PCA dimensionality reduction and the discriminative power can not be re-boosted by simply introducing more Gaussian distributions.

for a GMM, each of Gaussian essentially models a small partition of the feature space and many of them are needed to depict the whole feature space.


Remark (comparison in the Euclidean case) In the special case H = R d , we can make a comparison with existing approximate methods for OL.

we update the featuremap ϕ, but we reset A tj and ω tj to zero.


Moreover, these methods utilize a fundamentally different stochastic gradient information: they have access to an unbiased gradient estimator.

algorithm 2: ASEGA: Accelerated SEGA 1 Initialize: Sample S k = I S k , where S k ⇠ S, and compute g k , h k+1 according to (4), ( 6) The method and analysis is inspired by [2].


( 5) becomes separable in x i , and we can solve for each b i separately.


In order to do that efficiently, a few adaptations are required.

if γ H = 0, theoretical upper bounds on the mutual information are unfortunately not available.


Conditional on all parameters, H C and H T are independent.

we thus obtain the final components of our hierarchical model: In order to apply PAC, we must specify a nucleotide substitution model, that is, the probability that a nucleotide i mutates to a nucleotide j over evolutionary distance t. In the above, η parametrizes this model.


These issues have motivated much of the recent progress on faster stochastic optimization in vector spaces by using variance reduction [10; 18; 28] techniques.

we set ⌘ = 1 100n , and choose m = n in Algorithm 1 for RSVRG, and use suggested parameters from [38] for other algorithms.


Additionally, Figure 3c shows the average position error (in absolute value) for our iFDM and the genie-aided method.

the FFBS tends to overestimate the number of speakers, as shown in Figure 4e (bottom).


On the one hand, they need to train a lot of iterations since DSDH updates the hash code bit-by-bit, while HashNet requires to increase β iteratively.

basic setting Our model is implemented with Pytorch [23] framework.


Given a transition model T and a state trajectory {s 1 , s 2 , .

sampling based approaches include Medusa [4], which learns using state-queries, and [7], which learns using policy   queries.


If s is constant across stimulus strengths, the other two parameters of the model must explain differences in behaviour, between stimulus strengths, by taking on values that depend on stimulus strength.

a high coherence RDM stimulus has a large proportion of motion in the correct direction with very low variability of measurements whereas a low coherence RDM stimulus tends to have lower proportions of motion in the correct direction, with high variability (cf.


The safety and exploration aspects of the algorithm that we presented in the previous section rely on the correctness of the confidence intervals C t (s).

this can damage the platform or its environment.


But, since neither method identifies the small cluster, their union fails to find it as well.

these are shown to the teacher (in our scenario, a human expert) for labeling, and the cycle repeats.


The generalisation behavior of the Gaussian process is determined by its prior support (which functions are a priori possible) and its inductive biases (which functions are a priori likely), which are in turn encoded by a kernel function.

the RBF kernel in comparison can only model a single Gaussian centered at the origin in frequency (spectral) space.


Notice that we could differently weight the encoding and the reconstruction energies in the loss function.

sparse representations can provide a simple interpretation of the input data in terms of a small number of "parts" by extracting the structure hidden in the data.


The advantage of Adam has been confirmed by MNIST experiments, where Adam indeed considerably reduced the cases for which we observed mode collapsing.

since the FID criterium only works for images, we measured the performance by the Jensen-Shannon-divergence (JSD) between the model and the real world distribution as has been done previously [21].


The product and quotient distributions required above are not in general solvable in closed form.

we propose a novel multimodal variational autoencoder (MVAE) to learn a joint distribution under weak supervision.


Note that we do not need to know the label of a training sample in order to enforce this loss.

based on the results, we can see that in both cases we can significantly improve the accuracy when we have a small number of labeled samples.


Surprisingly, the hierarchical baselines (HSVM,TD and OT) experience a very large drop in performance on LSHTC-small when compared to the flat baselines, indicating that the hierarchy information actually mislead these methods rather than helping them.

formally, the generative model for M1 is The parameters of the root node are drawn using user specified parameters w 0 , Σ 0 , a 0 , b 0 .


PCA is a special case when k = 1 and the center is an r-dimensional subspace.

we use r = 10 for rank-r approximation and k = 10 for k-means clustering.


the observed dimensionality) is increased.

we refer to a matrix A ∈ R p×q as generic, with a fixed sparsity pattern when the nonzero entries of A are drawn from a distribution which is absolutely continuous with respect to Lebesgue measure 2 .


In this paper, we propose a non-negative risk estimator for PU learning: when getting minimized, it is more robust against overfitting, and thus we are able to use very flexible models (such as deep neural networks) given limited P data.

the replacement of π p with some π p > π p introduces additional bias of R pu (g) in estimating R(g), but it also pushes R pu (g) away from R pu (g) and then pushes nnPU away from uPU.


From here, we will apply the confidence set results from Section 5 to obtain our regret bounds.

let A = {R ú , R k oe R k 'k} and B = {P ú , P k oe P k 'k} and condition upon these events to give: The posterior sampling lemma ensures that 1≠8" by a union bound on {A c fi B c }.


To ensure that we have sufficiently incoherent initial iterate, we perform thresholding proposed in [4].

we generate orthogonal matrices U = [u 1 , .


a subjective opinion can be derived easily from the parameters of the corresponding Dirichlet distribution using b k = (α k − 1)/S, where S = K i=1 α i is referred to as the Dirichlet strength.


Instead, we consider a fine discretization of the domain of C and settle for an approximate solution.

this can only hurt the performance of our algorithm.


2, the conditional distribution of (x vt1 , .

another problem, "pruning", is a phenomenon where the optimizer severs connections between most of the latent variables and the data [24].


Otherwise, the value function is learned with neural networks that we depict in Appendix F, hereinafter referred to DeepExposure I.

from Table 1, we can see that our method consistently outperforms the involved algorithms.


This is because (i) the reference predictors do not need it; and (ii) if we did include the cost of observing the loss function for the reference predictors, then the loss of each predictor would just be increased by c d+1 T , and so the regret R T would just be reduced by c d+1 T , making it substantially easier for the learner to achieve sublinear regret.

the standard "batch learning" framework has a pure explore phase, which gives the learner a set of labeled, completely specified examples, followed by a pure exploit phase, where the learned predictor is asked to predict the label for novel instances.


We then reformulate the sparse PCA optimization problem to explicitly reflect the maximum additional variance objective on each round.

the conditional variance is the Schur complement of the vector variance x T Σx in the full covariance matrix V . By substituting sample covariance matrices for their population counterparts, we arrive at a new deflation technique: Schur complement deflation Schur complement deflation, like projection deflation, preserves positive-semidefiniteness.


It can be shown that this problem is equivalent to Eq.

the training sets can be combined into a single dataset (x i , y i ) n i=1 , with y i = (y i1 , .


Consider the Hamming loss � Ham defined in Example 3, for n = 2 r . For each i ∈ [r], define σ i ∈ R n as Then the loss matrix L Ham satisfies where e is the n × 1 all ones vector.


We find a consistent contribution of AoA to naming latency, as well as the conditions under which there is an independent contribution from frequency in some tasks.

still more recent studies question this finding and find that both AoA and frequency are significant and contribute independently to naming latency (Ellis & Morrison, 1998;Gerhand & Barry, 1998,1999.


Our natural idea is replacing One Stage PG in Algorithm 5 with One Stage SVRG.

first, we would like to remind you that the procedure of deterministic APG is given as described in Algorithm 5.


With the recent push towards larger neuromorphic systems and higher integration density of these systems, this has resulted in novel approaches especially for the synapse realization.

a voltage drop below the negative threshold.


The only parameter that was adjusted in the experiments was the scale of the images upon which the interest point detector was run.

it follows that Given a new test image x, and parameter values θ * induced from a training example, we will take the label for the image to be arg max y∈Y P (y | x, θ * ).


There are also other applications of GCD, such as non-negative matrix factorization [11], large-scale linear SVM [29], and [8] proposed an approximate way to select variables in GCD.

each GCD update only costs O(`) using this trick of maintaining g. for solving kernel SVM, GCD is faster than SCD and CCD since there is no additional cost for selecting the best variable to update.


The diagonal component is denoted with a vector d and the columns of the matrix U and V are denoted by u j and v j respectively.

several efficient ways of computing the full covariance matrix are discussed by Seeger [31].


Meanwhile, it reduces the memory requirement from O(md) to O(m 2 ) where d could be billion-scale but m is often less than 10.

when we increase the feature number to 512M, the L-BFGS fails with an out-of-memory exception, while VL-BFGS can easily scale to 1B features.All of these clearly show the scalability advantage of VL-BFGS over traditional L-BFGS.


We will assume a noisy-OR gate, and thus our model is closely related to causal power.

the two leading psychological theories can both be seen as estimating the parameters of a fixed graph.


They also demonstrate some generalisation over network architectures.

to start, we note the fact that the methodology just described represents a transfer attack from the original net to the net as modified by the inclusion of the resampling unit.


the Schatten k-norm) and not the whole matrix itself, we can be more efficient on the sample complexity by a factor of r 2/k in rank and a factor of log d in the dimension.

. . , w k+1 ) with w 1 = w k+1 , where we allow repeated nodes and repeated edges.


Nevertheless, finding the maximum score bipartite matching (with any set of degree constraints) can be accomplished easily using standard combinatorial optimization algorithms (e.g., [6]).

most common are (conditional) probability queries, where the task is to compute the marginal probability of one or more variables, possibly given some evidence.


Every policy has a unique value function, which fulfills the Bellman equation, Eq.

the standard tabular DSDP approach can also be derived using the Galerkin method.


As mentioned above, the features T cannot be sampled from the exact reachability distribution ⇤ T , because it is inaccessible (and complex).

[3] proposed a model-free approach to learn influence functions as coverage functions; Narasimhan et al.


Typically these 1 -algorithms provide excellent unsupervised clustering results and improve upon the standard 2 (spectral clustering) method [10,13] in terms of both Cheeger energy and classification error.

this degeneracy of a continuum of critical points arises from a lack of uniqueness in the underlying combinatorial problem.


No special care was required for the other baselines, since they explicitly take the images as inputs and the poses as outputs.

this confirms that our approach is well-suited to learn shared-private factorizations, and shows that CCA-based approaches [1,11] tend to be sensitive to noise.


In this way, only the background zone of the output of the C-ReLU layer has non-zero activations.

how to generate high-quality attention maps is essential for offering reliable initial heuristic cues for training segmentation networks.


We would like to thank Matt Ricci for his early contribution to this work and further discussions.

the protocol was approved by the University IRB and was carried out in accordance with the provisions of the World Medical Association Declaration of Helsinki.


Strikingly, by proper adjustments of these normalizations, we were able to train various complicated models without hurting the classification performance.

for a layer with d−dimensional input x = (x (1) , x (2) , ..., x (d) ), L ∞ batch normalization normalize each dimension where µ k is the expectation over x (k) , n is batch size and C L∞ (n) is computed similarly to C L1 (n) (derivation appears in appendix).


Hence, it is also instrumental to investigate whether we can reshape the test datasets into multiple domains to achieve better adaptation results.

intuitively, we would like any two different domains Pk (x) and Pk (x) to be as distinctive as possible.


Indeed, the original purpose of Resolving was not to improve upon a blueprint strategy in a subgame, but rather to compactly store it by keeping only the EV at the root of the subgame and then reconstructing the strategy in real time when needed rather than storing the whole subgame strategy.

1 For example, a better strategy for P 2 would be to choose Heads with probability 3 4 and Tails with probability 1 4 .


Best Attribute Identification: We collect full-grained histograms of the globally top-2k attributes from local machines in order to compute their global distributions.

when the number goes up to 16, the convergence speed is even lower than that of using 8 machines.


The above objective sums over all data and annotations.

among all the N data observations O, we only crowdsource pairwise annotations for a small portion of O, denoted by O L . Each worker only provides annotations to a small amount of items in O L and the annotation accuracies of non-expert workers may vary with observations and levels of expertise.


This form of coding was loosely inspired by the idea of "energy landscape" coding proposed by Hinton and Brown [2].

we started from an interpretation of synaptic integration in single neurons as a form of inference in a hidden Markov chain.


Let R n be the set of decreasing n-tuples of elements in R ∪ {∞}.

we seek an element in O k (S) = arg max {S1,S2,...,S k }∈C k (S) seperation({S 1 , S 2 , .


Removing the label noise provides an alternative way of setting the width parameter rr of the Gaussian kernels.

we wish to ensure that the conditional probabilities P(ylx) can be evaluated accurately on the basis of the sampled estimate in Eq.


Thus any globally maximal partition cannot contain empty subsets.

then (9) shows that lim k→∞ an arbitrarily ill-balanced partition leads to arbitrarily poor values of its Product Cut.


( 9), we need to find the global maximum of Φ(x, x) for x.

in this paper, we denote x = (X 11 ...X n1 , ..., X 1n ...X nn ) T as a column-wise vectorized replica of X.


Observe that, by the hypothesis on t , we have z t ≤ L x t . We first consider two cases, based on the norm of θ t . Case 1: With this assumption, and using the third property of Lemma 2, we have We now use the second statement of Lemma 1.

we derive the Dimension-Free Exponentiated Gradient from the general OMD above.


[2015], which maximizes a submodular set function; it maintains two solutions initialized at 0 and 1, goes over coordinates 3 Our results also extend easily to arbitrary axis-aligned boxes (i.e., "box constraints").


c ⊆ X which ultimately implies u(x, c) = u(X * ) = u(X ), X * = {x, c} ⊆ X .

to instantiate Eqn (4) concretely, it is finally necessary to define a specific form for the likelihood term p(x|c).


In this paper we have presented 3D Steerable CNNs, a class of SE(3)-equivariant networks which represents data in terms of various kinds of fields over R 3 .

we compute conventional 3D convolutions with filters that are a linear combination of pre-computed basis filters.


. . , v N ), whose expected log-likelihood will be maximized.

for the shadow Dirichlet, we normalized each column of the similarity matrix S to sum to one so that it was left-stochastic, and used that as the M matrix; this forces puzzles that are often bought together to have closer estimated proportions.


The objective penalizes the differences among the average predicted ratings of user groups.

second, each individual is either someone who enjoys and would excel in STEM topics or someone who does and would not.


According to modern brain theories, dynamics of synchronization of rhythmic activities in distinct neural networks plays a very important role in interactions between them.

end Now we discuss the estimation of the coefficient matrix.


However, these approaches output rather weak 3D information, where typically a 2D bounding box around the object is returned along with an estimated discretized viewpoint.

we demonstrate the effectiveness of our approach in indoor and outdoor scenarios, and show that our approach significantly outperforms the stateof-the-art in both 2D [1] and 3D object detection [2].


hyperedges, thereby endowing hyperedges with vector weights capturing these costs.

the differences between inhomogenous, homogenous, and pairwise-relation based cuts are even more evident for large graphs and they may lead to significantly different partitioning performance in a number of important partitioning applications.


For example, the stochastic optimization problems found widely throughout machine learning have exactly the same form, but with i.i.d.

recall that during an epoch, RESCALEDEXP is running FTRL with ψ t (w) = ψ(w)/η t . Therefore our first order of business is to analyze the regret of FTRL across one of these epochs, which we do in Lemma 3 (proved in appendix): Then the regret of FTRL with regularizers ψ t (w) = ψ(w)/η t is: Lemma 3 requires us to know the value of L in order to set p. the crucial point is that it encompasses the case in which L is misspecified on the last loss vector.


(8) If we further have η(t) ≥ r (t), then the conditions of Theorem 2 and Theorem 3 are satisfied, which guarantee that L r is a Lyapunov function and that the energy E r decreases.

first-order methods have seen a resurgence of interest due to the significant increase in both size and dimensionality of the data sets typically encountered in machine learning and other applications, which makes higher-order methods computationally intractable in most cases.


We show that our method significantly outperforms (or matches) MC-dropout.

ensembles, even for M = 5, significantly improve uncertainty quality in all the cases.


We develop a framework which provides convergence conditions and error bounds along with simple proofs and connections to methods in numerical linear algebra.

its iterates converge in distribution) if and only if [13,Lemma 7.3.6] the deterministic part of the update map (4) has spectral radius less than unity, i.e.


The ex ante coordinated strategy profile for the team is implicitly represented by the pair ( λ, ωT ,σ ).

a powerful, game-theoretic way to think about ex ante coordination is through a coordination device.


3: end for 4: Initialize an MDP Model with state space S, action space A, reward function R, discount factor γ and transition function specified by A i for i ∈ {1, . . . , n S } as described above.

the following lemma, whose proof is fairly straight-forward and therefore omitted, relates the error of an estimate θT x for a fixed input x based on an inaccurate estimator θ to the quantities ||q||, ||v||, and Recall that when ||q|| and ||v|| are both small, our algorithm becomes confident of the least-squares estimate.


The proof of Theorem 3 can be found in Appendix ??.

in Flixster dataset, we observe that TIM-U,TIM-L hold greater advantage in case of larger number of ε-AS nodes and larger ε.


Toward the end, we will also elaborate three other quantities operating on the restricted covariance matrix Σ T T : C max , which is defined as the maximum eigenvalue of Σ T T : C max := λ max (Σ T T ); D − max and D + max , which are denoted as ∞ -norm of matrices Σ −1 T T and Σ T T : Our result also involves in two other quantities operating on the conditional covariance matrix of (X T c |X T ) defined as We then define ρ u (Σ Toward the end, we denote a shorthand ρ u and ρ l . We establish the following result for Gaussian random design whose covariance matrix Σ obeys the two assumptions.

where λ is the positive regularization parameter and l 1 -norm β 1 is defined by During the past few years, there has been numerous studies to understand the 1 -regularization for sparse regression models [23] [11] [10] [17] [4] [2] [22].


Note that, as opposed to [12], our approach is relatively insensitive to the number of training examples and to the dimension of the data.

we tested our approach on the same square as before, but allowing it to deform by letting the edge between its two facets act as a hinge, as shown in Fig.


Inference performs hard-sampling, where sampled words are used instead.

applications of such models include conversational systems [8], paraphrasing [9], machine translation [10], authorship obfuscation [11] and many others.


Figure 1(d) shows the box plot for log σ, grouped by ν, where σ is the bandwidth selected by γ.

and H is an RKHS with a measurable and bounded k. which is the Parzen window classifier.


Classifying short video clips which contain simple motions and actions has been solved well in standard datasets (such as KTH [1], UCF-Sports [2] and UCF50 [3]).


That work demonstrates sample complexity improvements for learning linear halfspaces (and some boolean function classes) in the lifelong learning setting in comparison to solving each task in isolation under the assumption that the tasks share a common low dimensional representation.

for each new task, the algorithm first attempts to achieve good prediction performance with a weighted majority vote over the current base hypotheses, and uses this predictor for the task if successful.


SD data was created from Mainichi news articles, and the size was 2095 sentences consisting of 822 subjective sentences.

the recursive set operations of Equations ( 9) to (11) can be executed as well as


The cost function ~~c(x , Y,~) is convex, differentiable on IR and c(x, y, 0) = 0 for every (x,y) E X x Y.

the kernel k : X x X -+ IR is a real analytic function on its domain.


Given a set of documents W, CTM infers the posterior distribution p(η, Z, Φ|W) ∝ p 0 (η, Z, Φ)p(W|Z, Φ) by the Bayes' rule.


Since typical crowdsourced tasks are tedious and the reward is small, errors are common even among workers who make an effort.

we do not allow allocating tasks adaptively based on the answers received thus far.


In this case, computing x 0 is as simple as finding the conjugate of ψ.

defining a = i / ∈W a i and b = i / ∈W b i , then (P ) is equivalent to minimize (P) has been reduced from a problem with m piecewise functions to a problem of size |W |.


For example, a robot exploring in an unfamiliar terrain may reach a dangerous location and sustain heavy damage, or wander off from the recharging station to the point where a costly rescue mission is required.

algorithm 3 shows the randomized point-based value update.


(2.1) is unidentifiable in the case of = 3, see more discussion in [4,18].

to our best knowledge a closed-form solution to Eq.


In general, the upper bound becomes tighter as λ N (Π) increases; however, an increase in λ N (Π) may result in a commensurate increase in λ 2 (Π), leading to worse connectivity in the graph and adversely affecting consensus among agents.

we begin with comparing the accuracy of CDSGD with that of the centralized SGD algorithm as shown in Fig.


We stop the algorithm when F (X k ) − F (X k+1 ) < 10 −6 .

since R(•) F is only a surrogate of dist(•, X ), we need to establish a relationship between them.


The corresponding neural network representation of this algorithm is one with two layers with weights W, H and nonlinearities (.)

rather than having each hidden unit connect to the entire input image, each unit is instead connected to a small patch (see figure 2a for an illustration).


There exists n 0 ( , δ, α) such that for all n > n 0 , with probability 1 − δ: It is worth pointing out a central difference between Theorem 1.3 and other generalizations of the Glivenko-Cantelli Theorem: for example, the seminal work of Vapnik and Chervonenkis [24] shows that for every class of events F of VC dimension d, there is n 0 = n 0 ( , δ, d) such that for every n ≥ n 0 , with probability 1 − δ it holds that ∀A ∈ F : p(A) − p n (A) ≤ .

assume that E V ∼µ [V 1+θ ] ≤ C for some θ > 0 and C ≥ 1.


This leaves us with a separate test set for each scenario: (1) the unseen 1,000 conformations of molecule trajectories included in the training set and (2) all 5,000 conformations of the remaining 20% of molecules not included in training.

we use the proposed cfconv layers in R 3 to model interactions of atoms at arbitrary positions in the molecule.


Unfortunately, MCMC algorithms are typically serial, and do not scale to the large datasets typical of modern machine learning.

it is possible to define , using partial posteriors in place of subposteriors (cf.


More precisely, the vector of weights connecting a unit to its previous layer (together with the non-linearity) can be viewed as a separator or decision boundary in the activation space of the previous layer.

the new unlabeled images now constitute a less biased sampling of the feature space in layer k −1.


We compare the power of the hypercontractivity coefficient and other correlation coefficients in the binary hypothesis testing scenario of Theorem 2.


Figure 1f shows our model's behavior when the ISI is uniformly distributed [11].

they treat the two major issues we have neglected: world model learning and action planning.


Ideally, the classifier will selectively pay more attention to target objects than the background.

the attention map A c corresponding to each input image sample is specific.


In [1] this goal is called minimizing strategic regret.

during the exploit phase of the algorithm, all buyers are incentivized to bid truthfully.


After verifying the chip functionality, a DN chip with a scalable number of units will be further developed for recognising multi-channel, time-varying biomedical signals in implantable microsystems.

the EXP-elements implement the first three terms multiplied with e −αV Xj in accordance with Eq.


such an impossibility result suggests two natural relaxations: the first is to make additional assumptions about the structure of errors, such a stochastic error model.


The posterior for any f (m) (x) conditioned on previous queries at all fidelities is not Gaussian due to the ζ (m) constraints (A2).

viola & Jones face detection (V&J): The V&J classifier [31], which uses a cascade of weak classifiers, is a popular method for face detection.


With such construction any φ ∈ Φ, such that h 3 is uniformly better than φ, has generalization error significantly larger than the one of h 3 .

we show in this example that for not too small training sizes (as specified by the conditions of Theorems 11 and 4.2) the learning rate of the regular ERM in X space is 1/ √ n while the learning rate of the privileged ERM in the joint X × X * space is 1/n.


a local error bound with = 1/2, see Definition 2.1 for details), which is weaker than strong convexity, one can still obtain a linear convergence with a dual subgradient algorithm.


We consider discrete-time nonlinear state-space models built with deterministic functions and additive noise (1b) The dynamics of the system are defined by the state transition function f (x t ) and independent additive noise v t (process noise).

problems with severe nonlinearities and/or non-Gaussian likelihoods can lead to heavily multimodal smoothing distributions that are better represented using particle methods.


In this work we consider the framework of OCO with memory, detailed as follows: at each round t, the online player chooses a decision x t ∈ K ⊂ R n . Then, a loss function f t : K m+1 → R is revealed, and the player suffers loss of f t (x t−m , .


While the objective function ( 2) does not depend explicitly on the cortical representation variables, it does depend on their distributions, through the marginal likelihoods For all but the simplest probabilistic models, optimising these integral expressions directly is computationally prohibitive.

the sensory input is processed to infer beliefs about the latent causes P θ (L i | S i ).


Table 4(a) demonstrates that, as suggested by theory, layer-by-layer training of LDAMP is optimal; additional end-to-end training does not improve the performance of the network.


For GD, the number of iterations to escape the i-th saddle point increases as κ i (κ is a multiplicative factor larger than 1), and thus GD requires exponential time to escape d saddle points.

in the construction thus far, the saddle points are all on the boundary of tube.


Thus, the overall receptive window of the convolutional network is 15 × 15, which provides the required amount of context of the co-evolution data to predict the contacts.

we posit that this may have longstanding implications for evolutionary coupling analysis, some of which we discuss below.


z pres,i t is a binary variable representing whether the object is present at the given time-step or not.

while this approach is inspiring, its focus on modelling individual (and thereby inherently static) scenes leads to a number of limitations.


While the performance of EBC is clearly datadependent, SMA (purple lines in Figure 4) exhibits dramatic performance improvement compared to alternatives in all instances (see the Supplement, Section 3, for extensive additional experiments, including comparisons to other classifiers, and varying adversary's budget constraints).

finally, the UCI data set was divided into 476 training and 119 test instances in five-fold cross validation, with four times as many advertisement as non-advertisement instances.


This is not guaranteed to find the best hash function in terms of the original problem (1), and indeed it produces a pretty suboptimal function.

in addition, our framework facilitates the design of optimization algorithms for arbitrary types of loss and hash functions.


Based on the convergence result we further constructed an adaptive restart heuristic which aimed at estimating the RSC parameter on the fly and adaptively tune the restart period.

the effective RSC µ c = γ 2 − 8τ (1 + c) 2 Φ 2 (M) links the convergence speed of Rest-Katyusha with the intrinsic low-dimensional structure of the solution which is due to the regularization.


(1) A worst-case adversary is defined by vacuous restrictions P t (x 1:t−1 ) = P. any mixed strategy is available to the adversary, including any deterministic point distribution.


We have found that a wide class of GMMs are walk-summable: Proposition 1 (Walk-Summable GMMs) All of the following classes of GMMs are walksummable: 2 (i) attractive models, (ii) trees and (iii) pairwise-normalizable 3 models.

this leads to a new interpretation of BP in trees and of LBP in general.


A multi-neuron version of this model is inferred by setting B = 1.

the analysis objective is to examine the degree to which one may relate (predict) the LFP data from one brain region using the J-neuron spiking data from all brain regions.


To improve the stochastic (proximal) gradient descent, we need a variance reduction technique, which allows us to take a larger learning rate.

. . , β m Initialize x1 Iterate: for s = 1, 2, . . .


The contributions of this paper are twofold.

we identify situations where it is more interesting to use multiple views for learning instead of classical single view learning.


According to the auto-regressive model in (2), given {A t } T t=1 , we can characterize the linear dependence of ROI means at time t + h on those at time t by u t+h = Ãt,t+h u t + noise independent of u t where Ãt,t+h = t+1 τ =t+h A τ , and in t+1 τ =t+h , τ decreases from t + h to t + 1.

as illustrated in Figure 3a, the lower right triangle of ∆ indicates the linear dependence of PPA activity on previous EVC activity (EVC leading PPA, lower-to higher-level), whereas the upper left triangle indicates the linear dependence of EVC activity on previous PPA activity (PPA leading EVC, higher-to lower-level).


Note that the trace is a linear function of , keeping the problem convex.

for a given point Ü , all the points in its class satisfy Ô´ µ » ½.


Let r i = y πi y i and Since y and y ′′ disagree on exactly |k − k ′′ | locations (and similarly for y π and y ′′ π ), the number of locations where r and r ′′ disagree is therefore at most 2|k − k ′′ |.

the first term on the RHS becomes where each permutation π induces a particular sequence r ′′ (π) ∈ S y ′′ (previously we used r π i which is now r i (π)).


When Pr and Pr ′ differ only in Pr(x) and Pr ′ (x), we have β(x, y) = Pr ′ (x)/Pr(x), where β is a reweighting factor for the training examples.

our reweighting method achieves significant improvement in classification accuracy over the unweighted SVM (see [7]).


Furthermore, the problem of learning the structure of BNs exactly is known to be NP-complete even when the number of parents of a node is at most q, for q > 1, [1].

in Appendix B.1, we show that the PC algorithm fails to recover the structure of this GBN while our method recovers the structure exactly.


Supposing G has infinite capacity, then the optimal generative model in Eq.

unlike traditional variational techniques, the variational autoencoder introduces an amortized inference model f 2 F and thus a new source of posterior regularization.


But when following our philosophy of 'letting the machines learn', a calibration session of approximately 20-30 min was so far required, even for subjects that are beyond the status of BCI novices.

note that this evaluation only corresponds to a real BCI scenario where many calibration trials of the same day are available.


If standard linear, polynomial or GRBF kernels are used in the score-space, then the space is assumed to have a Euclidean metric tensor.

when incorporated within an SVM kernel, the kernel is known as the Fisher kernel.


Each of the 3 algorithms (constrained EM, constrained K-means, and constrained complete linkage) was tested in three modes: (i) basic algorithm without using any side information, (ii) constrained version using only positive equivalence constraints, and (iii) constrained version using both positive and negative equivalence constraints.

all algorithms were given initial conditions that did not take into account the available equivalence constraints.


In Figure 1c, the t-c partition for the works with relation is {(S, S), (S, F ), (F, S), (F, F )}.

the probability that the relation holds is the same for all pairs in a given class.


In this section we assume that the parameters of the target mixture distribution are known.

unfortunately our loss is not convex with respect to h ∈ H, so we need to resort to a more powerful technique, namely the Brouwer fixed point theorem.


Note that all the parameters in our algorithm were fixed for all the experiments.

[15,20] try to combine both of those two frameworks.


If the BCI classifier score pdfs, l0 and l1, are fixed, after performing the integral over z h t+1 , the mutual information is only a function of P 1 t . The objective function is now conveniently parameterized by P 1 t , the total prior probability of characters within a flash group.

we believe that the limitations associated with a grid interface layout can be addressed with additional refinements of the stimulus space constraints, such as imposing spatial restrictions on characters within a flash group to minimize adjacency distractions.


Also note that this approximation converges to the real gradient of Eq.

complex Bayesian inference is becoming almost as user friendly as deep learning [4,5].


Beyond intrinsic images, ordinal relations have been used widely in computer vision and machine learning, including object recognition [32] and learning to rank [33,34].

our dataset covers a much wider variety of scenes; it can be easily expanded with large-scale crowdsourcing and the virually umlimited Internet images.


Let We use the above theorem to prove that Algorithm 1 also converges to a good solution.

notation For a vector v, we let v h(k) and v t(k) denote the head(k) and tail(k) of v. v h(k) denotes the vector containing just the k largest coordinates of v in absolute value with all other coordinates set to 0 and We refer to v h(k) as the "top k coefficients of v".


There are two possible reasons for the unfavorable result on iPhone.

there are only 14  We build a DenseNet-like network called DenseNet-41 as our baseline model.


We generate the training data as X = XM where X ∈ R n×p is a random matrix with IID Unif(−1, 1) entries, and M ∈ R p×p is an upper-triangular matrix that determines whether the design is IID or correlated.

aspects of the proof would be different, since impurity measures used for classification are different than those of regression.


Consider that a neuron at a particular layer in a network computes a real-valued function over the network's input domain.

in our experiments, we utilize this flexibility to compare representations across different random initializations, architectures, timesteps during training, and specific classes and layers.


Furthermore, the Gibbs empirical risk R S (G i ab ) is small when the training points are located far away from the Bayes decision surface G i ab (x) = 1/2 (with G i ab (x j ) → y j ∀j ∈ i).

the risk bound depends on the Kullback-Leibler divergence KL(Q P ) between the posterior Q and the prior P which, in our case, gives For these classes of posteriors Q and priors P , the PAC-Bayes theorem of  reduces to the following simpler version.


From the general model (7) we instantiate four different models as explained in the following.

examples of these functions include facility location functions, matroid rank functions, monotone concave over cardinality functions, etc.


As for the dynamical programming algorithm of [3], the Loopy Belief Propagation algorithm runs in O(M N 3 ), however 4 or 5 more iterations are needed for it to converge.

moreover, the introduction of the centroid variable is also valuable in light of a possible extension of the algorithm to multi-frame tracking.


encoder: We utilize the same model as our two-stream model, however we must make one change in order to input the static image instead of the latent code.


Structures with the same edge sets but slightly different transition times will probably have similar likelihoods.

while this is the most interesting setting, it is also the most difficult since one of the unknowns is the number of unknowns.


However, one might expect richer showing behavior when teaching more complex reward functions.

is there a difference between doing something and showing someone else how to do something?


We are now ready to establish that these updates ensure monotonic ascent in the log-likelihood.  )}

but contrary to what one may expect, leveraging the Kronecker product structure for speeding up DPP learning turns out to be more difficult.


For example, the sensing operator A asy (•) is unbiased ( EA asy (•) = 0) but the symmetric sensing operator is clearly not [Cai and Zhang, 2015].

in the following we only need to show that Lemma 10 constructs an estimation sequence with t = O(δ t ) → 0.


We use the subset of OCR dataset chosen by Taskar [8], which contains 6876 sequences.

where W i is the number of parameters in group i ∈ {w, u, θ}.


This suggests three areas where the λ-return might be improved-it could be modified to better account for the correlation of returns, the bias of the different returns, and the true form of Var(R The γ-return uses an approximate formula for the variance of an n-step return in place of Assumption 3.

in some cases it may perform worse because it is still based on the false assumption that all of the returns are unbiased estimators of V (s t ).


Now we characterize the error events of the algorithm ALG in assignment of x.

hellinger distance comes out to be the right measure both for lower and upper bounds.


Sections 2 and 3 provide theoretical insight into the fundamental limits of estimation of v 0 from quadratic observations of the form βv 0 v 0 T + Z.

a direct calculation shows that v is an eigenvector of the matrix X + A T YA with eigenvalue λ = v, X v . We then obtain the following sufficient condition for optimality.


Channel-Nets use three instances of channel-wise convolutions; namely group channel-wise convolutions, depth-wise separable channel-wise convolutions, and the convolutional classification layer.

the connection pattern between input and output channels becomes sparse, where each output feature map is connected to a part of input feature maps.


Eliminating x i in (2.3) by the representation above yields j .

we want mention that our adaptive strategies also work well for noisy data sets, we refer the readers to [8] for some examples.


[2] extended this idea to selecting exemplars from videos that maximize 'coverage' and 'diversity'.

the next question we consider is to define the notion of diversity of a selection of points on a manifold.


Although this approach is conceptually simple, our analyses indicated that it captures the influence of a fairly large number of relevant decision features.

the largest deviations from this line represent the largest deviations in the data from the model's predictions.


The following states the nontrivial quality of local optimal solutions and their connections to related convex problems.

when the learned kernel is restricted to be a linear combination of multiple basis kernels, the problem of learning the combination coefficients as well as an SVM classifier is usually called multiple kernel learning (MKL).


In addition to being able to describe the strategic game faced by agents at convergence, we can also investigate how the strategic incentives agents evolve over the course of learning.

next, we wanted to see if such a strategy could emerge in the multi-agent case.


The most common mapping operation is the projection operation, which, given a point x t+ 1 2 outside the manifold, would find the closest point in M. Unfortunately, the projection operation is very expensive to compute for the manifold of low rank matrices, since it basically involves a singular value decomposition.

we further compute the mean average precision (mAP), a widely used measure in the information retrieval community, which averages over all values of r. Comparisons.


An interesting question is whether similar bounds can be obtained for other concept classes, and for other problems (such as clustering).

the feedback is akin to an "INSERSION SORT" move.


the clips were harvested from three popular TV shows: 3 from Buffy the Vampire Slayer, 27 from Friends, and 4 from LOST.


In order to assess the effect of using our novel approach, we carry out experiments.

, diag(0.25, 0.25)} are both mixtures of nine bivariate normals with equal probability of being sampled, but the centers of the bivariate normals of F 1 are on the grid points (10, 20, 30) × (10, 20, 30) and have covariance diag(1, 1), and the centers of the bivariate normals of F 2 are on the grid points (11,21,31) × (11,21,31) and have covariance diag(0.25, 0.25).


samples {(x i , y i )} N i=1 , the 2 -regularized Empirical Risk Minimization (ERM) problem for our task (2) is (3) is a hard optimization problem in general due to the simultaneous minimization w.r.t.

the intractability of (4) only lies in the combinatorial constraint M = ZZ T for some Z ∈ {0, 1} N ×K .


The step size is ⌘ = 3 ⇥ 10 5 , and the algorithm runs with 8 ⇥ 10 5 total samples.

given any orthogonal matrix Q 2 R r⇥r and any feasible solution U , the product UQ is also a feasible solution and gives the same column span as U .


We call every m iterations of SGD as one epoch.

in this section, we analyze the linear convergence of SVRG-BB (Algorithm 1) for solving (1) with strongly convex objective F (x), and as a by-product, our analysis also proves the linear convergence of SVRG-I.


As an attempt to show (15) for the random circulant matrix A, we invoke the following lemma, which controls the error in a first order approximation to exp(iϕ(•)).

the study of structured random measurement for phase retrieval is still quite limited.


However the correlation between random noise and current inputs is quite weak, which is insufficient to predict the future precisely.

specifically a Sampling module produces a collection of high quality proposals, facilitated by a multiple choice adversarial learning scheme, yielding diverse frame proposal set.


A differential equation describes the activation of the neural tissue at different position in the neural network.

when both competition and cooperation are enabled the network produces context-dependent effects in the correlation space that are equivalent to the ones observed in the mean-rate domain: the correlation among neurons that received inputs with highest correlation is amplified, with respect to the feed-forward case, while the correlation between neurons that were stimulated by weakly correlated sources is comparable to the correlation between all other neurons in the array.


[6] pioneered non-linear metric learning, using convolutional neural networks to learn embeddings for faceverification tasks.

it is important to find the right non-linear form for φ, and we believe an elegant solution lies in gradient boosted regression trees.


This fact is often referred to as the propagation error problem in hierarchical classification.

in this paper, we address this problem and introduce new bounds on the generalization errors of classifiers deployed in large-scale taxonomies.


A coefficient is indeed a member of many neighborhoods as shown in Figure 4, and the structure of the dependencies implies ).

we propose the linear generative model where x ∈ R n , Φ = [ϕ 1 , .


the error-free zone) is wider than that in the artificial cases.

to favor a more random p (as discussed in Sec.


These heuristics were included to model patterns like people who share the same research interest are likely in the same affiliation or a person is related to a department if the person belongs to a group in the department.

we solve the regularized optimization problem min via alternating least-squares, which is a block-coordinate optimization method in which blocks of variables are updated alternatingly until convergence.


Since the norm monotonically decreases, it suffices to prove the lemma statement for this x t+1 .


A natural next choice for C would be a collection of comparisons that represent the Cartesian products between traditionally-protected groups, defined by race, gender, etc.

this is the sense in which metric multifairness provides fairness through computationally-bounded awareness.


Further, let H z n (θ, λ) denote the empirical Hessian of the regularized loss function, defined as Next we present the set of assumptions we need to prove the main result of the paper.

theorem 1 Under Assumption 1, let assuming the inverse exists.


Note that all the candidate vectors are highly correlated with each other and with the target vector.

. . , w 6000 were smaller than 3 • 10 −4 .


σ * over-estimates σnoise because the model is piecewise linear while the true manifolds are non-linear.

the idea is to construct a "good" statistical generative model of the data taking the noise into account, and to assume that its topology is therefore a "good" model of the topology of the manifold which generated the data.


We establish conditions that guarantee the infinity-sample consistency of classifiers obtained in the risk minimization framework.

in this framework, f c (x) is often regarded as a scoring function for category c that is correlated with how likely x belongs to category c (compared with the remaining k − 1 categories).


For instance, the existence of the edge (1, 2) makes it impossible that 1 corresponds to a and 2 to c, since W(a, c) is zero.

furthermore, consistency is with respect to the random graph model, and not to any particular graphon representing the model.


In the worst case scenario EigenPro, if we mislabel all glottal stops, the corresponding frame-level error increases from 31.7% to 32.5%.

he thanks Suvrit Sra, Daniel Hsu, Peter Bartlett, and Stefanie Jegelka for many discussions and helpful suggestions.


For example for a three class problem (with equal prevalence), a posterior label vector of (1, 0, 0) (certain that the class is one) comes from a good annotator while a (1/3, 1/3, 1/3) (complete uncertainty about the class label) comes from spammer.

the obtained rankings and the scores can be used to allocate monetary bonuses to be paid to different annotators and also to eliminate spammers from further labeling tasks.


Our goal now is to show that for k sufficiently large and ǫ > 0 sufficiently small, the point X = Xk + ǫ Q belongs to X c and is closer to X k than Xk is to X k . This would then contradict the fact that Xk is the projection of X k onto X c . To begin, let σ k be the vector of singular values of Hence, for i = 1, . . . , m, by passing to a subsequence if necessary, we can classify the sequence {σ k i } k≥0 into one of the following three cases: (A) σ k i ≤ τ for all k ≥ 0; (B) σ k i > τ and σ i ( Xk ) > 0 for all k ≥ 0; (C) σ k i > τ and σ i ( Xk ) = 0 for all k ≥ 0.

if σ i ( Xk ) > 0 for all k sufficiently large, then Proposition 4.3 gives λ i < 0.


In fact,  showed that when the number of objectives m grows as the cardinality k i.e., m = Ω(k), the problem is inapproximable (unless P = N P ).

given f : 2 N → R, recall that its multilinear extension over ).


The goal of the decision maker is to maximize the reward.

to build further intuition, we consider the settings of Examples 1 and 2, and simplify the PI estimator to highlight the improvement over IPS.


The result follows by noting that for any measurable set A c R P where The previous theorem provides a basis for selecting () such as to maximize Do.

an alternative approach is to define an upper bound on E(J and to directly minimize this bound.


It explains how neurons in association cortex learn to 1) temporarily store task-relevant information in non-linear stimulus-response mapping tasks [1,3,4] and 2) learn to optimally integrate probabilistic evidence for perceptual decision making [5,6].

the training of synaptic weights to memory neurons in parietal cortex can explain how the monkeys valuate the symbols [19].


For simplicity here, we summarize the special case where each class (resp.

we are interested in the consistency of the unknown permutation π * when K > 2, which is a more difficult problem.


The MDS problem endeavors to find an ensemble of points in a prescribed metric space (usually a Euclidean space) such that the distances between these points are close to the set of input distances.

next, we explain how to use triangle fixing to solve the MN problem for the remaining p norms, 1 < p < ∞.


With more hidden nodes the relative performance of our algorithm improved.

key properties of these regression boosting methods deviate significantly from the classification boosting approach.


This is the reason why we call condition (a) the "linear independence of features" assumption.

note that condition (a) means that L is non-singular, and so is V . condition (a) indicates that the features in x t are linearly independent.


We first consider the general online α-divergence inference and learning framework and compare the performance of different α values on a toy online regression dataset in fig.

it is unsuited to this task since stochastic optimisation assumes that the data subsampling process is uniformly random, that the training set is revisited multiple times, and it typically makes a single gradient update per mini-batch.


We introduce a new formalism to describe transformations that "decontaminate" f obs under sufficient conditions on f tar and f con .

we construct a weighted KDE where the kernel weights are lower in low density regions and higher in high density regions.


The key contributions of this paper are summarized as follows: 1.

the characteristic function of L(ω) is given by: where the Lévy measure ν(dβ) is any σ-finite measure which satisfies the following integrability condition A Lévy process can be viewed as a combination of a Brownian motion with drift and a superposition of independent Poisson processes with differing jump sizes β.


For a correct index i, V t i = G(x t , ξ t i ) where G is the gradient estimator.

while this cost seems reasonable for small dimensions, such as, e.g., mobile robots meeting in a 2D or 3D space, it becomes a real issue in the context of machine learning, where d may be as high as 160 billion [30] (making d a crucial parameter when considering complexities, either for local computations, or for communication rounds).


Key to the data analysis is the ability to share information about the overall trajectory between the single trials without forcing unrealistic smoothness assumptions on the single trials themselves.

the higher level nodes in the mGP share the same temporal resolution and only vary in smoothness.


This demonstrates the large receptive fields of IT cells that have often been reported in the literature [3].

the weights E ' e) UT ¡ ¤£ 1 B between the V4 nodes and IT nodes are trained by Hebbian learning of the form to produce object representations in IT based on inputs in V4.


For example, given the sentence "Gene A causes disease B", the object x = (A, B) has true class y = 1.

to do so, we define the noise-aware empirical risk L α, β with regularization parameter ρ, and compute the noise-aware empirical risk minimizer This is a logistic regression problem, so it can be solved using stochastic gradient descent as well.


The stack automaton can evaluate regularities that require checking information in arbitrary positions in a sequence, something that is facilitated by a display in which the entire sequence is available.

the stimuli were sequences of heads (H) and tails (T) presented in 130 point fixed width sans-serif font on a 19" monitor at 1280 × 1024 pixel resolution.


Then, the error from the real value function is For these algorithms, the selection of the set B remains open, raising similar issues as the selection of belief points in PB algorithms.

the reward of a POMDP cannot model this since it is only based on the current state and action.


Consider x ∈ X such that X ∩ (B(x, h/4)) = ∅.

x(1) X( 2) X( 3) X( 4) X( 5) X( 6) X( 1) X( 2) X( 3) X( 4) X( 5) X( 6) These ordered lists of children are used to implement the operation nextChildren defined iteratively as follows.


For example, ResNext [25] aggregated a set of transformations with the same topology, Xception [2] and MobileNet [9] used separable convolutions with 1 × 1 filters, and ShuffleNet [26] encouraged pointwise group convolutions and channel shuffle operations.

smaller receptive field would enable neurons to detect fine details.


The structure from sound (SFS) problem addresses the problem of simultaneously localizing a set of N sensors and a set of M external acoustic events, whose locations and emission times are unknown.

what is of concern, however, is the fact that minimizing Eq.


This can be motivated by the structure of high-dimensional data, where the centered data points often have roughly the same norm 2 .

the respective eigenvalues are λ 1 = 0.0457, λ 2 = 0.00108 and λ 3 = 0.00078.


These results as well as the experimental results shown in the last subsection demonstrate (i) the power of transfering the symmetric NMF (2) to a nonsymmetric one (3); and (ii) the efficieny of alternating-type algorithms for sovling (3) by exploiting the splitting property within the optimization variables in (3).

among these methods, a block principal pivoting method is remarkably efficient for tackling the subproblem (5) (and also the one for updating V ) [8].


Figure 3(e) show that relatively small values of α are more suitable.

the solution f * of the optimization problem (14) satisfies Proof.


The results are summarized in Table 2, where "actual" means the gross profit computed on the basis of the historical data regarding sales quantities and prices over the 20 days, from the 1066-th to 1085-th, and costs c (d) i = 0.3P i5 .

further, actual models do not always satisfy the substitute-goods property.


The performance metric we use is the predictive perplexity on the test set, which cannot be directly evaluated.

the Lagrange parameter in Alvarez and Salzmann [2] and hyperparameters for priors in Gan et al.


In most cases, each signal is itself sparse, and so we could use the CS framework from above to encode and decode each one separately.

2(a) shows that, for sufficiently large J, we can recover all of the signals with significantly fewer than N measurements per signal.


Since adjacent transpositions of permutations may be identified with a down move followed by an up move over the Hasse diagram, o !£ ¥ $ © ¢" is equal to Kendall's Tau " £ ¥ $ © ¢" .

the elements in the C th grade, all of which are incomparable, are denoted by ¨© ¨ § .


We introduced weakly additive noise models, which extend the additive noise model framework to cases such as the linear Gaussian, where the additive noise model is invertible and thus unidentifiable, as well as cases where additive noise is not present.

iMAGES required background knowledge to direct the edges.


The cost to the alignment of changing a label Yi is 2 Lj Yjk(Xi' xj)/IIKIIF , so that if a point is isolated from the others, or if it is equally close to the two different classes, then changing its label will have only a very small effect.

(S, k, y) obtained by this y will be a lower bound of the optimal alignment, hence we have One can hence estimate the quality of a dichotomy by comparing its value with the upper bound.


The class we consider covers non-smooth convex optimization problems, including those with convex constraints.

just as before, our SR1 method is nearly as good as the best algorithm.


We will also consider Bayesian modelings where often a variance estimate comes for free, along with the trained model.

our reliability assessment can also be seen as indication for meaningful projections, i.e.


S consists of a labeling s i for every pixel, where s i is a 1-of-(L+1) encoded variable, and L is the fixed number of parts that combine to generate the foreground.

the Penn-Fudan dataset (at 200 ⇥ 100 pixels) was then split into 10 train/test cross-validation splits without replacement.


Recently, some researchers propose to integrate trainable higher-order pooling (HOP) methods (e.g., second-order and third-order pooling) into deep CNNs [19,29,39,27,8], which distinctly improve representation ability of deep CNNs.

to evaluate the proposed method, we conduct experiments on two large-scale image benchmarks, i.e., downsampled ImageNet-1K [6] and Places365 [44].


For each bit of the hash codes, we define two linear hash functions as follows: x x) and g(y) = sgn(w T y y), where sgn(•) denotes the sign function, and w x and w y are projection vectors which, ideally, should map similar points to the same hash bin and dissimilar points to different bins.

the hash functions for each bit of the hash codes are learned by solving DC (difference of convex functions) programs, while the learning for multiple bits proceeds via a boosting procedure so that the bias introduced by the hash functions can be sequentially minimized.


If the agent takes only optimal ac~ions to the T-junction, it must remember the observation from the starting position for N timesteps to determine the optimal action at the T-junction.

errors are backpropagated through the CECs for an indefinite amount of time, using an efficient variation of RTRL [5, 3J.


Notably, this filter bank is dominantly using the signals measured at the forward part of the scalp (Figure 4, Left).

critically, these linear projections can be included in a convolutional neural network (CNN) architecture to facilitate end-to-end learning with interpretable convolutional filters and fast test-time performance.


A simple and natural dependency statistic is the correlation between pixel intensities, and it works very well.

isomap uses the geodesic distances in the neighborhood graph, whose relationship with the real distance is really close to linear.


We define the generator matrix of the Gallager code to be where I is the M × M identity matrix.

explicit calculation gives the following theorem.


The existence of interactions or univariate variables being modeled by first layer hidden units is determined by the nonzero weights entering those units [31].

our experiment on synthetic data is the baseline disentangling experiment discussed in §3.


For fixed U minimize (8) with respect to M . until No more progress is made or a maximum iteration count has been reached.

in evaluation, 10, 20 or 50 ratings from those of the 100 test users are selected.


Section 3 introduces the MC-UCB algorithm and reports performance bounds.

as explained in the proof in Appendix B of , this rate is a direct consequence of the high probability bounds on the estimates of the standard deviations of the arms which are in O(1/ √ n), and those bounds are tight.


Spikes from neurons outside the chip come in the form of AER events, and are targeted to the correct AER synapse by the X-Y Decoder.


The figure on the right plots the F1 scores along the optimal path to the goal for the case where the MAP clustering has forty instances (twenty per cluster) instead of 5. this model is perfect and exactly reflects the pairwise F1 score.

q(s, a) = θ • φ(s, a), where φ(s, a) are features over the state-action pair s, a.


Specifically we present a new chip with 32 × 32 cells, that can sequentially select the most active regions of the input stimuli, the Selective Attention Chip (SAC).

several software [1,2,3] and hardware models [4,5,6,7] based on the concept of saliency map, winner-takes-all (WTA) competition, and inhibition of return (IOR) [8] have been proposed.


Considering these limitations of convex regularizations, we study non-convex regularizations [33]- [35] [39], which have the advantage of producing mildly or slightly shrunken parameter estimates so as to be able to preserve weak-effect disease-related brain regions and the advantage of avoiding selecting many disease-irrelevant regions.

the linear transformation explored by LDA may not be effective.


the first sentence in the first example).

when the validation loss stopped decreasing, the softmax layers were re-inserted and training recommenced.


Note that in the first step, the network has not yet received any feedback.

we instead evolve the policy using a variant for Natural Evolution Strategies (NES; [25,26]), called Separable NES (SNES; [19]).


With the (N × N ) kernel matrix K = 1 N Y T Y we define the Gaussian partition function x is an N dimensional integration variable.

using , we can generate expressions that can be used in (2) to sum over the data which are not contained in the set D In the following λ k and u k will always denote eigenvalues and eigenvectors of the data dependent (i.e.


Suppose a random walk visits "dog" then "cat".

then, we evaluate the three estimators using the Frobenius norm between P and the true transition matrix P * : error( P) = i,j ( P ij − P * ij ) 2 .


Strong convexity of f is defined with respect to the same product and norm 1 .

we will adopt this notion in Section 4, when comparing SEGA to coordinate descent.


An algorithm is called p,-margin successful if, for any input labeled sample, it outputs a hypothesis half-space that classifies correctly as many sample points as any half-space can classify correctly with margin p, (that is, discounting points that are too close to the separating hyper-plane).

a hyper-plane h(w, t), where w E lR n and t E lR, correctly classifies (X, 17) if sign( < wx > -t) = 17 where < wx > denotes the dot product of the vectors w and x.


When applied to the reconstruction of high-resolution 3D objects from single RGB images, we outperform several state of the art methods with a variety of representation types, across two evaluation metrics.

the removal only occurs if there is agreement of at least two ODMs for the removal of a voxel.


The problem of unmixing the dyes can be formulated as a matrix factorization problem: Here X is an n s × l column matrix, where l is the number of pixels and the entry X ij is the brightness of the i th pixel in the image in to the j th spectral band.

we use a setup based on a set of fixed bandpass filters.


One partial explanation is that our approach can be easily adapted to a wide class of "link functions," beyond just the sigmoid function addressed by the above results.

there is no partitioning of the data according to the sign of the label, and the unbiased estimator that we construct does not rely on any Gaussianity assumption.


We show that there exists a family of preconditioners that can bring the condition number close to 1, thereby greatly speeding up the iteration-to the extent that a single step would suffice in practice.

in vision applications, it's suitable to employ smoothness priors admitting discontinuities [4].


Our framework is also similar to the Anytime Edge Evaluation (AEE*) framework [25] which deals with edge evaluation on a GBG.

in order to specify BISECT, we need to define two options -a candidate test set selection function SelectCandTestSet(x A ) and a test selection function SelectTest(T cand , θ, x A ).


Due to the non-linear activations between consecutive layers, calculation of the resultant posterior on the weights is intractable.

the history of learning uncertainty-aware predictors is concurrent with the advent of modern Bayesian approaches to machine learning.


PNs achieve better performance than rectifier networks on pedestrian detection [20] and on dependency parsing [10], and outperform kernel approximations such as the Nyström method [5].

this is not surprising, since kernel SVMs require 3,208 support vectors on letter, as indicated in Table 2 below.


Latent distance and latent class models provide concise, easily interpreted descriptions of social networks and relational data.

there are at most K unique rows of C and so C is of rank K at most.