By Theorem 1.19 -1.23 of Durrett [2016], it can be proved that, for arbitrary η > 0, there exists t 0 , such that ∀t > t 0 max That is to say, when the size of the stored samples is larger than t 0 , the mixing time of the new data process with experience replay is 0.

the experience replay trick improves the mixing property of the data process, and hence improves the convergence rate.


for all t ≥ 0, x(t) always lies in the domain We argue that inf x∈D V (x) is positive, which follows readily by the following sequence of observations.


Therefore, we can just subtract this bias.

when H 0 is true L(ĝ 0 , D 0 e ) L(ĝ, D e ) will be close to 0.


The predator scores are all low, comparable to the scores in the first cluster.

we argue that ATOC leads to better cooperation than the baselines even in competitive environments and the learned policy of ATOC predators and preys can generalize to the opponents with different policies.


In this domain, number of citations is commonly viewed as a valid measure of authority given disciplined scholarly practice of citing prior related work.

we consider citation-count based ranking as the "ground truth".


By "general" we mean the reductions are not restricted to particular classes of graphs or algorithmic approaches, but show that any computational progress on the target problem immediately transfers to progress on the source problem.

for example, one of our main results establishes that the problem of determining whether given marginals, whose induced graph (the "data graph") falls within some class G, are consistent with any joint distribution reduces to the problem of MAP inference in Markov networks falling in the same class G. for instance, we immediately obtain that the tractability of MAP inference in trees or tree-like graphs yields an efficient algorithm for marginal consistency in tree data graphs; and any future progress in MAP inference for other classes G will similarly transfer.


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

z j = ∂ m h (x)/∂h j should discriminate between relevant and irrelevant covariates.


Despite of the specific structure of any image captioning model, it is able to give p(c|I), the probability of a caption conditioned on an image.

all image captioning models can be used as the target or the reference in CL method.


We shall denote by S the K max -selected variables: The computational complexity of the K max -long regularization path of LASSO solutions is Most of the time, we can see that the Lasso effectively catches the true changepoint but also irrelevant change-points at the vicinity of the true ones.

we propose to refine the set of change-points caught by the Lasso by performing a post-selection.


To allow a fair comparison, the subset selection methods SRM SGMA and SRM PostApp were forced to select a given number B of basis functions (instead of using the stopping criteria proposed by the authors of the respective methods).

all methods form their predictions as a linear combination of exactly B basis functions.


We show that the probability of a batch having at least one positive is a monotone submodular set function, and that sequentially simulating the one-step policy with the pessimistic oracle equivalently maximizes the marginal gain of this function.


If y n is bounded and has non-trivial probability of being greater than zero, we lose little by restricting x n • θ to be bounded.

we will assume that the parameter space is bounded.


Empirically, we find that an inverse kernel with size of 150 is typically sufficient to generate visually plausible deconvolution results, and that a matrix M with size of 50 × 50 contains the most values larger than zero.

we set m = 50 and d = 150 in this paper.


Consequently, hidden state transitions depend explicitly on the elapsed time since the last observation, i.e., on the IEIs ∆t e . The transition probability a i j (∆t e ) from hidden state i to hidden state j is then given by where g i j is the conditional probability of making a transition from state i into a new state j, given that j = i.

g i j has to satisfy the constraint ∑ j g i j = 1, with g ii = 0.


Once again, it is worth noting that when the SNRs of the experiments are large, almost every design has the same E-optimal performance as long as the experiments are not too correlated.

greedy design is also expected to give good results under these conditions.


However, we do not train a one-class classifier, instead, we learn the probability distribution of the inliers.

the novelty test simply becomes the evaluation of the probability of a test sample, and rare samples (outliers) fall below a given threshold.


Note that the penalization on the margin errors of unlabeled data can be included if needed.

we have the following form of TSVM that can be derived through the duality: In order to adjust the strength of the regularization raised from the unlabeled examples, we introduce a coefficient ρ ≥ 0, and modify the above problem (3) as below: Obviously, it is the standard TSVM for ρ = 1.


The lead field matrix is defined for the three x, y, and z orientations in each of the source locations and was normalized to correct for depth bias.

the lead field matrix X is of size 275 × 11589.


as a performance measure for the DLD problem one can alternatively use the classification risk R P (.).

we will establish some basic properties of this performance measure in the following.


The weight matrix W (τ ) hh obtained by P δ (•) is a solution of the following optimization: Lemma 5 indicates that our method can bring back the weight matrix into the feasible set with minimal variations in the parameters.

our procedure P δ (•) has minimal impact on the minimization of the loss function.


(Note the reported values are ELBO per cell per timestep, so must be multiplied by 348 cells and around 100,000 time-steps to obtain the raw-ELBO values, which are then highly significant).

the ELBO is able to recover features of real biological connectivity (biological connectivity is also sparse [1,2]).


However, this will only occur if the weight range is large enough accomodate for the offset mismatch.

we sacrifice weight linearity to increase the weight range.


We downsample the channels by 2x and features are single pixel lookups in the aggregated channels.

given a h × w detection window, there are h/2 • w/2 • 10 candidate features (channel pixel lookups).


This mechanism is already included in step 2 of the dereverberation procedure, that is, F 0 estimation is applied to O( R1 )X.

more accurate F 0 can be obtained in step 2 than in step 1.


This is chosen since TORPIDO uses A3C as its RL agent.

this comparison will directly show the value of transfer.


This will reduce the middle data, and consequently improve the ternarization error from BTQ.

it is possible to obtain better accuracy on the quantized models if we carefully configure a properly small λ.


We proceed to formally define the new mean reversion proxy and the use of our new algorithm in this model.

denote by y t ∈ R n the prices of n assets at time t, and by x t ∈ R n a distribution of weights over these assets.


Key signals, such as reward prediction errors, are not only determined by the current reward, but also a potentially extensive history of past inputs.

it is inadequate merely to find brain regions showing marked BOLD changes just in response to reward.


The estimator corresponding to the Bayes risk (for the cross-entropy or KL-divergence loss function) is the posterior.

the simulation-on-the-fly training paradigm guarantees generalization and calibrated posteriors (assuming small optimization error).


In the case of hard clustering we also find thatI(Tj ; U j ) = H(Tj ) (where H(P) is Shannon's entropy).

roughly speaking, we may say that H(P) is decreasing for less balanced probability distributions p. increasing (3-1 will result with a tendency to look for less balanced "hard" partitions and vice verse.


For a complex algorithm like DP-SLAM, asymptotic analysis may not always give a complete picture of real world performance.

we provide a comparison of actual run times for each method on three different data logs.


The spectrahedron manifold has the structure of a compact Riemannian quotient manifold [23].

optimization on the spectrahedron manifold is handled in the Riemannian optimization framework.


Also, the rare degenerate basic solutions that do remain, even if suboptimal, are sparser by definition.

locally minimizing our new problem ( 14) is clearly superior to locally minimizing (1).


Kolter and Wong [15], which used the same network and hyperparameters as ours, reported that they could defend from perturbations with its ∞ -norm bounded by 0.1 for more than 94% examples.

in the ∞ -norm, our work is inferior, if we ignore their limited applicability and massive computational demands.


Note that we are still solving an N -dimensional minimization problem with M N constraints, while we need M -dimensional dynamics.

we consider the dual optimization problem of maximizing g(λ) where g(λ) = inf x L(x, λ) is the dual Lagrangian of the problem.


This is to be expected as this choice of g(x) gives a function with very long tails.

a few "outliers" dominate the two estimates of E(g(x)) in (3) which we use to estimate a, b.


However, the construction of efficient control variates can be strongly dependent on the form of the probabilistic model.

it would be highly desirable to introduce more black box procedures, where simple stochastic gradients can work well for any model, thus allowing the end-user not to worry about having to design model-dependent variance reduction techniques.


If (SDP) has a compact search space, then it admits a global optimum of rank at most r, where r(r+1) 2 ≤ m [Pataki, 1998, Barvinok, 1995.

if one restricts the search space of (SDP) to matrices of rank at most p with p(p+1) 2 ≥ m, then the globally optimal value remains unchanged.


background videos that do not contain the events of interest.

we use the Event-Kit data collection in the experiments.


We will treat each rating type separately.

the variables in the model are: all of the voxel measurements V s (l, t), for all s, t and voxels l selected to be relevant to rating j; and all of the ratings R s (j, t) (for all s, t).


Furthermore, highly accurate eigenvalues/eigenvectors are not essential for many applications.

we propose a fast early termination strategy (MSEIGS-Early) to approximate the eigenpairs of A by terminating MSEIGS at a certain level of the hierarchy tree.


Both features are differently pronounced over time and exhibit a large trial to trial variability and can therefore be considered as temporally blurred.

the proposed method combines at one hand the MRP with the oscillatory feature and on the other hand gather information across time as introduced in [8,16].


The final templates for each set of input vectors, b rF k , b sF k , respectively, are compared with each other with the similarity (b rF k ) t b sF q .


Compared to classical techniques, KDR has the significant advantage that it avoids making strong assumptions about the distribution of X.

kDR has been found especially suitable for high-dimensional problems in machine learning and computer vision [8,10,11].


Surprisingly, even infinitely differentiable functions (s = ∞) are not immune to this problem (m = Ω(2 d/2 )) [18].

further assumptions on the multivariate functions beyond smoothness are needed for the tractability of successful learning [13,14,16,19].


Further, notice that the offset function w(x) = f ta (x) − f so (x) = x, is just a linear function.

instead of directly using T ta to estimate f ta , we can use the target domain samples to find an estimate of w(x), denoted by ŵ(x), and our estimator for the target domain is just: Figure 1b shows this technique gives improved fitting for f ta .


As noted above, in a natural environment an individual is confronted with the task of discriminating between stimuli important for survival (" targets") and stimuli that are irrelevant (" distractors") .

an organism must not only keep up a high rate of detecting targets but, at the same time, must strive to minimize " false alarms" to irrelevant stimuli.


The proposed Genetic-Gated actor critic methods (G2AC and G2PPO) have the following main features : Multi Model Race: A single critic evaluates the state values while multiple agents follow unique policies, so the population matrix can be applied to the last hidden layer of actors.

our method is composed of multiple policy actors and a single critic.


As seen in, e.g., the Maximum Variance Unfolding (MVU) method (Weinberger et al., 2004) for nonlinear dimensionality reduction (see (So, 2007) for related discussion) and Pairwise Constraint Propagation (PCP) (Li et al., 2008) for constrained clustering, a nice feature of such a framework is that the problem formulation often becomes straightforward.

the major challenge in optimizationbased kernel learning lies in the second component, where the key is to find an efficient procedure to obtain a positive semidefinite kernel matrix that satisfies certain properties.


[6], we can implement this by maximizing a lower bound on mutual information between generator ids and generated images: where q(c|x) is the distribution approximating p(c|x), p g (x|c) is induced by each generator G c , KL is the Kullback Leibler divergence, and the last equality is a consequence of Lemma 5.1 in [6].

by modeling q(c|x) with a neural network Q(x; γ), the encoder network, maximizing I(c; x) boils down to minimizing a cross entropy loss: Utilizing the Wasserstein GAN [2] objectives, discriminator (critic) and generator maximize the following, where D(x; w) : X → R is the critic function: We call this model Disconnected Manifold Learning WGAN (DMWGAN) in our experiments.


On the other hand, when λ is small such that the classification model relies more on the auxiliary text training data L s , the classification performance is relatively stable.

we suggest to set the trade-off parameter λ to a small value, and in these experiments, all the λs are set to 1, based on Figure 3.


Without strong assumptions, non-convex optimization theory is always in terms of finding points with small gradients (i.e., approximate stationary points or local minima).

to understand non-convex stochastic optimization better, perhaps we should first figure out the best rate for convex stochastic optimization.


In contrast, head-mounted cameras instrument people rather than the scene.

one camera is used to estimate each head pose.


In previous work (NIPS, 1998)  we demonstrated that an analogous model derived from the statistics of natural images accounts for non-linear properties of neurons in primary visual cortex.

divisive normalization appears to be a generic mechanism for eliminating a type of statistical dependency that is prevalent in natural signals of different modalities.


The gradients of both sum and g function can be easily obtained.

accNet as a composition of the two basis calculations can be easily trained by the back-propagation algorithm.


However, the increase in average contribution to the postsynaptic membrane potential for the correlated group of neurons renders this population slightly more likely to be active during the causal regime than any single member of the uncorrelated group.

the synaptic strengths for this group of neurons will increase with respect to the uncorrelated group, further augmenting their likelihood of causing a postsynaptic spike.


In [2], we establish that the above algorithm finds an -suboptimal robust policy in at most O(nm log(1/ ) 2 ) flops.

the extra computational cost incurred by robustness in the infinite-horizon case is only O(log(1/ )).


The solution to (6) falls inside the set {θ j }.

a simple linear search after sorting samples suffices (by book-keeping the ordering, sorting the whole block once is enough for the entire procedure).


Another difference from traditional GANs is that noise is not necessary anymore since the generator is conditioned on an image I A , which is similar to [17].

we have the following loss function for the discriminator D and the generator G2 respectively, where L bce denotes binary cross-entropy loss.


For confounded feature combinations, the association might be large in the entire dataset D, but small for conditional datasets D j .

the CMH test will not deem such feature combinations significant.


A fundamental difference between our setup and that of the standard stochastic multi-armed bandit problem [23,8] is that the latter allows each item to be recommended an infinite number of times.

the solution concept for the stochastic multi-armed bandit problem is to determine the best item (arm) and keep choosing it [3].


In the proposed model, computations do not rely on the shape of PSPs, which alleviates the restriction imposed by the length of their rising segment.

we may use a simplified model of synaptic currents; we model synaptic currents as Diracs, which means that we do not take into account synaptic time constants.


We assume that each real-valued h k follows a univariate Gaussian distribution.

we define the conditional distributions as where W i• and W •k denote the ith row and kth column of W, respectively.


is not identifiable in the compressed model.

we propose a natural convex program for recovering the underlying compressed lowrank component P ?


We use the last hidden state of the GRU to create a compressed representation.

each sentence x is represented by a vector E(x) = h x ∈ R 2048 , where E denotes our general-purpose sentence encoder.


10) is minimized when Z = Re(Z) ≥ 0 for a fixed value of |Z| 2 .

the problem is reduced to seeking a real value Z = y ∈ [0, M ] that minimizes If M = 1, then y = cos 2θ 1 from eq.


The estimated dimension can be used to estimate the noise level present in the data set.

the idea is to measure the error between the projected label vector Ĝ = π d (Y ), which approximates the true label information G. The resulting number êrr = A Note on Consistency Both the estimate of Ĝ and the noise level are consistent if the estimated dimension d scales sub-linearly with n. The argument can be sketched as follows: since the kernel PCA components do not depend on Y , the noise N contained in Y is projected to a random subspace of dimension d. Empirically, d was found to be rather stable, but in principle, the condition on d could even be enforced by adding a small sub-linear term (for example, √ n, or log n, to the estimated dimension d).


a , where D GF # and D HF # can be, for the time being, thought of as free distributions to be optimized.

using Jensen's inequality, we have the following lower found on the log likelihood: maximizing the lower bound of the log likelihood (call it f £ D !


Consequently, the marginals in observed and latent space are also KDEs, and the dimensionality reduction and reconstruction mappings are given by kernel regression (the conditional means E {y|x}, E {x|y}): We allow the bandwidths to be different in the latent and ambient spaces: They may be tuned to control the smoothness of the mappings and densities [1].

lELVM naturally extends a LE embedding (efficiently obtained as a sparse eigenvalue problem with a cost O(N 2 )) to global, continuous, differentiable mappings (NW estimators) and potentially multimodal densities having the form of a Gaussian KDE.


The TD error δ t is a random quantity that is defined according to δ t = r t+1 − Ĵt+1 + V (s t+1 )− V (s t ), where V and Ĵ are consistent estimates of the state-value function and the average reward, respectively.

these estimates satisfy E[ V (s t )|s t , π] = V π (s t ) and E[ Ĵt+1 |s t , π] = J(π), for any t ≥ 0.


However, the probabilistic inference task in MRFs -computing the posterior distribution of one or more variables -is tractable only in small tree-width networks, which are not often an appropriate model in practice.

one typically must resort to the use of approximate inference methods, most commonly (in recent years) some variant of loopy belief propagation [11].


However, meta-training has access to more data than simply unlabeled data: it has access to the values of the meta-training functions.

meta-training may perform better than these other algorithms.


Next observe that due to the Boolean nature of ϕ, (4) admits a simple closed form: where in general we use (•) to denote the probability of satisfying a specification using uniformly random actions.

we denote by {ξ} the probability of randomly generating demonstration ξ within M . Further, note that by the law of the excluded middle, for any specification: ¬ϕ = 1 − ϕ.


However, the discriminators alone cannot guarantee generating human-perceivable images.

a reconstruction loss is introduced to minimize the L1 differences between the generated image y k and its corresponding real image y k , which is shown to be helpful for more stable convergence of training the generator.


The intuition and motivation behind this approach is that at the solution of the optimization problem, all variable copies should be in agreement with the consensus variables.

prioritizing subproblems whose variables are in greater disagreement with the consensus variables might facilitate faster convergence.


Another possibility uses the fact that, given a data point x in the product density space, the d input mixture labels are conditionally independent [4].

one can define a parallel Gibbs sampler which alternates between sampling a data point conditioned on the current input mixture labels, and parallel sampling of the mixture labels given the current data point (see Figure 1).


This procedure can lead to biases when the neuronal populations are strongly coupled.

future developments should focus on the integration of dynamic decomposition with connectivity estimation within an overarching Bayesian model.


an average over some training set {x i , y i }), using a loss function (p, y), where p is the network's prediction and y is the target value.

we consider the optimization problem where w, V, θ are unconstrained.


The online updates are summarized as: Unless r n = 0, the sum in (1) only contains one term since the only possibility is that The indexing convention is such that if r n = 0 then y n+1 is the first observation sampled from the new parameters θ.

the marginal posterior predictive on the next data point is easily calculated as: the predictions from BOCPD fully integrate out any uncertainty in θ.


The mixing time can be seen as the number of time steps required for the Markov chain to get close enough to its stationary distribution.

the mixing time also determines the rate at which policy evaluation will converge to the optimal value function [3].


Both of these models are generative and show very good performance, yielding better results than the original DRAW model.

the active memory approach seems to be a better choice for image models.


However, in some directions f may be smoother than in others.

if we knew in advance the set of directions along which the best performing reference functions f are smooth, we could use this information to control regret better.


However, the SE analysis in [24] is restricted separable Lipschitz denoisers that can be described as follows: Let g 1n (r 1 , γ 1 ) be the n-th component of the output of g 1 (r 1 , γ 1 ).

then, it is assumed that, for some function scalar-output function φ(•) that does not depend on the component index n. the estimator is separable in the sense that the n-th component of the estimate, x 1n depends only on the n-th component of the input r 1n as well as the precision level γ 1 .


However, if the time scale of synaptic depression is large, the recovery of the synaptic depressed region is slowed down, and cannot catch up with the bump motion.


Similar results obtain for User S, not shown here.

repeated feedback given to Cobot for a non-uniform set of preferences clearly pays off in a corresponding policy.


This means that if v > g max , the network is unable to track the stimulus.

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


Specifically, the area of the ellipse is proportional to the average power of the audio signal (computed over the same periodogram window) while the eccentricity is controlled by the the entropy of the normalized periodogram.

observed changes in the image sequence are functionally related to the recorded audio signal.


Creating new options that each have their own function approximator concentrated on a subset of the state space may result in better overall policies by freeing the primary value function from having to simultaneously represent the complexities of the individual option value functions.

skill discovery offers an additional representational benefit in continuous domains.


We can set to a small constant, because we can tolerate a small multiplicative error in estimating the spectral norm of M and we only need an approximate top eigenvector (see, e.g., Corollary 16 and Lemma 18).

the power method takes time O(dN log m).


In addition, for each category, we also acquire generally higher IoUs.

2D semantic segmentation for depth or RGB can promote the final completion.


If we assume that the gains of individual features are independent, then the estimated gain for H is 1 V arq,I [f ] is intractable when we have tied parameters.

we approximate it by assuming that the occurrences of f are independent to each other: i.e.


However, having some tolerance in the position of an object within a patch is critical as during full image inference most objects will be observed slightly offset from their canonical position.

during training, we randomly jitter each 'canonical' positive example to increase the robustness of our model.


Finally, note that when [31] showed that a favourable trade-off was possible for kernel ridge regression (KRR), they strongly leveraged the fact that KRR is a γ-regularized problem.

all eigenvalues and eigenvectors in the Φ n Φ T n covariance matrix smaller than the γ regularization do not influence significantly the solution.


Otherwise, it selects the actions with the number of observations below the minimum requirement for making the empirical divergence of each suboptimal point q ∈ C c 1 larger than log t. Unlike the N -armed bandit problem in which a reward is associated with an action, in the partial monitoring problem, actions, outcomes, and feedback signals can be intricately related.

we need to solve a non-trivial optimization to run PM-DMED.


A standard calculation shows that where Note that P c ⇢ c (x, y) = 1 for all (x, y).

we can rewrite, @L(W ) @Wq,r = 1 m P (x,y) x r (⇢ q (x, y) 1[q = y]) .


For each query, an algorithm was chosen uniformly at random from the union of the set of algorithms plus an additional random algorithm whose queries were used for the hold-out set.

each algorithm makes approximately 4000 queries.


More generally, virtually every cell type of interest has a known tendency (e.g., high or low) for most measured attributes.

it is reasonable to assume that there is an underlying distribution (on distributions) governing flow cytometry data sets, that produces roughly similar distributions thereby making possible the automation of the gating process.


Our algorithm is a unsupervised filter method, while almost all the existing filter methods are supervised.

we compared our algorithm with data variance which can be performed in unsupervised fashion.


The rationale behind this was that we expected that the participants would need a few seconds in the beginning of each trial to get used to the new rhythm.

the data would be less suited for training but might still be good enough to estimate the model accuracy on unseen data.


[8] is to first identify inactive predictors that have 0 components in the solution and then remove them from the optimization.

we can work on a reduced feature matrix to solve Lasso efficiently.


This way, the communication cost reduces to an α fraction (per round), while the improvement in the value of the solution is at least αλ(Q − f (A gd [m, ])).

we can trade-off the communication cost per round with the total number of rounds.


Our goal is to cluster these multi-dimensional time-series automatically into a small number of motion templates without pre-labeling of the trajectories or assuming an a priori number of templates.

the system has to discover the underlying motion templates, determine the number of templates as well as learn the underlying skill sufficiently well for robot application.


Although, pairs of genes are not expected to be similar under all experimental conditions it is critical to be able to discover local expression patterns, which can for instance correspond to joint participation in a particular biological pathway or process.

while clustering aims to identify global structure in the data, biclustering take a more local approach by jointly clustering both objects and features.


These transformations, namely the diffeomorphic component deformations and the time component reparametrizations, characterize respectively the spatial and the temporal variability of propagation among the population.

individual trajectories may write in the form of where the functions γ i are obtained from γ 0 through the applications of the two transformations φ i and ψ i described below.


Let (h, j) be the deepest node in T n that has been expanded by the algorithm up to round n. Thus h ≥ h * n . Now, from the definition of the algorithm, we only expand a node when its value is larger than the value of all the leaves of equal or lower depths.

since the node (h, j) has been expanded, its value is at least as high as that of the optimal node (h Remark 2.


We show that choosing k to be strictly pd violates these conditions and k is therefore characteristic to P. Examples of strictly pd kernels on is a strictly pd kernel if k is strictly pd, where f : M → R is a bounded continuous function.

translation-variant strictly pd kernels can be obtained by choosing k to be a translation invariant strictly pd kernel.


Most clustering methods consider the number of clusters k as a required input, and then they apply an optimization procedure to adjust the parameters of the assumed cluster model.

in exploratory analysis, where the data characteristics are not known in advance, an appropriate k value must be chosen.


Since log P (D) is constant for all hypotheses, its value does not enter into the minimization problem, and we can state that the hypothesis of choice ought to be such as to minimize the quantity -log P(D I H)log P(H) (3) If we follow Rissanen and regard the quantity -log P(x) as the description length of x, D L (x ), then Equation 3 instructs us to select the hypothesis that minimizes the total description length What this means is that the hypothesis that is optimal from the standpoint of the Bayesian decision maker is the same hypothesis that yields the most compact two-part code in Equation 4.

besides the merits ofbrevity for its own sake, we see that maximal descriptive compactness also corresponds to maximal inferential power.


Both the Martin kernel and Binet-Cauchy kernel are computed by DLEs.

theorem 4 can be employed to compute the gradients w.r.t.


As compared with ordinary linear models, latent variable models feature the ability to exploit a richer representation of the space of instances.

they often achieve superior performance in practice.


We write the total utility of recommending A as where w 2 < d + is a parameter vector indicating the user's interest level in each topic.

f (A|w) corresponds to the weighted information coverage of A, and depends on the preferences of the particular user.


As shown in Table 1, both the IFO complexity and hard thresholding complexity of SVRG-HT are O (n + κ s ) log 1 .

although the IFO complexity of SVRG-HT substantially improves over FG-HT, the overall complexity still scale linearly with respect to the sample size n. when the data-scale is huge (e.g., n κ s ) and the per-iteration hard thresholding operation is expensive, SVRG-HT could still be computationally inefficient in practice.


The physical interpretation is that of a sum of potential and kinetic energy terms, where the total energy of the system is conserved.

in a system where this Hamiltonian function is constant, we can exactly compute its evolution through the pair of differential equations: These are solved exactly by x(t) = µ + a sin(t) + b cos(t) , where a and b can be identified at initial conditions (t = 0) : the exact HMC algorithm can be summarised as follows: • Initialise the allowed travel time T and some initial position x 0 .


It is not practical if the goal is to compress model within a short period of time.

performance before retraining is important and GroupReduce in general obtains good results.


The process is non-Markovian and generates a sequence of states X t as follows.

after arriving at state X t , the walker promptly "spaces out" and forgets the state X t−1 , yet it still wants to transition according to the higher-order transitions P . it invents a state Y t by drawing a random state from its history and then transitions to state X t+1 with probability P Xt+1,Xt,Yt .


Figure 1(a) shows how information flows between agents and the environment, and how Q-values are processed by the action selector in order to produce the action, u a t , and message m a t . Since this approach treats agents as independent networks, the learning phase is not centralised, even though our problem setting allows it to be.

the agents are treated exactly the same way during decentralised execution as during learning.


For brevity, we will use z ∈ K to denote a global mimimizer of f which belongs to K. Recall that Algorithm 2 outputs a weighted average of the queries.

we may employ Jensen's inequality to bound its error as follow, Combining this with T −1 t=0 α t ≥ Ω(T 2 ), implies that in order to substantiate the proof it is sufficient to show that, , is bounded by a constant.


The "good" arm is drawn independently in the beginning of each batch according to a discrete uniform distribution over {1, . . . , K}.

the identity of the "good" arm can change only between batches.


The final update equation for the marginals is given by: where C i is the normalization constant for variable x i , and θxixj is the normalized reward:   For EM, this complexity is only O(d 2 ).

the computational complexity of each iteration of EM is lower than that of MPLP by a factor of deg.


One restriction required by our analysis is the ability to play any ranking.

all rankings must be valid in all contexts, which is a natural restriction in domains such as information retrieval and recommendation.


Without any symptoms being positive, the agent cannot perform disease prediction.

it is evident that in the early phrase of symptom probing, the agent must employ a strategy that can quickly find some positive symptoms during reinforcement learning.


As the reward gap 1 becomes larger, more attack is needed to reduce the reward of arm 1, and the slope increases.

furthermore, note that Ignoring log log T terms, we have for some constant C > 0 and large enough T . We thus expect the log-cost curve as a function of log log T to behave like the maximum of two lines, one with slope 1/2 and the other with slope 1.


Therefore, no explicit computation of the direction or magnitude of weight updates is necessary-the circuit naturally performs these computations for us.

we only need to indicate when the circuit should adapt, not how it does adapt.


However, for some complicated cases, a single attention network is not sufficient to locate the correct region for class semantic descriptions.

we iterate the above semantics-guided attention process using multiple attention layers, each extracting more fine-grained visual attention information for class semantic descriptions.


Indeed several authors have shown that favorable empirical/theoretical performance in mean square error for the preference matrix often does not translate to better performance when performance is measured using ranking metrics [11; 33; 23].

collaborative preference estimation may be better posed as a collection of coupled learning to rank (LETOR) problems [25], where we seek to jointly learn the preference rankings of a set of entities, by exploiting the low dimensional latent structure of the underlying preference values.


The marginal for the brightness of a pixel in natural image patches is heavy tailed, closer to a Laplace distribution than Gaussian.

rNADE-MoG must fit predictions of the first pixel, p(x 1 ), with several Gaussians of different widths, that coincidentally have zero mean.


An immediate consequence is that given error tolerance 2 (0, 1) and with choice 2 (0, 1 4 2 ), then upper bound (10) is at most (by having each of the two terms on the right-hand side be  2 ) if n > m log 2m (i.e., = 1 + log 2 / log m), and This means that if we have access to a large enough pool of labeled time series, i.e., the pool has ⌦(m log m ) time series, then we can subsample n = ⇥(m log m ) of them to use as training data.

then with choice = 1 8 2 , generalized weighted majority voting (8) correctly classifies a new time series S with probability at least 1 if the gap between sets R + and R needs to grow logarithmic in the number of latent sources m in order for weighted majority voting to classify correctly with high probability.


Since Conv1 output is 1D, there is no orientation in its space to agree on.

no routing is used between Conv1 and PrimaryCapsules.


Child evaluation contains randomness due to the stochastic training procedure.

over time we see an improved validation score, even after convergence, due to lucky evaluations.


This problem is modeled as a contextual bandit problem, where the context consists of both user and article information, the arms correspond to articles, and the reward of a displayed article is 1 if there is a click and 0 otherwise.

the value of a policy is exactly its overall CTR.


The computational overhead of Algorithm 1 mainly comes from the calculation of the partial gradient with respect to Z, whose time complexity is O(rd 2 ).

our algorithm has a per-iteration complexity of O(rd 2 ).


Obviously, a query that is not identifiable in the substantive model is not recoverable from missing data.

a necessary condition for recoverability of a causal query is its identifiability which we will assume in the rest of our discussion.


12 20 While the above reveals the structure of V, we don't know V. However, we recover its column space U 2 R s(r)⇥K from the moment matrix M r (y ⇤ ), for example with an SVD.

we can relate U and V by a linear transformation: V = UQ, where Q 2 R K⇥K is some unknown invertible matrix.


First, the function computing the output pose vectors of one layer is left-equivariant regarding applications of the group law if Second, the function computing activations of one layer is invariant under applications of the group law Since equivariance is transitive, it can be deducted that stacking layers that fulfill these properties preserves both properties for the combined operation.

if we apply a transformation from G on the input of a sequence of those layers (e.g.


Hence, it follows that (3) Note that B id ab has an hyperbolic decision surface.

b id ab is not representable as a conjunction of rays.


Once each N × K subband is collected for each channel, the entropy for each oriented pyramid is computed pixelwise and they are averaged separately.

subband Entropy wishes to measure the entropy of each spatial frequency and oriented filter response of an image.


The intuition is that with t samples, the uncertainties in the indexes, coming from both the score calculation and the bias term, can be upper bounded at the order of O logt/t .

to not miss a competitive worker, we set the tolerance to be at the same order.


The another is that the iHMMs have one hidden state sequence s 1:t to be inferred, while the dIRM needs to estimate multiple hidden state sequences z 1:t,i given one time sequence observation.

we may interpret the dIRM as an extension of the iHMM, which has N (= a number of objects) hidden sequences to handle relational data.


We can then differentiate Equation 3 to produce As described below, we will assume that the synapse strengths to each neuron are balanced between positive and negative values and that each neuron receives 256 inputs, so we can expect µ to be close to zero, and µ, ñi and cij to be much less than σ.

the right term of Equation 4containing the denominator σ 3 j , can be expected to be much smaller than the left term containing the denominator σ j .


By contrast, the brain structures that seem to be associated with the evaluation of reinforcement, such as the ventral tegmental area or nucleus basalis, make only sparse projections to early sensory cortex; and these projections are frequently modulatory in character, rather than synaptic.

exact computation of It might seem at first that the former of these two problems would also apply to the weight α(V i ) (in the first term of (3c )), in that execution of this portion of the update would also need to be delayed until this value-dependent weight could be calculated.


], one can show that  A suffer an expected regret of at least (1/2) • √ B/2 = √ B/4 in this interval.

it remains to consider the case with N 2 < √ B/2.


( 5) and see Algorithm 3.2): ; =1 2Nonlinear conjugate gradient methods, such as Polak-Ribiere's CG (see Mizutani and Jang [13]) and Moller's scaled CG [14], are also widely-employed for training MLPs, but those nonlinear versions attempt to approximate the entire Hessian matrix by generating the solution sequence {Ih} directly as the outer nonlinear algorithm.

they ignore the special structure of the nonlinear least squares problem; so does Pearlmutter's method [15] to the Newton formula, although its modification may be possible.


( 8) is not convex with respect to all three unknowns (B, S and Θ) together.

a good algorithm in general exhibits convergence behavior to a stationary point and we can use Block Coordinate Descent algorithm [1] to iteratively update B, S and Θ as follows: while not convergent do For i = 1, . . . , N , solve min Solve min Solve min end do Since p(x|η) is in the exponential family, the subproblem (10) with respect to B is convex and smooth with simple constraints, for which quasi-Newton methods such as projected L-BFGS [22] are among the most efficient methods.


Further assume that there exists a constant r > 0 such that Φ is differentiable for any ν such that ν − µ ∞ ≤ r. Then, a subset of a linear subspace.

for −Θ t , −Θ t−1 ∈ V , w t+1 = w t . Hence, by Theorem 3.9, On the other hand, note that f i ∞ ≤ M . Then where the last inequality is due to Hoeffding's inequality.


The goal in many works in revenue maximization is to find a price p such that r * − r(p) ≤ , or alternatively, to bound r * /r(p).

given a revenue-estimation error n , one can clearly maximize the revenue within an additive error of 2 n by simply posting a price p * n ∈ arg max p r n (p), thereby attaining revenue good revenue estimation implies good revenue maximization.


Past research [9,18,38] has demonstrated that an elastic net encourages the grouping effects among variables so that highly correlated variables tend to be in or out of a mixture model together.

it can potentially augment the aforementioned method with the ability of dealing with the situation where the features of a high dimensional sample are highly correlated.


However, it is well-known that the Wasserstein distance is not negative definite [Reininghaus et al., 2015] (Appendix A).

we may not obtain positive definite kernels, built upon from the Wasserstein distance.


• The retrieval quality of X q measured by the total similarity x∈Xq s(q, x) should be large.

our objective is to retrieve a set of items that maximizes the ranking quality while lowering the computational cost (keeping the candidate set as small as possible).


Then by introducing the variable u = p 1 n 1, the objective in problem (7) satisfies hp, zi = z + hu, zi = z + hu, z zi because hu, 1i = 0.

thus problem ( 7) is equivalent to solving Notably, by the Cauchy-Schwarz inequality, we have hu, z zi  p 2⇢ kz zk 2 /n = p 2⇢s 2 n /n, and equality is attained if and only if Of course, it is possible to choose such u i while satisfying the constraint if inequality (8) holds for the vector z-that is, there is enough variance in z-we have For losses `(✓, X) with enough variance relative to `(✓, X that is, those satisfying inequality (8), then, we have A slight elaboration of this argument, coupled with the application of a few concentration inequalities, yields the next theorem.


Moreover, our method uses static linear policies and a simple local exploration scheme, which might be limiting for more difficult RL tasks.

better evaluation schemes are needed for determining the benefits of more complex RL methods.


As n becomes large-i.e., the spike count is obtained over a larger period of time-the binomial is well approximated by a Gaussian: Using the Gaussian approximation, Equation 1 can be rewritten in the form of a logistic function: , where and fxi = f xi /n denotes the observed spike rate for a feature detector.

because of the logistic relationship, if attentional priority is given to locations in order of their target probability, P (T x |F x , ρ), then it is equivalent to rank using r x + n 2 s x .


Note that like many sophisticated Bayesian models, posterior inference remains as a key challenge of developing novel RegBayes models.

one of our key technical contributions is on developing efficient and accurate algorithms for BMC, as detailed below.


The rank-k matrix A k obtained by computing the SVD is also optimal with respect to any rotationally invariant norm, such as the operator and Schatten-p norms.

such norms can also be solved exactly in polynomial time.


In this model, each (discrete) component in the observation vector of an instance depends only on one of the active latent features of that object, randomly drawn from a multinomial distribution.

different components of the observation vector might be equally distributed.


In fact, FTL is shown to be the minimax optimizer for the binary losses in the stochastic expert setting in the paper of Kotłowski [2016].

we ask the question of whether there are other regularities that allow FTL to achieve nontrivial performance guarantees.


By Lemma 3, every d-cell in the partition induced by the k objects corresponds to an equally probable ranking of those objects.

the probability that a query is ambiguous is the number of cells intersected by the corresponding hyperplane divided by the total number of d-cells, and therefore A(k, d, U ) = P (k,d) Q(k,d) .


Social media and social networking sites are increasingly used by people to express their opinions, give their "hot takes", on the latest breaking news, political issues, sports events, and new products.

there has been an increasing interest on leveraging social media and social networking sites to sense and forecast opinions, as well as understand opinion dynamics.


In the negative direction, even a family of regular languages as simple as the shuffle ideals is not efficiently properly PAC learnable under general unrestricted distributions unless RP=NP.

the search for a nontrivial properly PAC learnable family of regular languages continues.


A powerful technique for partitioning simple graphs is spectral clustering.

we generalize spectral clustering techniques to hypergraphs, more specifically, the normalized cut approach of [16].


CANNs, also known as neural field model, have been successfully applied to describe the encoding of head-direction in neural systems [16].


In addition, since the layers between two adjacent weighted layers are usually activation function or pooling operation along kernel dimensions (not the permuted dimensions along the channels), we can merge the output permutations of the previous layer with the input permutations of the next one.

on average, each layer only requires one reordering data movement.


Take y = x * + ( /κ) ĝt , and observe that y − x * ≤ /κ.

the ( , κ, x * )-SLQC assumption implies that ĝt , y − x t ≤ 0, and therefore Setting η = /κ, the above implies, after T iterations for which f It can be shown that strict-quasi-convexity and (G, /G, x * )-local-Lipschitzness of f implies that f is ( , G, x * )-SLQC ∀x ∈ R d , ∀ ≥ 0, and x * ∈ arg min x∈R d f (x).


For preprocessing method A, normalization generally produced a small improvement.

promising results can be obtained using the average ERP in response to standard beeps, using ICA followed by normalization (fourth results column): error rates of 5-15% for some some subjects are comparable with the performance of, for example, well-trained patients in an SCP paradigm [1], and correspond to information transfer rates of 0.4-0.7 bits per trial (say, 4-7 bits per minute).


Note that the performance for the full graph is consistently lower than that for the chain graph.

interestingly enforcing more order constraints does not necessarily imply better performance.


Consistent with [31], the first hidden layer with L 1 or L 2 regularization is capable of keeping the interactions separated, but at the second hidden layer, nearly all hidden units entangle the interactions at every threshold when at least one of the interactions is modeled.

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


l), the independence is guaranteed also for whole column vectors of u.

standard leA can be applied to patches of sources which yields 0 as the de-mixing matrix.


A common practice in the collaborative filtering community is to remove all users with fewer than some minimal number of ratings.

the results reported on the standard datasets, such as MovieLens and EachMovie, then seem impressive because the most difficult cases have been removed.


Moreover, adding high-quality labels to training data manually is often expensive.

it is desirable to use regularization methods that exploit unlabeled data effectively to reduce over-fitting in semi-supervised learning.


Obtaining E t from A t can be achieved by the polar-decomposition, which is a cubic-time operation: currently there are no algorithms known that can update an existing polar decomposition from an updated Cholesky factor in less than cubic time.

if our goal is to apply the fast Cholesky update, we have to perform the update without this correction factor This introduces some error, but we will show in the following that we can expect this error to be small and to decrease over time as the algorithm converges to the optimum.


The results of the previous section imply that even though the discriminative logistic regression algorithm has a lower asymptotic error, the generative naive Bayes classifier may also converge more quickly to its (higher) asymptotic error.

as the number of training examples m is increased, one would expect generative naive Bayes to initially do better, but for discriminative logistic regression to eventually catch up to, and quite likely overtake, the performance of naive Bayes.


As a consequence, we have to use a different Rademacher complexity with the absolute value inside the supremum [35,36], whose contraction makes the coefficients of ( 15) doubled compared with Lemma 8 of [19]; moreover, we have to assume G is closed under negation to change back to the standard Rademacher complexity without the absolute value [28].

the differences of ( 13) and ( 14) are mainly due to different proof techniques and cannot reflect the intrinsic differences of empirical risk minimizers.


Importantly, it can be shown that the updated one still satisfies the conditions of Theorem 2 for large n. Since the bound given in Theorem 2 is uniform, the inequality ( 8) can be recursively applied to the sequence of f (t) (t = 1, 2, . . . ).

, we have that where poly(d, K) means a polynomial of d, K. if s 2 < 1 and n is sufficiently large compared with d and K, then the second term is smaller than the first term and we have S n ≤ Cn − 1 1+s with a constant C. Furthermore, we can bound the L 2 -norm from the true one as in the following theorem.


However, in our transfer settings, all distributions involved depend on the family of tasks under consideration and making such assumptions is likely to limit the applicability to specific problems.

we take a different approach to derive a more general, but still well-grounded, solution.


The reason for this reverse prediction is the following: most widely accepted performance measures target information retrieval (IR) applications -that is, given a label we want to find a set of relevant instances.

the measures are averaged over the set of possible labels.


Figure 1(b) illustrates how belief state B can be reached in one step from tangent belief state B , and how the backed up value function improves B 's current value.

if we add a node to the controller that maximizes the value of B , its improved value can subsequently be backed up to the tangent belief state B , breaking out of the local optimum.


In particular, this generative model implements assumptions about the expected distribution of measurements.

the likelihood of a measurement is large when measurements are assumed, by the decision maker, to be reliable and small otherwise.


Next, we compute the variability in RKHS norm of a set of conditional mean embeddings as the deviance of the RKHS norms of that set.

using the KCDC measure S X→Y with we compute the deviance in RKHS norm of the set {p(Y |X = x i )} n i=1 .


We do not observe A(M ) directly; rather, we estimate each entry (A(M )) i by preparing many copies of the state M , measuring the Pauli observable S i on each copy, and averaging the results.

we observe y i = (A(M )) i + z i , where z i is binomially distributed.


Since PPO is not metatrained, there is no difference between both directions.

the performance of PPO is the same as shown in Figure 6.


This is the textbook contextual bandit problem [9].

there are |S| = m different ads to select from, and each round we receive, for each ad s ∈ S, a feature vector z s . the complete context is z = [z 1 , .


For this, we need the following result: Lemma  This result establishes that, when C t converges to a certain shape (but not necessary to a certain scaling), A t and thus E t will also converge (up to scaling).

thus, as we only need the norm of p σ,t+1 , we can rotate the coordinate system and by multiplying with E t we obtain if E t E T t−1 t→∞ −→ I, the error in the norm will also vanish due to the exponential weighting in the summation.


Note that the function in equation (3.1) is a concatenation of two quadratic functions, connected together with a linear function.

the box penalty will favor sparsity only for a = 0, case that is defined by a limiting argument.


We find that the biological spike generation mechanism has higher information capacity than the Poisson encoder and IF neurons.

neurons act as AD converters with stronger noise-shaping than IF neurons.


Generally, human action can be observed from multiple views, where the same action appears quite different.

it is important to learn discriminative view-invariant features, especially for action recognition from unknown or unseen views.


The corresponding probability bounds c d,x,y are 0.1, 0.05, 0 (no dependence on d, x, y).

and in the same broad spirit as for COMPAS, decreases in income, small changes in age, and small increases in education (events (1), ( 2)) are permitted with small probabilities, while larger changes in age and education (event (3)) are not allowed at all.


A practitioner asking by how much two samples differ does not want to receive a blizzard of answers for every conceivable kernel and bandwidth setting, but a single measure that satisfies some "reasonable" notion of distance across the family of kernels considered.

in Section 4, we propose a generalization of the MMD, yielding a new distance measure between P and Q defined as which is the maximal RKHS distance between P and Q over a family, K of positive definite kernels.


As expected, the bounds suggest that kernel machines will generalize well for bipartite ranking.

we recover the results of [2] obtained in a specific framework of algorithmic stability.


In addition, weights W h,k and w π,k are additional parameters.

moS can be regarded as an additional layer or mixing technique rather than the improvement of the activation function.


It incorporates our assumptions about which spike-patterns should be regarded as similar "messages".

the choice of the kernel-function is closely related to specifing what the search-space of potential neural codes is.


Hence it can be minimized using Queyranne's algorithm [2].

we have a procedure to compute optimal 2clusterings.


In addition, the mean square error, as shown in the above equation, preserves almost the same convergence rate as if the full data is employed and the true model is known.

we expect a similar or better performance of message with a significantly lower computation load.


Initialize() sets the initial g-values of all vertices to infinity and sets their rhs-values according to Equation 1¡ 03-04¢ .

initially E GF IH QP RF is the only locally inconsistent vertex and is inserted into the otherwise empty priority queue with a key calculated according to Equation 2¡ 05¢ .


Furthermore, in the inner zero-sum game of Equation ( 6), π is chosen as the maximizer of ρ(π, τ ).

we can see Definition 3 as a special case where π is fixed rather than chosen dynamically.


The motion energies from two neighboring locations are considered as the retinal images to the left and right eyes.

we can construct a differential motion opponency by placing two populations of phase shift motion energy neurons at different spatial locations and the energy ( ) v E Δ Θ of the opponency is the squared modulus of the averaged phase shift motion energies over space and phase, where ( ) , , w x y Θ is the profile for differential motion opponency and v Δ is the velocity difference between the two spatial regions defined by the kernel ( ) , , w x y Θ .


Furthermore, although these properties might only hold in an approximate or heuristic sense, the created active learning algorithm will be "safe" in the sense that it will eventually converge to the same solution as a passive supervised learning algorithm.

we believe this approach can be widely used to reduce the cost of labeling in situations where labeling is expensive.


One of the strengths of the proposed method is that it is agnostic to the input data, in particular to the way input alignments are constructed and to the inference parameters (regularization strength).

one could envision using alignments of close homologs to elucidate the co-evolution of a variable region in the protein (e.g.


YGGDRASIL, on the other hand, scales well up to D = 20, for which it runs up to 6× faster.

for the Yahoo dataset, YGGDRASIL's speed-up is even greater because of the higher number of features p -recall that the communication cost for PLANET is proportional to 2 D and p. for D = 18, YGGDRASIL is up to 24× faster than Spark MLLIB.


We have upperbounded log(8em/k i ) by log(8em).

where Given the training data size and the number of labels, Theorem 1 reveals one important factor in reducing the generalization error bound for the GCC model: the minimization of the sum of reciprocal of square of the margin over the labels.


Proof of Theorem 4.5: A and g B defined in Lemma 4.8.

it follows from Lemma 4.6 and Lemma 4.7 that for V 2 R n⇥d with V T V = I we have the Fair PCA problem is equivalent to We proceed to prove the claim by contradiction.


Equation (3) defined a prior on s with parameters W . We now add a hyperprior on W under which the expected power of both tangential components at the vth voxel is determined by a hyperparameter α v . For notational convenience we collect the α v into a vector α and introduce a d s × d v indicator matrix J, with J iv = 1 if the ith source is located in the vth voxel and 0 otherwise.

each column of J contains exactly two unit entries, one for each tangential component of the corresponding voxel dipole.


For most real-world scenarios such as road scenes, objects often lie on the ground.

the quaternion has only one rotational degree of freedom: i.e., q ∈ R. As shown in Fig.


As these techniques do not reliably measure sub-threshold potential but report only spiking activity, they would reveal only the strongest connections that can drive a neuron to fire [27][28][29][30].

such combination would reveal only a small fraction of the circuit.


Thereby it extends pure Hebbian learning, which requires only the coincidence of pre-and postsynaptic activity.

experiments have shown an asymmetric exponential dependence on the timing of spike pairs and a molecular mechanism mostly dependent on the influx of Ca 2+ (see [4,5] for reviews).


But it is also known that deep neural networks are over-parameterized to aid generalization.

to achieve faster speeds, some prior works explore new structures such as fully convolutional networks, or lightweight models with fewer channels and small filters [22,25].


Given a multitask problem consisting of m tasks, we construct a LGNN for all tasks with the shared parameters.


Hence, it is impossible to upper bound the multitasking capacity of every network with average degree d by f (d)n with f vanishing as the average degree d tends infinity.

the generality of the suggested tradeoff between efficiency and concurrency is not clear under this definition.


For computational efficiency reasons, Bayesian Sets is typically run on binary data.

each item in the data collection, x i ∈ D, is represented as a binary feature vector x i = (x i1 , .


We thus have and where in the last line, we use the Taylor expansion again to expand f around Q k c + 1 − Q 2 k e and the bracket • denotes the average over two independent random variables c ∼ P c and e ∼ N (0, 1).

we have where the function G(Q) is defined in (11).


In contrast, if this sub-module is fast but numerically or statistically unstable, the errors will propagate in unpredictable ways, and can adversely affect the parameter estimation.

we need a scheme that balances performance and efficiency.


When solving R h , we often observe that many of the eigenvalues of the data covariance matrix T qn are close to zero, which makes the solution of R h very unstable.

we introduce a L2 regularization to the cost function.


Thanks to the CFT, the samples from the reverse simulation contribute most strongly to the integral in the JE.

if we can use the reverse paths to estimate the forward work distribution, p f will be quite accurate in the region that is most relevant for evaluating JE.


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

for Experiment 2, we developed a paradigm in which showing how to do a task, as opposed to merely doing a task, makes a difference for how well the underlying reward function is learned.


The overall performance, in terms of Kendall 's τ and rank is comparable to the Thurstonian model and the Borda count method.

there does not appear to be any overall advantage of this particular approach.


Nevertheless, categorization in humans is a standing problem in Neurosciences and Psychology, and no one is certain what information is utilized and what kind of processing takes place when constructing object categories [8].

the task of classifying object shapes is often cast in the framework of supervised learning.


If 0 < pc,r < ✏, replacing or retaining r doesn't affect the performance of SEQ-ELIMINATE significantly.

in other words we've reduced the problem to testing whether pc,r ≤ 0 or pc,r ≥ ✏.


The Optimization Problem It has been argued in [3,18,11,17] and finally shown in [5] that AdaBoost and Logistic Regression under certain condition asymptotically converge to a combined hypothesis minimizing the respective loss on the training sample, where is a linear combination of hypotheses from , i.e. .

they solve the optimization problem: where we defined a matrix with .


In Triple-GAN, D may memorize the empirical distribution of the labeled data, and reject other types of samples from the true data distribution.


The encoder used in [14] is a simple feedforward function which can also be seen as a small convolutional neural network: This function has been shown to produce good features for object recognition [14], however does not include a shrinkage operator, thus its ability to produce sparse representations is very limited.

we propose a different encoding function with a shrinkage operator.


Nowadays, hardware is heavily optimized for current architectures and does not necessarily reflect the concept of any-time-computation.

we focus on analyzing the number of multiply-accumulate operations (MAC).


This process repeats through more levels until fractions of the single "elephant" signature have reached all leaf nodes.

a single class signature emulates the estimated statistics of a full training set of class-labeled instances with attribute predictions.


It can be shown [12] that optimization of a cumulant-based criterion, similar to equation ( 2), can separate independent sources with nonstationary variances.

the maximization of the objective function can also be interpreted as estimation of generative models in which the activity levels of the sources vary over time, and are temporally correlated over time.


Otherwise, g(s goal ) is already equal to the cost of an optimal solution.)

the actual sub-optimality bound for ARA* is computed as the minimum between and the ratio (lines 05' and 13', Figure 3).


As we mentioned before, we would like to promote low-dimensional vectors for regularization that are not strongly correlated in high-dimensional space h, therefore we propose the function exp(−|a|/β) that takes the highest values for a close to 0.

we promote the pairs of vectors in the criterion L M AC for which distances are around M/2 and put less force to the pairs for which the distances in high-dimensional space are close to 0 and M . While optimizing L M AC in each iteration of gradient method we assume that b h,k are constant and calculated from the h(x) layer of discriminator by application of the sign(•) function.


Under the conditions of Theorem 4.1, for any M ∈ M \ Q, (z, η) is not M-proper.

proof Since the columns of V are in the ambiguity sets and form a basis of R d , span(∪ c−1 j=0 A j ) = R d . the n-th column of any arbitrary M can be represented as m n = c j=1 α n,j w j for some w j ∈ A j and some coefficients α nj .


If ρ(r, r(A)) and ρ(c, c(A)) are both at most 1, then under the assumption that r(A) − r 1 + c(A) − c 1 > ε , our progress is at least Likewise, if either ρ(r, r(A)) or ρ(c, c(A)) is larger than 1, our progress is at least 1/2n ≥ 1 28n ε 2 .

we terminate in at most 28nε −2 log(s/ ) iterations.


In Figures 2a and 2b, we cut the plot in 50% because, in these two databases, the discrete attributes present a mode value that is present for more than 80% of the instances.

the SIBP and the BPMF algorithms assign probability close to one to the mode, which results in an artificial increase in the average test log-likelihood for larger percentages of missing data.


The function that returns this next state deterministically is called simulate(s,a).

given the state s and the action a, the next state s has probability P a (s, s ) = 1 if s = simulate(s, a), and 0 otherwise.


The stationary condition for q( w qm , s qm ) is where Z is a normalizing constant that does not depend on { w qm , s qm }.

we have q( w qm |s qm = 0) ∝ q( w qm , s , where C = e log p(Y, wqm,sqm=0,Θ) q(Θ) is a constant that does not depend on w qm .


(2007) show that the stick lengths (i.e., partitions) induced by a Poisson point process on [0, 1] with the beta Lévy measure have the same distribution as those in the stickbreaking construction of the DP.

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


In this example, a context can be defined as the neural activities of other nearby neurons, or as neural activity in the past.

it is plausible that the activity of each neuron depends on its context.


On the other hand, the optimization is dominated by the unregularized part of the objective function.

the iterates of the optimization algorithm will be close to an optimum of the unregularized objective function.


For each trial of the EEG raw data, we only use part of the sample points, i.e., from No.1001 to No.1750, as the experiment data since they carry most of the information in the EEG signal.


It can be solved in O(n 3 ) using algorithm due to Edmond and Karp [8] or max-product belief propagation by Bayati, Shah and Sharma [9].

this is an approximation that can be evaluated.


Theorem 2 implies that θ * λ is inside a ball centred at θ * λ0 with radius Recall that to make our screening rules more aggressive in discarding features, we need to get a tight upper bound .

it is desirable to further restrict the possible region A λ of θ * λ .


( 2), can be written as , and shows that PCA will maximize variance, no matter whether this variance comes about through a single marginalized variance, or through mixtures thereof.

we need to modify this objective function such that solutions w that do not mix variances-thereby falling along one of the axes in x-space-are favored over solutions w that fall into the center in x-space.


Previous work in CDec-POMDPs develops an actor-critic RL approach when the joint reward is additively decomposable among agents [25], and is unable to address non-decomposable team rewards.

we develop multiple actor-critic approaches for the general team reward setting where some (or all) joint-reward component may be non-decomposable among agents.


With such a hierarchical and flexible model, there would be significant risk of over-fitting, especially when we consider all possible interactions between K latent factors.

regularization has to be introduced for better generalization property of the model.


The random variable K t , which denotes the index of the current theoretical peak index, is a deterministic function of its parents, such that p(K t = K t−1 + δ t |K t−1 , δ t ) = 1.

δ t > 1 corresponds to the deletion of δ t − 1 theoretical peaks.


M be the best linear predictor of i,j|S to be the entry in β Note that in general β , where Pa (k) (j) denotes the parents of node j in G (k) .

when ij , then there exists a set S such that β (k) i,j|S stays invariant across k = {1, 2}.


Thus, synchrony between A and B occurs whenever N A * F L = N B * F R , i.e., for a specific set of filter pairs (F L , F R ).

in our model, sounds presented at a given location induce specific synchrony patterns, which then activate a specific assembly of postsynaptic neurons (coincidence detection neurons), in a way that is independent of the source signal (see Goodman and Brette, in press).


Note that if we examine the posterior distributions of the weights we see that if each x n contains only one nonzero value then each factor in the likelihood is dependent on only one of the K weights and can be multiplied into the corresponding k th spike-and-slab.

since the product of a spike-and-slab and a Gaussian is still a spike-and-slab, if we stimulate only one neuron at each trial then this posterior is also spike-and-slab, and the variational approximation becomes exact in this limit.


However, in the "conditional random sample" obtained from CRS, at least one element at the D s th column is non-zero.

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


While the first term is available in closed form, the second is in general not.

using the concavity of the logarithm function, Jensen's inequality yields a lower bound that can be used in place of the intractable original objective, resulting in the final component identification optimization: A more detailed derivation of the optimization may be found in the supplement.


Using this inequality we obtain Note that L is unbiased and g does not depend on S i or S j .

for every fixed setting of S i and z, E Sj ∼P g(S i ) • L(S j←z , S j ) = g(S i ) • E P [L(S j←z )] = 0.


These updates simply require vector matrix operations.

the update complexity on each iteration is O(k 2 ).


Using the above procedure, at each timestep the number of bits stored in each B i h grows by: If the entries of z i,h are not close to zero, this compares favorably with the naïve cost of 32 bits per timestep.

the total storage cost of TBPTT for a RevGRU model with hidden state size H on a sequence of length T will be 7 : in the idealized case, the number of bits stored equals the number of bits forgotten.


In the extreme case of only two quantization levels, spike or no spike, each measurement contains only 1 bit of information.

to achieve reasonable reconstruction quality using quantized measurements, a larger number of trials M>>N is required.


Furthermore, since XOR_K maximizes this sum over all possible strategies a ∈ A, the sum it finds will be at least as good as the one attained at a * , which is already over T /2 .

we conclude that when k < k 0 , XOR_K will return true with high probability.


Indeed, when µ 1 > 0.9 and 2 (T ) with a probabilistic argument, where (T ) converges to 0 as T goes to infinity.

for large µ 1 and small µ 2 (so are µ i for i 2), we have that E[μ 1 (t i (k))] µ i = ⌦(µ 1 µ i ) holds for any i and k 2.


Also by definition of 'ljJ7r, F( ()) = L,s ,a p7r (s )n( a; s, ()) ' ljJ7r (s, a )' ljJ7r (s, a) T. Substitution leads to: Solving for w gives w = F(()) -l\71}(()), and the result follows from the definition of the natural gradient.

sensible actor-critic frameworks (those using f7r(s , a; w)) are forced to use the natural gradient as the weights of a linear function approximator.


Thus the duality gap at the k-th iteration is given by: We define the relative duality gap as: Rel.gap := Dgap/(1 + |pobj| + |dobj|), where pobj and dobj are respectively the objective function values of the primal problem (12) at point X k , and the dual problem (2 )}, we measure the relative changes of objective function value F (X) and the iterates X and Y as follows: We terminate ALM when either Note that in (19), computing log det(X k ) is easy since the spectral decomposition of X k is already available (see ( 14) and ( 15)), but computing log det( Σ − Λ k ) requires another expensive spectral decomposition.

in practice, we only check (20)(i) every N gap iterations.


Given E, a normalized version of the Laplacian can be defined as L = 2(diag(1 T E) − E)/(1 T E1), where 1 is the m × 1 all-ones vector.

the average squared error between adjacent lattice outputs can be compactly represented as inclusion of this term penalizes first-order differences of the function at the scale of the lattice.


This is the case even if the adversary has access to the entire list of probability distributions P before it commits to the causal graph G. We prove this in Section 3.

by Theorem 2.3, we have that min[O(log log n), log ω(U)] experiments are sufficient.


Computing the Mahalanobis distance is an O(d 2 ) operation.

total cost of line 12 is O(kd 3 + nkd 2 ) and the total running time of the algorithm, given τ iterations, is O(τ kd 2 (n + d)).


Many real-world anomalies can be detected in time series data.

systems that detect anomalies should reason about them as they occur over a period of time.


It is easy to see that the above lemma is still valid even when the condition of Ω-isomerism is replaced by k-isomerism.

hereafter, we may say that a space is isomeric (k-isomeric, Ω-isomeric or Ω T -isomeric) as long as its basis matrix is isomeric.


As for the optimal arm, when N 1 (t) , with high probability N 1 (t) = max j N j (t).

the controller does not need to pay compensation in time slots with a(t) = 1 and N  The second algorithm we propose is a modified "-greedy policy, whose details are presented in Algorithm 2.


[3]) goes in the other direction and provides a wavelet interpretation of deep neural networks.

we believe that there are ample opportunities for future work in the interface between wavelets and deep neural networks.


On the contrary, cluster 4 is stable in membership.

we can imagine that the group of energy and gas is a dense and strong community.


( 5) shows that the MSE is inversely proportional to the number r of workers per target item, while the number k of control items per workers only refines the multiplicative constant.

the resources assigned to the control items are much less "useful" than those assigned directly to the target items, suggesting the optimal k should be much less than the budget .


Regardless of the specific setting being considered, the main challenge in the analysis of privacy amplification by subsampling resides in the fact that the output distribution of the mechanism µ = M S (x) ∈ P(Z) is a mixture distribution.

in particular, writing µ y = M(y) ∈ P(Z) for any y ∈ Y and taking ω = S(x) ∈ P(Y ) to be the (finitely supported) distribution over subsamples from x produced by the subsampling mechanism, we can write µ = y ω(y)µ y = ωM , where M denotes the Markov kernel operating on measures defined by M. proving privacy amplifications results requires reasoning about the mixtures obtained when sampling from two neighbouring datasets x X x , and how the privacy parameters are affected by the mixture.


2, it suffices to pick For Theorem 3, it essentially asks for a well-conditioned design matrix at the sparsity level 2s + r. Note that (3) implies κ 2s+r ≥ σ max (Σ)/σ min (Σ), which in return requires a well-conditioned covariance matrix.

to guarantee that κ 2s+r ≤ 1 + ǫ for some ǫ > 0, it suffices to choose Σ such that σ max (Σ)/σ min (Σ) < 1 + ǫ and pick .


For example, we might want to detect objects of the scene as well as infer dynamics and track identities of any persistent objects.

we introduce Sequential Attend, Infer, Repeat (SQAIR), whereby AIR is augmented with a state-space model (SSM) to achieve temporal consistency in the generated images of the sequence.


By discarding the augmented variable λ k d , we get the samples of the posterior distribution p(η k d |η ¬k d , Z, W).

we can easily draw a sample from a univariate Gaussian distribution.


Concurrent UCRL is a deterministic approach according to which all the parallel agents construct the same optimistic MDP conditioned on the common shared information up to that time.

the concurrent UCRL agents do not diversify their exploratory effort.


Although somatic currents vary slowly, information that could be communicated by their analog amplitude far exceeds that of binary signals, such as all-or-none spikes, of the same sampling rate.

faithful digital encoding requires sampling rate of the digital signal to be much higher than the cut-off frequency of the analog signal, socalled over-sampling.


Since the eigenvalue decomposition is invariant under permutation, Ā and ĀP have the same eigenvalues and eigenvectors.

as e → ∞, K clusters of columns appear in ( ĀP ) e . ĀP can be made block-diagonal by clustering the columns of ( ĀP ) ∞ .


An autonomous agent acts rationally in such settings by constantly maintaining beliefs of the physical state and sequentially choosing the optimal actions that maximize the expected value of future rewards.

solutions of POMDPs map an agent's beliefs to actions.


in the general version of sLDA, the previous specification in step 3 of the generative process is replaced with so that The reader familiar with GLMs will recognize that our choice of systematic component means sLDA uses only canonical link functions.


Letting dq t (x) = df t (x, •) ∈ R Y , the market price at time t is given by, where 1 y is an indicator vector.

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


Thus, for that Player i, there exists some strategy k ∈ S i \ {j} such that x ik (t) ≥ x ik (0) + 1 2(ni−1) • x ij (0), and hence • min k∈Si x ik (0) max k∈Si x ik (0) .

the regret of Player i is at least 1 εiT times the RHS of the above inequality.


When ρ is small, we call the corresponding optimization problem as weakly semisupervised learning.

it is important to find an appropriate ρ which adapts for the input data.


The key point is to realize that the distributions ( 12) and ( 13) exactly match the distributions (4) assumed by the ML adaptation functions (5).

the ML adaptation should work provided that the maximizations in (5) yield the correct parameter estimates.


We need to bound δ t = w t (η) • t + 1 η ln(w t (η) • e −η t ), which is a convex function of t by Lemma 10.

its maximum is achieved when t lies on the boundary of its domain, such that the losses k t are either 0 or 1 for all k, and in the remainder of the proof we will assume (without loss of generality) that this is the case.


In particular, previous approaches proposed algorithms in which the optimal statespace decomposition was computed based on the optimal solution in the original (non-hierarchical) representation 15,16 .

the resulting state-space partition was designed for a specific (optimal) environment solution rather than the dynamics of the planning algorithm itself, and also required a priori knowledge of the optimal solution to the planning problem (which may be difficult to obtain in general and renders the resulting hierarchy obsolete).


The reward obtained for each of these events diminishes after repeated exposure to the event.

automatically, the skill of achieving the simpler events are learned before those for the more complex events.


In this case, the reward of seed selection is only instantiated after the seed selection, and is only one of the random outcomes.

when the stochastic reward function is unknown, we aim at maximizing the expected reward overtime while gradually learning the key parameters of the expected reward functions.


Initial safe policy Lastly, we need to ensure that there exists a safe starting point for the learning process.

we assume that we have an initial policy π 0 that renders the origin of the system in (1) asymptotically stable within some small set of states S x 0 .


[2015] derived that the GTD algorithms to minimize (2.3) is equivalent to the stochastic gradient algorithms to solve the following convex-concave saddle point problem with x as the parameter θ in the value function, y as the auxiliary variable used in GTD algorithms.

we consider the general convex-concave stochastic saddle point problem as below where X x ⊂ R n and X y ⊂ R m are bounded closed convex sets, ξ ∈ Ξ is random variable and its distribution is Π(ξ), and the expected function φ(x, y) is convex in x and concave in y. Denote z = (x, y) ∈ X x × X y X , the gradient of φ(z) as g(z), and the gradient of Φ(z, ξ) as G(z, ξ).


For instance using RNN cells with good long-term memory, like EURNNs [21] or NARX RNNs [26,8], for the Slow cell might boost the long-term memory of the FS-RNN architecture.

the FS-RNN architecture might improve performance in many different applications.


As noticed by Herbster and Warmuth [HW98], multiplicative updates drive the weights of poor experts to zero so quickly that it becomes difficult for them to recover if their experts subsequently start doing well.

the second share update prevents the weights of experts that did well in the past from becoming too small, allowing them to recover quickly, as shown in Figure 4.


The Rice distribution has the property that For simplicity we perform inference using R 2 , as opposed to R, and transform accordingly: The complete likelihood ( 8) is the product of two exponential family models and is exponential family itself, parameterized with base measure h and partition factor g: By inspection we see that the natural parameters η and sufficient statistics S are the same as a Gaussian with unknown mean and variance.

we apply the normal-gamma prior on (ν, τ ) as it is the conjugate prior for the complete data likelihood.


a false zero entry on A allowing several orderings leading to several lower triangular versions of A, only one of those being actually correct.

we propose not only to use the best candidate but a set of top candidates of size m top = 10.


The average of these functions reaches its minimum of r , so we can view optimizing these functions as the task of discovering the vectors v reven if only v k is missing, a suboptimality better than b/(6 p k) > ✏ cannot be achieved.

the deterministic algorithm must complete at least k rounds of optimization, each comprising at least ⌃ m 2 ⌥ queries to h F in order to optimize F . The key to this construction is that even though each term |hx, v r 1 i hx, v r i| appears in m/2 components, and hence has a strong effect on the average F (x), we can force a deterministic algorithm to make ⌦(m) queries during each round before it finds the next relevant term.


However, a validation set matching the network sparsity would have too few links.

we compute the validation log likelihood at network sparsity by reweighting the average link and non-link log likelihood (estimated from the 50% links validation set) by their respective proportions in the network.


Many general-purpose solvers for SDPs exist in the public domain (e.g., [2]), but even for systems with sparse constraints, they do not scale very well to large problems.

for small networks, this approach to sensor localization is viable, but for large networks (n ∼ 10 4 ), exact solutions are prohibitively expensive.


Intuitively, limiting action selection only to temporally-extended options might hamper the exploration of the environment by restricting the policy space.

we argue that in addition to the exciting work being done in heuristic and algorithmic approaches that leverage and/or dynamically discover options, it is important to build a formal understanding of how and when options may help or hurt reinforcement learning performance, and that such insights may also help inform empirically motivated options-RL research.


In total, the dataset contained 785, 751, 531 features after hashing, which means that each instance has about 313 features on average.

the average sparsity of each data point is 0.0012.


Nonetheless, for many of the SDPs that appear in machine learning, feasible points are easy to identify, and equality constraints are either absent or fortuitously pose no difficulty.

we can gain further intuition by observing that Random Conic Pursuit's iterates, X t , are positive weighted sums of random rank one matrices and so lie in the random polyhedral cones Random Conic Pursuit optimizes the SDP (1) by greedily optimizing f w.r.t.


However, especially in the biomedical domain, obtaining labeled training examples through experiments can be costly.

combining information from several related tasks can be a cost-effective approach to best exploit the available label data.


DNA storage datasets will be separated with r 2 r 1 .

recovering the clusters corresponds to finding pairs of strings with distance at most r 1 .


It is well known that REINFORCE may learn slowly than other methods that use a learned action-value function (Sutton et al., 1999).

we next present a function approximator for Q π t , and show the computation of policy gradient by directly sampling counts n. One can approximate the action-value function Q π t (s t , a t ) in several different ways.


However, the sampler is very unlikely to reduce the number of states through these actions, if all states are used in multiple segments, so that convergence might take a very long time in this case.

we introduce the option to join all segments assigned to a neighboring (when ordered by their λ-values) pair of states into one state.


Since the theory contains no independent subtheories, there must be an atom a in C n which unifies with an atom a c in C c n , or C c n is empty.

after shattering, all unifications bind one variable from a to a single variable from a c . Because a contains exactly n variables from B, a c must also contain exactly n (Definition 4), and because B is a root binding class, the clause of a c also contains exactly n, which contradicts the definition of C c n . C c n is empty, and because the variables in B are root, they also appear in all atoms.


Importantly, the algorithm we present is based on iterative reweighting and ADMM and is fast enough-linear in the input size when k is fixed, and highly parallelizable-to allow for computing a regularization path of features by varying the pointer cost.

we may adapt the compression to the data at hand and select features that better elucidate its structure.


However, all of them are perfectly correlated.

expected uncertainty after querying all p = 1 nodes is still n/8.


Similarly, the exact factors ψ i , with i = 1, . . . , n, corresponding to the prior for the latent variables z, (3), only depend on ρ and z i .

the Gaussian part of the corresponding approximate factors can be removed and the multivariate Bernoulli distribution simplifies to a univariate Bernoulli.


In Theorem 4.5, ⇢ is the contraction parameter of linear convergence rate, and it depends on the step size ⌘.

we can always choose a sufficiently small step size by choosing a small enough C 0 , such that ⇢ is strictly between 0 and 1.


For instance, this quantity may depend on the dimension of the input n (see [17,Appendix C] in the extended version of this paper).

the number of iterations for reaching a desirable accuracy may be very large.


This can be explained by the increasing size of receptive field and feature complexity in the network hierarchy.

it is advantageous to use features at all five layers to fully capture the characteristics of a style from low to high levels.


That is, we update parameters from an arriving document and discard the document after doing l iterations.

we do not need to store statistics about discarded documents.


There are N x possible ways of choosing the positions of the x misclassified negative examples, and similarly N x possible ways of choosing the positions of the x = k − x misclassified positive examples.

in view of Lemma 2, the average AUC is given by:  Each curve corresponds to a fixed ratio of r = n/(n + m).


Fully connected layers Fully connected layers have weights ω in the form of a matrix, such that ω i ∈ R M i ×M i+1 .

the corresponding spline must have knots that also lie in the same space.


A simple two-dimensional example is visualized in Section 4.

gradient descent WGAN optimization is not necessarily asymptotically stable.


Note that if one considers a model of k filters with linear activation with k °1, one can always replace this model by a single convolutional filter that equals to the summation of these k filters.

we can formally study the statistical behavior of wide and deep architectures only after we have understood the non-linear activation function.


In its simplest form, their result shows that when m D K (µx 0 ) then with high probability, ) Here, D K (µx 0 ) is the Gaussian width, a specific measure of complexity of the constrained set K when viewed from µx 0 .

for our purposes, it suffices to remark that if K is properly chosen, and, if µx 0 is on the boundary of K, then D K (µx 0 ) is less than n. estimation is in principle is possible with m < n measurements.


They conducted experiments on three datasets, of which only the webspam dataset is public and reasonably high-dimensional (n = 350000, D = 16609143).


In fact, our lower bound holds even if the algorithm is allowed to output a rank-k approximation for any 2 ≤ k = o(min(m, n)) whose cost is at most that of the best rank-2 approximation to A.

we call the latter a bicriteria algorithm, since its output rank k may be larger than the desired rank k. in some sense obtaining additive error (1.1) is the best we can hope for.


However, MADDPG and COMA have to train an independent policy network for each agent, where each agent would learn a policy specializing specific tasks [11], and the policy network easily overfits to the number of agents.

mADDPG and COMA are infeasible in large-scale MARL.


This is a weak solution, however, since evasion tends to be rather quick, and re-learning is a costly task, since it requires one to label a large number of instances (in crowdsourced labeling, one also exposes the system to deliberate corruption of the training data).

several efforts have focused on proactive approaches of modeling the learner and adversary as players in a game in which the learner chooses a classifier or a learning algorithm, and the attacker modifies either the training or test data [13,14,15,16,8,17,18].


There are only 10 relevant images among 7,170 training images.

we also used Euclidean neighbor ground truth labels computed from visual data as in [6] (Figure 3c).


In the outdoor scenario, we assume that at least the vertical vanishing point is given, or equivalently, that the orientation (but not position) of the ground plane is known.

we only need to search for a 1-D angle θ, i.e., the azimuth, in order to estimate the rotation of the 3D box.


The indeterminacies actually reduce to just inevitable monotonic component-wise transformations in the case of modulated Gaussian sources.

our results pave the way for further developments in nonlinear ICA, which has so far seriously suffered from the lack of almost any identifiability theory, and provide a new principled approach to unsupervised deep learning.


It also suggests that the simple descent-ascent update rule might not converge-as it has also been observed before in the literature; see, e.g., [29] .

one should use algorithms similar to the two time scale approaches that give discriminator increasingly more advantage.


This property is particularly important for computationally efficient recovery methods.

even though it is in general NP-hard to check that RIP holds, there have been substantial efforts to find tractable proxies for it.


Let η = min σ∈Sn η σ , and let p be an arbitrary member of B(p, η).

by the definition of ε, we have: ∀σ ∈ A (p) , L (p , σ ) > L (p) + ε. Additionally, the definition of η gives ∀σ ∈ A (p) , L (p , σ) < L (p) + ε.


The NMDA channel has the following equation: For simpler notation, in general we use inverse time-constants In addition, the term a 1 − b 1 in the denominator is required for later easier integration in the Laplace domain.

we adjust for this by defining ḡ = 12 mS/ms which represents the peak conductance (4 nS) multiplied by b 1 − a 1 .


This is done by first considering the problem assuming the joint distribution of all the random variables is known, and is accessible via an oracle.


In order to avoid overly aggressive pruning in the early stage of the value iterations, we need to take into account the size of the value function at every iteration.

we use a sliding pruning strength specified as J E~=o j3i extent(R) where R is the initial reward diagram, j3 is the discount factor introduced earlier and n is the iteration number.


Notice that VCN using ε = 1 is equivalent to VCN as described previously, so the points for ε = 1 in Figure 3(b) correspond exactly to the VCN data in Figure 3(a).

if the variance in gradient estimates precludes learning, we suggest making the policies of the modules more deterministic by decreasing exploration and increasing exploitation.


c times the number of examples, where c is a small constant, in the case of SCML.

the practical computational complexity of both our approach and classical methods is linearly dependant on the number of examples.


This naive grammar is a poor one because its context-freedom assumptions are too strong in some places and too weak in others.

a variety of techniques have been developed to both enrich and generalize the naive grammar.


Finding a radius: Remember that @i P rns, f i is differentiable with a 1{γ-Lipschitz gradient.

@i P rns, f i is γ-strongly convex [14, Theorem 4.2.2, p. 83] and so D λ is γλ 2 -strongly concave: Specifying the previous inequality for Θ 1 " p Θ pλq , Θ 2 " Θ P ∆ X , one has By definition, p Θ pλq maximizes D λ on ∆ X , so we have: x∇D λ p p Θ pλq q, Θ ´p Θ pλq y ď 0.


If, instead, we minimize f 2 for v def = w/γ and remove the ∞ constraint, we recover exactly ridge regression for the quadratic loss case and 2 -regularized boosting for the exponential loss case.

we can obtain a 1 -regularized version of Equation 17 by repeating the above steps and using 4n q − 1 2n 2 ≤ 2 q − 1 2n ∀q ∈ [0, 1/n] since, in that case, we find that KL(Q To sum up, the KL-regularized objective function f immediately follows from PAC-Bayes theory and p regularization is obtained from a relaxation of f . PAC-Bayes theory favors the use of KL regularization if the goal of the learner is to produce a weighted majority vote with good generalization.


However, for Gaussian graphical models, it is well-known that the graphical structure is encoded in the inverse of the covariance matrix Σ −1 = Ω, commonly referred to as the precision matrix [12,14,3].

accurate recovery of the precision matrix is paramount to understanding the structure of the graphical model.


the standard deviation of the stock's logarithmic returns in one year.

a trading interval of [0, 1] specifies 1 year.


1 CF-2g closely resembles the serial Seq-2g, but the elements e 2 V are no longer processed in a fixed order.

the sets A, B are replaced by potentially stale "bounds" Â, B, where Â is a subset of the "true" A and B is a superset (a) Ser-2g   The coordination-free approach attempts to reduce the need to coordinate guarantees and logical ordering.


In our approach, we would partition the domain, say as {{1, 3}, {2, 4, 5}}, and search over only the following 4 assignments: all groundings in each part can be either all true or all false.

if we are lucky and the MAP solution is one of the 4 assignments, our approach will yield significant reductions in complexity even though no identifiable symmetries exist in the problem.


o(N −1/2 ), whenever H ≥ log N d . Thus, using P = O( √ N ) random features, we deduce that the complexity of building the matrix Then in order to solve the least squares system, one has to compute Ψ T Ψ, that has numerical cost O(P 2 N ), and then solve the system by inversion, which has numerical cost O(P 2.376 ) by [5].

the overall cost of the algorithm is O(2 d N 3/2 log N + N 2 ).