However, with a single epoch of training H-RLS does not perform worse than SVM (except on OHSUMED under the normalized H-loss) and comes reasonably close to H-SVM.

the performance of APPROX-H-BAYES is disappointing: on OHSUMED it is the best algorithm only for the uniform H-loss, though it was trained using the normalized H-loss; on RCV1 it never outperforms H-RLS, though it always does better than PERC and H-PERC.


It is well known that an ensemble of multiple instances of a target neural network trained with different random seeds generally yields better predictions than a single trained instance.

an ensemble of models is too computationally expensive at inference time.


Many existing systems on structured prediction focus on increasing the level of structural dependencies within the model.

this trend could have been misdirected, because our study suggests that complex structures are actually harmful to generalization ability in structured prediction.


Furthermore, the construction of kernel induced feature spaces, lends itself to efficient implementation of distance measures over spike trains that are better suited to comparing two neural population trajectories than the Euclidean distance in the original space of spike counts per bins [11,5].

sVR is a "static" method that does not take into account the smooth dynamics of the predicted movement trajectory which imposes a statistical dependency between consecutive examples.


As a simple example in the binary classification setting, if p(x) is supported on two disjoint sets and if P (Y = 1|X = x) is strictly greater than 1/2 on one set and strictly less than 1/2 on the other, then perfect knowledge of the decision sets reduces the problem to a hypothesis testing problem for which ǫ 2 (n) = O(e −ζ n ), for some constant ζ > 0.

if γ is small relative to the average spacing n −1/d between labeled data points, then ǫ 1 (n) = cn −1/d where c > 0 is a constant.


Our model, along with various others, addresses these issues at a cortical level via two basic mechanisms: DA modulation, which changes the excitability of neurons in a particular way (units that are inactive are less excitable by input, while units that are active can become more active), and targeted input from the BG.

models differ as to the nature and provenance of the BG input, and also its effects on the PFC.


: empirically, we found that 1 or 2 iterations of FISTA [4] are sufficient to reach an accuracy of 10 −6 in problem (7), which is sufficient to obtain a good decomposition in the overall algorithm.

choosing γ "too large" will provably cause the dictionary updates to eventually take forever to run.


LRR is an important robust subspace clustering technique and has found wide applications in machine learning and computer vision, e.g., motion segmentation, face clustering, and temporal segmentation [12,14,6].

the existing LRR solver [12] is based on ADM, which suffers from O(n 3 ) computation complexity due to the matrix-matrix multiplications and matrix inversions.


Imitation learning algorithms can be used to learn a policy from expert demonstrations without access to a reward signal.

most existing approaches are not applicable in multi-agent settings due to the existence of multiple (Nash) equilibria and non-stationary environments.


Meanwhile, mixed tabulation is 40% faster than both MurmurHash3 and CityHash, which showed similar performance as mixed tabulation.

these two hash functions do not have the same theoretical guarantees as mixed tabulation.


Quasi-convex optimization problems arise in numerous fields, spanning economics [20,12], industrial organization [21] , and computer vision [8].

it is well known that quasi-convex optimization tasks can be solved by a series of convex feasibility problems [4]; generally solving such feasibility problems may be very costly [6].


[12], our algorithm stems from a particular characterization of clique trees of chordal graphs.

our characterization is quite different, being recursive in nature.


Note that one of these F i can be X itself (identity).

f i are not restricted to being a function of X and we drop the X to indicate this.


We see in Table 1 that the box kernel and the square exponential kernel produce similar results on the CMB data.

the kernel width was not optimized and different values may prove to yield superior results.


al [13] propose an intriguing parallel scheme for packing and covering problems.

our results apply to more general LP relaxations, including set-partitioning problems like multiway-cut.


Moreover, the "incoherence" conditions required for the success of convex methods are hard to interpret and verify in general.

our conditions for success are transparent and based on the presence of correlation decay in the model.


Again, we observed (Figure 3-top left) that the JS-divergence estimate remains close to 1 while training DCGAN with BN.

after applying two different Lipschitz regularization methods, SN and GP in Figures 3-top right and bottom left, we observed that the hybrid d JSD,W1 changed nicely and monotonically, and correlated well with the quality of samples generated.


As could be expected, for a fixed level of discrepancy between the initial and retrained models, the cascade scheme is capable of producing sparser networks.

the computational distributability of the parallel scheme makes it a more favorable approach for large scale and big data problems.


The following DAG G satisfies A: W → X Y → Z .

inferring the ordering constraints Z < W and X < Y from each ancestral constraint of A leads to a cycle in the above DAG (W < X < Y < Z < W ), hence eliminating the DAG.


For any sequence of querying rules and any autonomous user indexed by {u j } j2[M ] , there is a fixed constant c 0 such that the cost to the user satisfies Proof.

ideally, none of the M queries causes a premature halt, and the total cost is at most 96 ⌧ 2 (1 + ln(M )), but the adaptive user may cause rounds to end prematurely and pay up to 6N t . by Lemma 3, with probability 1 t if one of the adaptive user's queries causes a round t to end prematurely, then the amount of data, N t , and the number of the user's queries answered in that round, M t , must satisfy Given M , there is a largest t for which this is possible since N t = 3 t N 0 and t = 2 t 0 .


With enhanced flexibilities, these recent approaches are often good at assessing individual risks, such as predicting a patient's hazard function or survival time.

except for the Gaussian process whose results are not too difficult to interpret for low-dimensional covariates, they often have difficulty in explaining how the survival is impacted by which covariates, limiting their use in survive analysis where interpretability plays a critical role.


σ i , the standard deviations of the observations, are dependent across i.


Just as for human observers, tracking in our model is harder when objects move faster or are closer together; inertia information is available, but may not be used; and objects can be tracked in features as well as space.

effects of the number of objects tracked do not arise from perceptual uncertainty alone.


Theorem 1 guarantees that the estimator μf(X) converges to µ f (X) when μX converges to µ X .

it says nothing about the speed of convergence.


The model definition applies to generic manifolds.

due to the lack of an explicit formulation for the normalizing constant, our estimation is limited to symmetric spaces, which include many common manifolds such as Euclidean space, spheres, Kendall shape spaces, Grassman/Stiefel manifolds, and more.


Among the most commonly used priors are Gaussian process (GP) [24], Dirichlet process (DP) [2] and Indian buffet process (IBP) [12].

standard nonparametric Bayesian models are limited in that they usually make very strict and unrealistic assumptions on data, such as that observations being homogeneous or exchangeable.


These methods train one user feature matrix and one item feature matrix first and use these feature matrices for all users and items without any adaptation.

all these methods adopt fixed rank values for the targeted user-item rating matrices.


We conjecture that it takes additional training steps for OPNs to learn to predict future observations.

vPNs learn to predict only minimal but sufficient information for planning: reward, discount, and the value of future abstract-states, which may be the reason why VPNs learn faster than OPNs.


Turbo AMP [10] also well exploits tree sparsity for compressive sensing with an iterative approximate message passing approach.

none of them has conducted numerous experiments on MR images to validate their superiority.


The doubling trick provides one way to adapt the learning rate; indeed, we observe that the regret of Hedge with the doubling trick is initially smaller than the regret of Hedge with fixed learning rate.

unlike AdaHedge, the algorithm never detects that its current value of η is working well; instead it keeps exhausting its budget, which leads to a sequence of clearly visible bumps in its regret.


an inner product or negative Euclidean distance.

this method, unlike label trees, is unfortunately still linear with respect to k. it does have better behavior with respect to the feature dimension d, with O(d e (d + k)) testing time, compared to methods such as One-vs-Rest which is O(kd).


Second, the approach in [1] though very novel, is mostly heuristic.

our method enjoys the same convergence guarantees and comparable numerical complexity as the basic unstructured online dictionary-learning [16].


Hence, if the vector z is the predicted label for the bag, ℓ ∆ (z, y) simply counts the number of misclassified instances in the bag.

the true labels are unknown, and we only have access to the set Z, knowing that the true labeling vector is in Z.


The points are assigned to clusters according to a probability distribution indicating the relative sizes of the clusters.

not only in our model f + and f − can be arbitrary probability mass functions (pmfs), we do not have to make any assumption on k or the cluster size distribution, and can allow for any partitioning of the set of elements (i.e., adversarial setting).


( 1) has interesting connections to neural computation [8] that we explore further in sections 2.2-2.3.

we begin by elucidating its basic properties.


[4] achieves the same rate up to a logarithmic factor.

not all online learning problems have one of the above feedback structures.


Subordinators help us establish a direct connection between the tuning hyperparameters t j and the latent variables η j (T (t j )).

when we implement the MAP estimation, it is challenging how to select these tuning hyperparameters.


When the spectrum of M is light-tailed (so that ρ T d and, simultaneously, det κ (M ) 1), with the smaller eigenvalues λ i corresponding to eigenvectors in which f is smoother (so that the ratios ∇ ui f 2 ∞ λ i remain controlled), then our bound improves on (2).

when no preliminary knowledge about good f is available, we may run the algorithm with M equal to the identity matrix and recover exactly the bound (2).


Recently, Jeon & Kim [12] has used similar ideas to extend the convolution operations in CNN.

their proposed Active Convolution Unit (ACU) focuses on the images where the need for location-variant filters is limited.


Writing Ĉt−1 = With such covariance matrices, computing the (regularized) natural direction v t is equal to (11) Using the Woodbury identity with positive definite matrices [7], we have is of size p × r (with r < p, thus yielding a covariance matrix of rank r), the cost of this computation is O(pr 2 + r 3 ).

since the Gram matrix G t = X T t X t can be rewritten as the cost of computing G t using G t−1 reduces to O(pr + r 3 ).


It illustrates that the saliency values of unseen natural image patches usually lie between −2.0 and 1.8 (for the training data, they are between −1.8 and 2.2).

our optimal stimuli have saliency values of 5.0 and 5.5, indicating that they represent the difference between fixated and background locations in a much more articulated way than any of the noisy measurements in our data set.


The first is that most existing exact screening methods are based on evaluating the norm of the subgradients of the sparsity-inducing regularizers with respect to the variables or groups of variables of interests.

for TGL, we only have access to a mixture of the subgradients due to the overlaps between parents and their children nodes.


Montavon and Müller [15] showed that an alternative, "centered" representation of the DBM results in successful generative training without a greedy layerwise pretraining step.

centered DBMs have never been shown to have good classification performance.


We fix d = 3 throughout to avoid having too many parameters to vary, although similar results are obtained for larger d. Exact prediction of learning curves by analytical calculation is very difficult due to the complicated way in which the random selection of training inputs enters the matrix K and vector k in (9).

by first expressing these quantities in terms of kernel eigenvalues (see below) and then approximating the average over datasets, one can derive the approximation [3, 6] This equation for has to be solved self-consistently because also appears on the r.h.s.


However, the problem of context length has almost been neglected so far and a naïve bag-of-words history has been employed in natural language processing.

in this paper we view topic shifts within a text as a latent stochastic process to give an explicit probabilistic generative model that has partial exchangeability.


If in addition to r1 also q1 is known, the two local minimia of F ∞ (p 1 = 0 and p2 = 0) allow to recover t0 = t 0 only.

if p1 = p 1 (or p2 = p 2 ) is known exactly, there are three local minima again-p 2 = 0, q1 = 0, r1 = 0-but now none of effective parameters is equal to its true value: ti = t i (i = 0, 1, 2).


As for the transition function, although it is clear that the brain contains detailed representations of action-outcome associations [19], their anatomical localization is not yet entirely clear.

some evidence suggests that the enviromental effects of simple actions may be represented in inferior fronto-parietal cortex [20], and there is also evidence suggesting that medial temporal structures may be important in forecasting action outcomes [21].


This improves efficiency, and also has the potential to aid the discovery of subtle features that might be missed in manual feature design.

learned features, which are implicitly represented by the trained weights of a deep model, come without intuitive significance.


Thanks to this, model selection of LSIF is computationally much more efficient than LogReg and KLIEP.

the regularization path tracking algorithm tends to be numerically unstable.


This result holds for a broad class of distributions f X,Y,Z (x, y, z) which satisfy some smoothness assumptions.

the samples generated by Algorithm 1 (U 2 in the algorithm) are not exactly i.i.d but close to i.i.d.


It turns out that our practical observations align well with our theory.

we also find that the feature matching objective has several drawbacks.


Like our approach, the works of [2] and [21] use notions of class balance, seperation, and regularization to learn unsupervised discriminative classifiers.

they are formulated in the max-margin framework rather than our probabilistic approach.


The reader may notice that the above expression resembles the recursive equations in [24,25].


In the binary labeling case, the M -best-diverse solutions form a nested set.

although the method [23] is a considerably more efficient way to solve the problem, compared to the general algorithm proposed in [22], it is still considerably slower than the sequential method [4].


In fact, this is equivalent to Follow the Perturbed Leader Algorithm (FTPL) (Kalai and Vempala, 2005) for bandit settings.

implementing the estimation step is hard because generally there is no closed-form expression for r ˜ .


Both papers give polynomial time reductions which yield efficient algorithms whenever a corresponding agnostic learning problem is solvable.

in this paper, we take a different approach: we attempt to directly satisfy the original definition of individual fairness from ?, but with substantially less information about the underlying similarity metric.


For groups not containing the neuron with the largest input, this condition can be satisfied if and only if they are in the top c groups .• The winner-take-all competition described above holds only for the case of strong inhibition (3 > 1 -a.

if (3 is small, the competition will be weak and may not result in group-winner-take-all.


Our framework can handle either scenarios and does not make any assumptions about the number of decision makers required to evaluate an item.

we do assume that each item is judged no more than once by any given decision maker.


We may assume that µ is a sub-Gaussian probability measure on R D (see §2.1 and the extended version of this paper).

in order to easily express the dependence of our probabilistic estimates on properties of the measure µ, we assume for simplicity that µ is compactly supported and denote by R µ the minimal radius among all balls containing the support of µ, that is, where B(0, r) is the ball around the origin 0 with radius r. We further assume that for some 0 < γ < 1, µ satisfies the following condition, which we refer to as the "two-subspaces criterion" (for γ): For any pair of (D − 1)-dimensional subspaces of R D , L 1 and L 2 : We note that if µ satisfies the two-subspaces criterion for any particular 0 < γ < 1, then its support cannot be a union of two hyperplanes of R D . The use of this assumption is clarified below in §3.2, though it is possible that one may weaken it.


Naturally, one would prefer segments that are as long as the 2-bar stimuli.

this would have reduced the amount of data left for training significantly and since only the East African rhythm sequences 2 and 3 had differences between the first and second bar (cf.


the class we study is defined in terms of the regularity of the Bayes decision boundary, denoted .


It could be seen that our approximation of the classification loss is accurate when Pr(y i = 1|x i ) is small.

likelihood estimation would severely penalize the misclassified positive examples with large Pr(y i = 1|x i ).


The augmented model raises the cross-validation score of model (c) to 1 bit/s, meaning that by incorporating dependencies between intervals, the model carries slightly more predictive information than a homogeneous Poisson model, despite the mis-specified stimulus filter.

this model-despite passing time-rescaling tests of both marginal distribution and independence-still carries less information about spike times than the inhomogeneous Poisson model (b).


distinguish the environments in their experiment in terms of the amount of top-down control available, implying that different mechanisms might be operating in different environments.

in our account, top-down control is not some substance distributed in different amounts depending on the nature of the environment.


In many convergence analyses for non-convex functions, one would like to show that L is one point strongly convex, and directly apply Lemma 2.5 to get the convergence result.

this is not true for 2-layer neural network, as the gradient may point to the wrong direction, see Section 5.3.


GANs were noted for their ability to produce sharp image samples, unlike the blurrier samples from contemporary VAE models [8].

unlike VAEs and autoregressive models trained via maximum likelihood, they suffer from the mode collapse problem [7].


are an attractive class of joint probability models because of their generality and flexibility.


Overall, CC-POMCP computes a good policy while generally respecting the cost constraint.

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


Convex optimization is a structural property of continuous optimization problems.

many machine learning problems, such as structure learning, variable selection, MAP inference in discrete graphical models, require solving discrete, combinatorial optimization problems.


In order to exchange such information, it is important to capture a high-level association between data modalities with a compact set of latent variables.

learning associations between multiple heterogeneous data distributions is a challenging problem.


In Saenko and Darrell [17], the use of dictionary definitions to train an unsupervised visual sense model was proposed.

the user was required to manually select the definition for which to build the model.


All of the above models are based on McFadden's random utility model [18], which often leads to an analytical solution.

our model is based on classical models of two-sided economies, for which there is no known analytical solution.


These curves show that the error has a minimum at a finite depth The reason for this is that for shallower networks, the overlaps have not been iterated sufficient number of times and hence remain further from the noiseless fixed point.

deeper networks will have an increased load at each layer, since thereby reducing the noise suppression of each layer.


Prior work on classifier adaptation [23,24,25] assumes that f t (x) = f s (x) + ∆f (x), where the perturbation ∆f (x) is a function of input feature x.

these methods require target labeled data to learn the perturbation function, which cannot be applied to unsupervised domain adaptation where target domain has no labeled data.


methods with geometrically decreasing regularizer/smoothing weights) appeared a lot in the literature [6,25,31,33].

to the best of our knowledge, all existing homotopy analysis either only work for specific algorithms [6,25,31] or solve only special problems [33].


Its variation across subjects can capture cognition [26,27] or pathology [17,3].

the effects of pathologies are often very small, as resting-state fMRI is a weakly-constrained and noisy imaging modality, and the number of subjects in a study is often small given the cost of imaging.


The frequency band and the time period should be chosen individually by closer analysis of each data set.

we are not focussing on this effect here, therefore we choose a setting which works well for all subjects.


The construction in (3) clusters the blocks, and therefore it imposes structure not constituted in the simpler model in (2).

the DP still assumes that the members of {x i } i=1,N B are exchangeable.


For example, one can think of losses as negative log-likelihoods in a conditional model that generates each successive layer given its predecessor; i.e., L 1 (W x, ) = log p W ( |x) and L 2 (V , y) = log p V (y| ).

(a loss based formulation is more flexible, since every negative log-likelihood is a loss but not vice versa.)


Setting aside architectural specifics, the vast majority of VQA models operate on a set of similar design principles -first producing vector representations for the image and question and then combining them to predict the answer (often through complex attention mechanisms).

when language biases are quite strong, the question feature may already be sufficiently discriminative and the model can learn to ignore the visual signal without facing significant losses during training (e.g.


Several Poisson-based MF models were proposed recently to model large and sparse static ratings, e.g., Poisson Factorization (PF) [25], and collaborative topic PF for modeling content-based recommendations [27]; and dynamic data, e.g., dynamic PF (dPF) [16], dynamic compound PF (DCPF) [34], and deep dynamic PF [24].

none of these can effectively and efficiently handle massive, dynamic and sparse ratings simultaneously (see more analysis in Section 2).


Under Assumptions 1 and 2, the iterates of CDSGD satisfy ∀k ∈ N: At a high level, since E[∇J i (x k )] is the unbiased estimate of ∇V (x k ), using the updates ∇J i (x k ) will lead to sufficient decrease in the Lyapunov function.

unbiasedness is not enough, and we also need to control higher order moments of ∇J i (x k ) to ensure convergence.


Image reconstruction from MRI raw data is viewed as a problem of inference from incomplete observations.

current reconstruction techniques are non-iterative.


If we restrict f V to have zero mean ( v∈V f (v) = 0), then the criterion (1) can be rewritten as follows: The obvious minimum of R(f ) under the constraint v∈V f (v) = 0 is reached for any function f such that f V is equal to the second largest eigenvector of L (the largest eigenvector of L begin the constant vector).

this only defines the values of f on the points V , but leaves indeterminacy on the values of f outside of V . Moreover, any arbitrary choice of f under a single constraint on f V is likely to be a mapping that overfits the known graph at the expense of the capacity to infer the unknown edges.


These analyses, which are inspired by the variants of the two time scale dynamic proposed by [8], do not directly require the convex-concavity of the objective function.

they require some kind of local (global) stability which is difficult to achieve unless there is local (global) convex-concave structure.


For this reason, linear methods based on convex optimization have been proposed for connectome evaluation [32,39] and simultaneous connectome and white matter microstructure estimation [15].

these methods can require substantial computational resources (memory and computation load) making it prohibitive to apply them to the highest resolution datasets.


The simplest way to control the capacity of a PMF model is by changing the dimensionality of feature vectors.


In the previous section, we leveraged the interpretation of multivariate functions as multilinear operators.

it is also possible to interpret multivariate functions as measures on a product space.


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

even in that case, r B B 2 (A, B) exists iff Im A ⇢ Im B.


For non-Gaussian priors, the computation of the posterior mean of a new input requires either to numerically solve an integral or to iteratively update variational parameters [13].

for Gaussian priors the posterior mean is the product between the input and a matrix that is independent of the input.


Different types of approaches have been proposed in the past including bootstrapping [31], active learning [37], semi-supervised learning [51], and data augmentation [20].

the approaches above utilize data samples that are either already present in the given training set, or additionally created by humans or separate algorithms.


To get a sense of the absolute performance, we would ideally compare to existing methods on the same problem.

rediscovering the DSSP function is not a common task in bioinformatics, and not many tools are available that would constitute a meaningful comparison, in particular because secondary structure annotation algorithms use different definitions of secondary structure.


As common practice of standard zero-shot learning, we can apply the trained model f c in Eq.

( 3) to classify the unseen data over only target classes T . in generalized zero-shot learning, things become more difficult as we have to make predictions over both source and target classes S ∪ T . Due to the huge gap between the disjoint source and target classes, a deep network trained on the source classes may still be under-confident for the target classes.


Given a set of positive (relevant) and negative (non-relevant) samples, the parameters of a retrieval system can be estimated using the AP-SVM framework, which minimizes a regularized convex upper bound on the empirical AP loss.

the high computational complexity of loss-augmented inference, which is required for learning an AP-SVM, prohibits its use with large training datasets.


Our analysis of the Light-Chain domain suggests that if the number of latent options is approximately known a priori, clustering algorithms like E-M can perform well.

in the general case, IGMM-based clustering is able to discover an appropriate number of options automatically without sacrificing performance.


The Wasserstein distance is also used to formulate a metric for comparing clusters in [5], and is applied to image retrieval [10], contour matching [11], and many other problems [12,13].

to our knowledge, this is the first time it is used as a loss function in a discriminative learning framework.


The relaxation with the best known worst case approximation guarantee yields a semi-definite program, see [3].

it is practically infeasible for graphs with more than 100 vertices due to the presence of O(n 3 ) constraints where n is the number of vertices in the graph.


Any node with degree strictly greater than |C| must be in C. The observation follows simply from the fact that if a node is omitted from C, then all of its neighbors must belong to C. Thus, if S is the set of all nodes in G with degree greater than k, then S is contained in every vertex cover of size at most k. We can compute U (k) in time exponential in k but polynomial in the number of nodes n for fixed k [18], but these algorithms remain impractical for our datasets.

the results motivate our algorithm in Section 3, which is based on taking the union of several minimal vertex covers.


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

in terms of multinomial estimation, this generality has a drawback because it uses a lower-dimensional topic representation to predict the next word, which may cause a loss of information.


The simplest algorithm starts with sorting the weights and then searches for l with a binary search.

a linear algorithm that recursively uses the median is given in [HW01].


Attention for Visual Reference Resolution While visual dialog is a recent task, VQA has been studied extensively and attention models have been known to be beneficial for answering independent questions [10][11][12][13][14][15][16].

none of those methods incorporate visual reference resolution, which is neither necessary nor possible in VQA but essential in visual dialog.


We use slice sampling from Neal [19] to update the size-biased weights and the surplus mass.

there is a class of priors where the total mass's density is intractable so an additional step needs to be introduced to sample the surplus mass.


¢ is the length of the suffix fq F6 § @9 A9 A9 !

§ 3 of the training sequence that the on-line algorithm had not seen yet when D G was generated, is the cumulative loss of D R on that suffix, and §¦ 0 G$ S k For the sake of simplicity, we will restrict to losses X with range V t % § @k e . it should be clear that losses taking values in arbitrary bounded real interval can be handled using techniques similar to those shown in Section 3.


Thus, in the high SNR regime, the main benefit of lasso is its ability to detect small coefficients, even when they are much below the average power.

if the range of component magnitudes is not large, so MAR is close to one, lasso and thresholding have equal performance within a constant factor.


As expected, small batch sizes combined with large step sizes lead to low improvement ratios.

the effect is non-trivial and problem-dependent, justifying the need for an adaptive method.


Even the best runs of SO do not recover ideal structure.

all 10 runs of our birth-merge algorithm find all 8 components, despite initialization at K = 1.


It is worth mentioning that their excess risk bounds for both convex problems and strongly convex problems are special cases of our Result II when θ = 0 and θ = 1, respectively.

the intermediate optimistic rates for θ ∈ (0, 1) are first shown in this paper.


While the original DDPG hyperparameters were set to achieve robust performance on a large set of benchmarks (and out-of-the-box DDPG performed remarkably well on the considered problems) our experiments indicate that the number of samples required to achieve good performance can be substantially reduced for individual tasks by hyperparameter optimization with BOHAMIANN.

dNGO did not perform as well on this specific task, getting stuck during optimization, see Figure 2 (right).


For some tasks, it may also be useful to feed the output of the localisation network, θ, forward to the rest of the network, as it explicitly encodes the transformation, and hence the pose, of a region or object.

it is also possible to use spatial transformers to downsample or oversample a feature map, as one can define the output dimensions H and W to be different to the input dimensions H and W . with sampling kernels with a fixed, small spatial support (such as the bilinear kernel), downsampling with a spatial transformer can cause aliasing effects.


This resembles biological synapses, whose plasticity is also triggered by mechanisms that are determined by local waveforms [5,6].

learning in memristors has so far been approached mostly on a pragmatic technological level.


As discussed when presenting results, one may also learn the CS dictionary in advance, off-line, with appropriate training images (using the model in ( 2)).

the unique opportunity for joint CS inversion and learning of an appropriate parsimonious dictionary is deemed to be a significant advantage, as it does not presuppose that one would know an appropriate training set in advance.


We gather the parameters into a n Then, for image x, the "classeme" descriptor h(x) is computed as the concatenation of the outputs of the classifiers learned for the training categories: The PICODE descriptor is also of this form.

the key-difference with respect to [27] lies in our training procedure, and the fact that the dimensionality C is no longer restricted to be the same as the number of training classes.


( 7) becomes Naive implementation of the above update is O(K 2 ) for each x i , or O(K 3 ) for sending messages to all neighbouring x i .


As expected our ability to recover the ground truth regression coefficients improves with increasing N (see Figure 3(a), left).

we see that the methods using the tilted bound perform best, closely followed by the log bound.


[2] proposed to extend the 2D HOG-based template detector of [14] to predict 3D cuboids.

since the model represents object's appearance as a rigid template in 3D, its performance has been shown to be inferior to (2D) deformable part-based models (DPMs) [1].


Since the O(1/k) convergence rate of the testing cost, achieved by SG methods with decreasing step sizes (and a single pass through the data), is provably optimal when the algorithm only accesses the function through unbiased measurements of the objective and its gradient, it is unlikely that one can obtain a linear convergence rate for the testing cost with the SAG iterations.

as shown in our experiments, the testing cost of the SAG iterates often reaches its minimum quicker than existing SG methods, and we could expect to improve the constant in the O(1/k) convergence rate, as is the case with online second-order methods [32].


In the case of contacts, the boundary might have a complex shape that is not well modeled by a GMM.

if we use the GMM to obtain a prior for linear regression, it is easy to determine the correct linear mode from the covariance of (x ti , u ti ) with x t+1i in the current samples at time step t. The time-varying linear dynamics can then capture different linear modes at different time steps depending on the actual observed transitions, even if the states are very similar.


Compared to the ground truths, some of the descriptions are comparable in consideration of the generated sentence and event temporal segment.


Ideally, we could perform a roll-out of our acquisition policy, to choose a point that appropriately balanced information gain and exploitation.

such roll-outs are generally intractable.


Here the right hand side, h models the uncertain demand and the covering constraints capture the requirement of satisfying the uncertain demand.

the adjustable robust optimization problem (1) is intractable in general.


In stereo, the same object is imaged and what varies from one view to the other is the field of view, scale, or pose.

in keypoint matching, the background is not controlled and even sophisticated descriptors may go wrong.


Traditional experimental design-which aims to show a statistically reliable difference between two alternative policies-requires testing many subjects for each policy.

if our goal is to determine the shape of the PPF, we may get better value from data collection by evaluating a large number of points in policy space each with few subjects instead of a small number of points each with many subjects.


To model all possible appearance variations of a target object (due to pose, illumination and view angle change), one could resort to a mixture of PPCA models.

it not only requires significant computation for estimating the model parameters but also leads to other serious questions such as the number of components as well as under-fitting or over-fitting.


Recent efforts have focused on developing statistical techniques to post-process the noisy labels in order to improve its quality (e.g., [RYZ + 10, ZLP + 15, KOS11, IPSW14]).

when the inputs to these algorithms are erroneous, it is difficult to guarantee that the processed labels will be reliable enough for subsequent use by machine learning or other applications.


For generative models, the recent Wasserstein GAN [11] improved the training stability of GANs by reformulating the optimization problem as a minimization of the Wasserstein distance between the real and generated distributions [12].

this method relies on an efficient way of constraining the Lipschitz constant of the critic, which was only partially addressed in the original paper, and the object of several follow-up works [13,14].


The average number of nonzeros is about 4000 which should be much larger than k (e.g., 500) for the hashing procedure.

about 10% (or 2.8%) of the samples have < 500 (or < 200) nonzeros.


Note that these divisions emerge from training under the oracle loss and are not hand-designed or pre-initialized in any way.

figure 4f show that the oracle assignments for a standard ensemble are nearly uniform.


This is an adversarial communication environment, where a speaker agent ('Alice') must communicate a message to a listener agent ('Bob'), who must reconstruct the message at the other end.

an adversarial agent ('Eve') is also observing the channel, and wants to reconstruct the message -Alice and Bob are penalized based on Eve's reconstruction, and thus Alice must encode her message using a randomly generated key, known only to Alice and Bob.


Although we have introduced RBM units with continuous values to better deal with the representation of input variables, they could also be considered for use in the hidden layers, in replacement or complementing the binomial units which have been used in the past.

gaussian and exponential hidden units have a weakness: the mean-field propagation through a Gaussian unit gives rise to a purely linear transformation.


Gene expressions form a rich source of data from which to infer gene regulatory networks; it is now possible to sequence gene expression data from single cells using a technology called single-cell RNA-sequencing [52].

this technology has a problem called dropout, which implies that sometimes, even when the gene is present it is not sequenced [25,12].


ASGARD-rs is the best due to the strong convexity of the problem.

it does not have a theoretical guarantee.


Given our assumptions, we obtain equations linear in W j 12 , W j 21 , and W j p1 For each delay k, we obtain three equations: one from E{R 1 }, and one from the projection of E{XR At first glance, it appears that the unknowns greatly outnumber the equations.

the system of equations is well-posed because the W j p1 W  q2 appear in the same combination for each of the three equations at a given delay.


To capture more complex material properties, nonlinear methods and probabilistic methods may achieve greater success.

when designing these more sophisticated methods, care must be taken to avoid the same pitfall encountered by shape recipes: not all properties of a scene can be scale-invariant simultaneously.


For example, if the actions are placed as the elements in {0, 1/2, 1} n , we use the l ∞ metric, and r ∈ (1/2, 1), it is easily seen that the sphere packing number is just 1.

the sphere covering number is at least 2 n = k log 3 (2) ≈ k 0.63 , since we need a separate sphere to cover every element in {0, 1} n . Third, consider the random Erdös -Rényi graph G = G(k, p), which is formed by linking every action i to every action j with probability p independently.


In that case we would directly represent Pr(Y t |X t , Y t−1 ), hence we could implement a sequential Monte Carlo algorithm simply directly sampling s t ∼ Pr(Y t |X t = x t , Y t−1 = s t−1 ) from slice to slice.

in [9], it was pointed out that MEMMs suffer from the label-bias problem to which as a solution CRFs were invented.


This is due to the fact that SMO's active set typically fluctuates heavily across the training set, thus a large fraction of the full kernel matrix must be evaluated.

iVM requires only d/n of K. Among the many proposed sparse GP approximations [1,8,9,10,11], our method is most closely related to [1].


Further, minimizing the average loss affords simple and efficient stochastic gradient descent algorithms [3,21].

the work in [20] shows that constructing learning objective based on the maximum loss may lead to improved performance for data with separate typical and rare subpopulations.


All three algorithms can find the optimal solution in cascading bandits.

when the feasible set is not a matroid, it is critical to maximize the product of the UCBs.


If the target dataset is small and the number of parameters is large, fine-tuning may result in overfitting, so the features are often left frozen.

if the target dataset is large or the number of parameters is small, so that overfitting is not a problem, then the base features can be fine-tuned to the new task to improve performance.


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

the algorithm executes this policy on the true MDP M. The only difference between the two is the transition model: on taking an action a j := πk (s) in state s in MDP Mk , the next state follows the sampled distribution where as on taking the corresponding action a in MDP M, the next state follows the distribution P s,a .


First-order GD achieve a O( √ T ) regret for any arbitrary sequence of convex losses [10].

if we know that the losses are strongly convex, setting a more aggressive step-size in first-order GD achieves a smaller O(log T ) regret [25].


sampling assumption is technical, extending our analysis to the case when samples are correlated requires generalizing quite a few results in supervised learning.

we believe that this can be done without problem following the work of [2].


Note the absence of dependence on the number n of input attributes.

the mistake-bound of the Winnow algorithm (Littlestone, 1988) has a logarithmic dependence on n and will build a classifier on all the n attributes.


These methods lead to faster convergence on many problems.

sAG and AG are not immediately applicable to SVI.


One draw back is that EXP would need as a parameter.

this can again be addressed by NormalHedge.DT for the exact same reason that NormalHedge.DT is independent of ✏.


The notion of shattering involves checking the existence of a unit-norm separator w for each labelvector y ∈ {±1} m . In general, there is no closed form for the minimum-norm separator.

the following Theorem provides an equivalent and simple characterization for fat-shattering: Theorem 5.2.


We considered several of these algorithms before deciding to use our own algorithm which turned out to be surprisingly effective in spite of its simplicity.

we will mention two existing algorithms that might be suitable for producing binary word hierarchies.


When training functions are available we directly use them.

our construction can be applied even if training functions are not specified.


In the case that the hidden unit dynamics is known to be highly stochastic, this class of models is arguably less appropriate.

stochastic hidden dynamics is often used in cases where one believes that the true hidden dynamics is too complex to model effectively (or, rather, deal with computationally) and one uses noise to 'cover' for the lack of complexity in the assumed hidden dynamics.


To solve this, a Huber approximation (see [1]) to the quasi-norm is used, allowing the derivation of a generalized shrinkage operator to solve the sub-problem efficiently.

this approximates the original sub-problem, unlike our approach.


The error bounds for fully supervised classification, by assuming these n + n ′ data are all i.i.d., would be of order O(1/ √ n + n ′ ).

this assumption is unreasonable for PU classification, and we cannot train fully supervised classifiers using these n + n ′ samples.


1 shows a pair of policies that achieve this desired interaction and depend only on each agent's level-zero beliefs about the state of the world.

as we will see, the agents cannot maintain their level-zero beliefs in isolation.


However , somewhat ] Jonathan Greene from CombiChem provided us with the Affinity data set.

due to the proprietary nature of it we cannot make it publicly available.


Application of the latter was often restricted to simulations which sometimes could support training or tuning of the real world robot parameters.

often the gap between simulation and the real world was too wide so that a transfer of training results from the simulated to the real robot turned out to be useless.


We can query a pair of nodes (u, v) to test whether s(u, v) = +1 indicating u and v belong to the same cluster or s(u, v) = −1 indicating they are not.

the query fails to return the correct answer with probability 0 < p < 1/2, and we want to query the minimal possible pairs.


The coordinate descent algorithm is guaranteed to converge, as it monotonically decreases the approximated structured prediction objective in Theorem 1, which is lower bounded by its dual program.

convergence to the global minimum cannot be guaranteed in all cases.


Generating high-resolution results has great importance on extending the application of face frontalization.

due to its difficulty, few methods consider producing images with size larger than 128 × 128.


Unfortunately, Proposition 1 only holds for polynomials in one variable.

its first statement may be generalised to polynomials of more than one variable: for every psd matrix P 0 the polynomial p (ρ) = θ ρ P θ ρ is non-negative everywhere, even if θ i is any monomial in ρ 1 , .


Under mild technical constraints, we see that losing each connection has detrimental effect on learning as it monotonically increases the MSD.

capturing agents communications with a graph, we introduce the notion of optimal edge as the edge whose addition has the most effect on learning in the sense of MSD reduction.


For this reason, Bayesian nonparametric models, such as Gaussian processes (GPs), are often the model of choice in MBRL, especially in low-dimensional problems where data efficiency is critical [Kocijan et al., 2004, Ko et al., 2007, Nguyen-Tuong et al., 2008, Grancharova et al., 2008, Deisenroth et al., 2014, Kamthe and Deisenroth, 2018.

such models introduce additional assumptions on the system, such as the smoothness assumption inherent in GPs with squared-exponential kernels [Rasmussen and Kuss, 2003].


In particular, it was recently shown ( [1], [2], and [3]) that SVM's can learn for all data-generating distributions.

these results are purely asymptotic, i.e.


This allows the sampling of outputs from the generator since gradients do not need to be passed back through the discriminator.

since a reward is provided for the entire sequence, gradients computed for the generator do not provide information on which parts of the output sequence the discriminator thinks is incorrect, resulting in long convergence times.


Authenticity and integrity of communications are central aims of modern cryptography.

traditional cryptographic schemes do not aim to hide the presence of secret communications.


Beyond accelerators, parallelization of computation on multiple computers is therefore popular.

it requires frequent communication to exchange a large amount of data among compute nodes while the bandwidth of network interfaces is limited.


Furthermore, the approach computes the scores of all locations at once, and so is not random-access; it cannot be efficiently combined with a cascade detection process.

our template evaluation algorithm does not require batching template evaluations.


As expected, the results at γ ≈ 0 validate x loc as a true local minimum.

even with γ = 1 yielding a random initialization, 59 of the 1,000 trials still result in an error of > 50%, thereby yielding a failure rate of 5.90 ± 2.24% up to three standard deviations.


For linear-Gaussian p i (u t |x t ) and (nonlinear) conditionally Gaussian π θ (u t |x t ) = N (µ π (x t ), Σ π (x t )), where µ π and Σ π can be any function (such as a deep neural network), the KL-divergence D KL (π θ (u t |x t,i,j ) p i (u t |x t,i,j )) can easily be evaluated and differentiated in closed form [6].

in the nonlinear setting, minimizing this objective no longer minimizes the KL-divergence between trajectory distributions D KL (π θ (τ ) p i (τ )) exactly, which means that MDGPS does not correspond exactly to mirror descent: although the C-step can still be evaluated exactly, the S-step now corresponds to an approximate projection onto the constraint manifold.


One limitation of these earlier studies is that they can only work with a relatively small number (typically less than 30%) of noisy pairwise constraints.

in semi-crowdsourced clustering, we expect that a significantly larger percentage of pairwise similarities are inconsistent with the true cluster assignments (as many as 80% [25]).


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

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


Thus, we can prune D(I, a) from iteration T 0 until iteration T 1 so long as In the worst case, this allows us to skip only R(I,a) U (I,a)−L(I) iterations.

in practice it performs significantly better, though we cannot know on iteration T 0 how many iterations it will skip because it depends on what is played in T 0 ≤ t ≤ T 1 .


This property suggests that ConvNets may have better applicability to real-world scenarios.

further analysis is needed to validate the hypothesis that ConvNets are truly good at identifying exotic character combinations such as misspellings and emoticons, as our experiments alone do not show any explicit evidence.


At first glance there is no clear difference in Figure 2A between the raw SFA responses during periods of pattern presentations and during phases of noise input due to the same firing statistics.

we found that on average the slow feature responses during noise input are zero, whereas a characteristic response remains during pattern presentations.


We note that the method simply using the KPCA basis does not seem to benefit from unlabeled data and, in fact, cannot outperform the standard fully supervised SVM classifier.

our algorithm using a basis subselection procedure shows results comparable to the state of the art.


In addition, prior knowledge can be easily incorporated in generative models in the forms of structured latent variables, such as lighting and deformable parts.

the enormous amount of content in high-resolution images makes generative learning difficult [6,7].


Randomized features provide a computationally efficient way to approximate kernel machines in machine learning tasks.

such methods require a user-defined kernel as input.


Influence functions study how the model or prediction would change if a training point was up-weighted infinitesimally, but require model differentiability and convexity to work.

it was recently shown that these assumptions can be relaxed and that influence functions can be used for understanding model behavior, model debugging, detecting dataset errors, and creating visually indistinguishable adversarial training examples [12].


Specifically, we first decompose noisy features into the sum of two components, a signal component and a noise component, and then truncate the gradient through the latter, i.e., treat it as a constant.

naively modifying the gradient would encourage the magnitude of features to grow in order to increase the SNR, causing optimization difficulties.


As a result, you realize that your apartment can be easily burnt down because you do not have any fire extinguishing mechanism such as a sprinkler system.

as you wonder about the cost and the effectiveness of the fire extinguishing mechanism, you notice that the fire extinguishing mechanism can only protect your apartment if a small fire originates in your apartment.


Stochastic optimal control (SOC) is a general and powerful framework with applications in many areas of science and engineering.

despite the broad applicability, solving SOC problems remains challenging for systems in high-dimensional continuous state action spaces.


A very recent result of Wang and Chen [32] removes the 1/p * factor in [8] for the tabular case and presents a worst-case bound of O(L|E| √ n), which in the tabular complete graph case improves over our result by O(L).

their analysis does not give structural guarantees that we provide with maximum observed relevance C * obtaining potentially much better results for the case in hand and giving insights for the complexity of IM bandits.


The problem is one of underspecification: there are many legitimate ways to organize complex high-dimensional data, and no algorithm can magically guess which a user has in mind.

a modest amount of interaction may help overcome this issue.


In a parametric approach, we consider a parameterized function f (x; θ), with θ being distributed according to some prior.

the nonparametric GP approach directly puts the GP prior over f as For a finite set of points, the GP model is simply a joint Gaussian: f (x 1:N ) ∼ N (m(x 1:N ), K), where K i,j = κ(x i , x j ) and N is the number of data points.


Running WSAT on 100 formulas with N = 10000 required 27771 seconds on the same servers, and would have taken even longer if about half of the runs had not been stopped by a cutoff without producing a satisfying con£guration.

the same 100 formulas were solved by SP followed with WSAT in 10,420 sec, of which only 300 seconds were spent in WSAT.


Given a joint probability distribution p(y, x) where y are observations and x are latent variables (possibly including model parameters that consist of random variables) and a variational distribution q v (x), the objective is to maximize the lower bound with respect to the variational parameters v. Ideally, in order to tune v we would like to have a closed-form expression for the lower bound so that we could subsequently maximize it by using standard optimization routines such as gradient-based algorithms.

for many probabilistic models and forms of the variational distribution at least one of the two expectations in (2) is intractable.


In most cases, approximating 1 − p(x, t) by a Gaussian profile is already sufficient to produce qualitatively satisfactory results.

higher order perturbation analysis is required to yield more accurate descriptions of results such as the overshooting in the tracking process (Fig.


Because the performance of Junctor only depends on n and w, we ran it only once for each combination of the two.

the performance of GOBNILP is very sensitive to various characteristics of the data, and therefore we ran it for all the combinations.


The relative pose is then 6 , where ⊕ denotes concatenation.

with relative pose P i of consecutive joints in hand, the encoding vector v h to represent the robot can be explicitly constructed as follows 3 : In the above section, we discussed how kinematic structure of the hardware can be explicitly encoded as v h . in most cases, we need to not only encode kinematic structure but also the underlying dynamic factors.


A method for using inferred reward functions (e.g., Abbeel and Ng [24]) could be incorporated into our method when this is not true.

this requires segmentation based on policy rather than value function, since rewards are not given at demonstration time.


One possible use of the relational information in PCA or PPCA is to first convert the link structure into the format of flat data by extracting some additional features from the links.

as argued in [10], this approach fails to capture some important structural information in the data.


For any λ, σ 2 > 0 there exists a unique α > α min such that λ(α) = λ (with the function α → λ(α) defined by λ(α The assumption of a converging problem-sequence is important for the result to hold, while the hypothesis of gaussian measurement matrices A(N ) is necessary for the proof technique to be correct.

the restrictions λ, σ 2 > 0, and P{X 0 = 0} > 0 (whence τ * = 0 using λ ) are made in order to avoid technical complications due to degenerate cases.


If an action is on a good trajectory but occurs after most of the useful actions (pops of correct constituents), then it does not receive credit for those previously occurring actions.

if it occurs before useful actions, it still does receive credit because we do not know (without additional simulation) whether it was a necessary step toward those actions.


We stipulate that code, which describes a sequence of operations to a processor, behaves similarly, and paraphrase this hypothesis to: Statements that occur in the same contexts tend to have similar semantics.

the above wording is vague, due to the possible meanings of the highlighted elements.


Some guidance is offered in [6] regarding how c might be chosen.

this is ultimately left as a manual task.


The objective is given by min Note that the formulation does not directly constrain that P has identical marginals, only that the means and variances agree.

the optimal solution does, as shown next.


At this stage, as far as our model is concerned, the recognition has already been performed.

since the task we are evaluated on is category-based, we combine the returned exemplars into a vote for categories using Luce's Axiom of Choice [17] which averages the exemplar responses per-category.


An immediate way of decoding the M 3d volume into 3d pose estimates for all the persons in the image, is to simply average 3d skeleton predictions at spatial locations given by the limbs selected by the people grouping module.

this does not take into account the differences in joint visibility.


Intuitively, the basis vector selection becomes less important if we make more effort at every iteration by refitting the basis vectors themselves.

on vowel, l 1 /l 2 is still substantially better than l 1 (89.57 vs. 87.83).


This seems to be an unavoidable side-effect of being decomposition-dependent.

the fact that our new approach is decomposition-invariant allows us to obtain sharper convergence rates for such instances.


BN normalizes each channel of features using the mean and variance computed over the minibatch: where nchw } is the batch-normalized response.

iN normalizes each example in the minibatch independently using per-instance feature statistics: where nchw } is the instance-normalized response.


The bound shows that we should take M as large as possible.

m impacts the numerical cost of the method.


A non-metric D is, a fortiori, non l 2 and thus its associated C is indefinite.

when C is indefinite, we can conclude that D is non l 2 , but not necessarily non-metric.


geometric) rates of convergence for the state-of-the-art methods listed above.

at most linear rates in turn become infeasible when the problem size is very large, with the number of nodes in the thousands and the number of matrix entries to be estimated in the millions.


The frequency of such abnormal neural events plays a major role in determining the SOZ.

capturing these abnormal neural events that occur in distinct locations of the brain alone is often not sufficient to establish an area in the brain as the SOZ.


This application of MWU is unlike [AG12,CJV15], where broadly speaking the MWU framework is applied in a novel way to determine how an individual element is picked (or how a direction for movement is chosen in case of continuous greedy).

we use standard algorithms for P 0 and pick an entire set before changing weights.


the estimated function ĝ still remains in the RKHS associated with kernel κ.

the norm ĝ Hκ may increase, and consequently may the regret.


Data set variance affected all algorithms, varying overall performance across panels.

trends in each panel are still valid, as they are based on the same data.


Despite lacking theoretical guarantees, Unsafe subgame solving did surprisingly well in most games.

it did substantially worse in Large NLFH with 30,000 buckets.


MANNs have been successfully applied to long sequence prediction tasks [14,33] demonstrating great improvement when compared to other recurrent models.

the role of memory in sequence generation has not been well understood.


Such analysis is typically done using a secondary structure for representing the decomposition of graphical models, such as decomposition trees (dtrees) [2].

the existing notion of treewidth does not provide a tight upper bound for the complexity of lifted inference, since it ignores the opportunities that lifting exploits to improve efficiency.


A sample (Figure 3a) might carry the right semantics, the learning model still might be blind to that sample if the pixels corresponding to important features are filled with smaller values.

a very noisy sample (Figure 3c) could still be correctly classified as long as the pixels corresponding to important features are assigned with decent values.


This means that data programming achieves the same learning rate as methods that use labeled data, while requiring asymptotically less work from its users, who need to specify O(1) labeling functions rather than manually label Õ( −2 ) examples.

in the crowdsourcing setting [17], the number of workers m tends to infinity while here it is constant while the dataset grows.


Recall that Exp and Poly have parameters set with respect to the number of actions N . We see from the figures that NormalHedge is completely unaffected by the replication of actions; no matter how many times the actions may be replicated, the performance of NormalHedge stays exactly the same.

increasing the replication factor affects the performance of Exp and Poly: Exp and Poly become more sensitive to the changes in the total losses of the actions (e.g.


The numerical procedures presented in section 2.1 provide a general and computationally efficient means for inference in non-Gaussian densities whose application could be useful for a range of probabilistic models.

our current understanding of the best approach to discretise the base densities is limited and further study of this is required, particularly for application in very large systems D 1.


Namely, only if the "truth proximity" assumption holds, then we have c(x) = c(x ′ ) which together with the condition h(x ′ ) = c(x) we can conclude that x ′ is indeed misclassified.

if small perturbations can change the ground truth, c(x ′ ) can be different from c(x), in which case, it is no long clear whether x ′ is misclassified or not.


Given that our goal is to compare RBM training approaches rather than achieving the best possible training across all free parameters, neither momentum nor adaptive learning rates were included in any of the implementations tested.

we do employ a weight decay regularization in all our trainings to keep weights small; a necessity for the weak coupling expansion on which the EMF relies.


This suggests that the dataset Microarray 2 did not include factors other than the first one as those strongly related to the prognosis.

wLRMF extracted the identical first factor to HCA-greedy, but extracted much more factors concerning Microarray 2, all of which may not be trustworthy because the number of samples observed in Microarray 2 was as small as 25.


1 using a similar proof technique (see Appendix B).

it is not clear to us how to prove an analog of Thm.


Such time and space complexities are clearly prohibitive for real applications, where the vocabulary usually contains tens of thousands of terms.

we can employ a trick similar as in [11] to speed up the moment computation.


One possible approach is to use loopy max-product to obtain approximate max-marginals and use those to approximate the M best solutions [19].

this is largely a heuristic and does not provide any guarantees in terms of optimality certificates or bounds on the optimal values.


Spectral clustering is a particularly powerful technique for computing the clusters when the pairwise similarities are encoded into the adjacency matrix of a graph.

many graph-like datasets are more naturally described by higher-order connections among several entities.


For Lie groups, an implementation of an equivariant Karcher mean would be a sufficient operator for M. It is defined as the point on the manifold that minimizes the sum of all weighted geodesic distances [Nielsen and Bhatia, 2012].

for each group there is a different number of possible realizations from which only few are applicable in a deep neural network architecture.


Classification with MEG kernels is shown to outperform models that ignore uncertainty due to sparse and irregular sampling.

various deep learning models including convolutional neural networks [12] have been successfully applied to fields such as computer vision and natural language processing, and have been shown to achieve state-of-the-art results on various tasks.


The previous literature on DP hypothesis testing has a few characteristics in common: 1) nearly all of these proposed methods first add noise to the data, and perform their test as a post-processing procedure, 2) all of the hypothesis tests use either asymptotic distributions or simulations to derive approximate decision rules, and 3) while each procedure is derived intuitively based on classical theory, none show that they are optimal among all possible DP algorithms.

in this paper we search over all DP hypothesis tests at level α, deriving the uniformly most powerful (UMP) test for a population proportion.


Those methods chose a decision boundary that minimizes the total number of bits needed to code the boundary and the samples it incorrectly classifies.

mICL uses coding length directly as a measure of how well the training data represent the new sample.


Thus, we consider that the significance test fails.

α true < α yields a pessimistic statistical test that decides correctly H 0 more often than predicted.


We first explore distributions that fits such heavy-tailed property.

a common approach to cope with heavy-tails is to use the L 1 distance, which corresponds to the Laplace distribution the tail of the noise distribution is often still heavier than the Laplace distribution: empirically, we find the kurtosis of the SIFT noise distribution to be larger than 7 for most dimensions, while the kurtosis of the Laplace distribution is only 3.


A single pixel conveys very little information about an object in the scene, both due to thermal and shot noise and due to the ambiguity of the single-channel signal.

by looking at all of the noisy pixels simultaneously and exploiting knowledge about the structure of natural scenes, the task of extracting the object becomes feasible.


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

the reshaping process for test datasets has a critical difference from reshaping training datasets.


. . , Ũk ← the clusters obtained by running k-means on the rows of A 5: Ṽi ← all vertices in V with at least θ|U i | neighbors in U i , where θ is as in Equation 3When developing the algorithm, we also tried using other clustering methods than k-means.

none of them delivered consistently better results than k-means and the differences in the outputs were mostly minor.


The result is proved by interpreting the incomplete observations as complete observations in a transformed graph, The PAC learnability result implies good sample complexity bounds for the DIC and DLT models.

the PAC learnability result does not lead to an efficient algorithm, as it involves marginalizing a large number of hidden variables (one for each node not observed to be active).


In other words, the noise is marginalized out and thus fails to drive the network to generate large visual variations.

our approach explains each input noise better because the network is unlikely to absorb the variations in input noise since it is never trained for learning textures.


In particular, representations learned by DAs greatly facilitate various recognition tasks and constantly lead to the improved performance in machine perception [6]- [9].

the Siamese architecture originally proposed in [10] uses supervised yet contrastive learning to explore intrinsic similarity/disimilarity underlying an unknown data space.


Any real-valued variable x ∈ [min, max] can be rescaled by the mapping x → x−min max−min .

the linear scale is inappropriate here and we should use a harmonic scale instead, hence map to Taking max = 1 and min = π we arrive at the following definition.


This discovery of the surprising vulnerability of classifiers to perturbations has led to a large body of work that attempts to design robust classifiers [8,9,10,11,12,13].

advances in designing robust classifiers have been accompanied with stronger perturbation schemes that defeat such defenses [14,15,16].


The distribution μ we produce here will be especially simple: we will round each x i independently with probability 1 2 .

then, clearly H(μ) = n. we similarly have Pr μ[(x i − x j ) 2 = 1] = 1 2 , since x i and x j are rounded independently.


There has also been a separate line of work on learning from demonstration, which is then iteratively improved through reinforcement learning [17,6,23].

we do not assume access to the expert reward function, which is required to perform reinforcement learning in the later stages of the above algorithms.


Many research efforts have been devoted to developing efficient solvers for SGL [5,16,10,21].

when the feature dimension is extremely high, the complexity of the SGL regularizers imposes great computational challenges.


For the specific case of the squared loss, it is indeed possible to obtain the same rates without regularizing; we defer details to the full version of the paper.

in practice, regularization has several additional benefits: it renders the ERM optimization problem well-posed (i.e., ensures that the underlying matrix that needs to be inverted is well-conditioned), and guarantees it has a unique minimizer.


Thompson sampling is computationally tractable for some problem classes, like the linear bandit problem, where the posterior distribution is Gaussian with parameters (µ t , Σ t ) that can be updated incrementally and efficiently via Kalman filtering as outcomes are observed.

when dealing with complex models, like neural networks, computing the posterior distribution becomes intractable.


Besides, compared with the algorithms adopting 1 -or nuclear-norm convex relaxation (e.g., [16,17,18,19]), directly solving problem (1) via FG-HT often exhibits similar accuracy guarantee but is more computationally efficient.

despite these desirable properties, FG-HT needs to compute the full gradient at each iteration which can be expensive in large-scale problems.


If approaches 0, then the rate of convergence becomes optimal but the sample complexity deteriorates.

if approaches 0.5, then the sample complexity becomes optimal, but the rate of convergence deteriorates.


As shown in Lemma 4, this regularizer also helps improve the robustness of the regression model to noise since maximizing f ld (S) minimizes the entropy of the perturbation error.

for a multivariate Gaussian distribution, f ld (S) also equivalent (up to an additive |S| factor) to the differential entropy of S. f ld (S) is undefined if S is rank-deficient and might also take negative values; the smoothed version f de (S) overcomes these issues.


. . , ξ Mg ] T is a vector of M g scalar operators.

one may make the assumption that the same set of operators that are used to describe f i also can be used to describe g, i.e., ξ g = ξ f . this assumption might need to be relaxed.


If the couch is predicted as clutter and the image evidence from the couch is ignored (Figure 1(c)), multiple room hypotheses can be selected based on the predicted labels of the pixels on the wall (Figure 1(d)) and there is still not enough evidence in the image to select one hypothesis over another in a confident manner.

if we represent the object by a 3D parametric model, such as a cuboid (Figure 1(e)), then simple volumetric reasoning (the 3D volume occupied by the couch should be contained in the free space of the room) can help us reject physically invalid hypotheses and estimate the correct layout of the room by pushing the walls to completely contain the cuboid (Figure 1(f)).


These terms are a consequence of the special case analysis for L 1 norm.

we consider the general case and simply get the scaled Gaussian width term Λ max (Σ) w(A).


As demonstrated in literature [5,6], learning a distance metric from training data to maintain class information is beneficial for MIL.

existing methods [5,6] learned only one global metric for a multi-instance data set, which is insufficient because the objects in multi-instance data by nature are highly heterogeneous.


Unfortunately, in the current state of research, there is little hope that in the near future a machine will be able to automatically find-or even engineer-the best kernel for a particular problem at hand [25].

by restricting to a less general problem, can we hope to achieve the automatic kernel selection?


Rao and Sejnowski [8] show that STDP emerges when a neuron attempts to predict its membrane potential at some time t from the potential at time t − ∆t.

sTDP emerges only for a narrow range of ∆t values, and the qualitative nature of the modeling makes it unclear whether a quantitative fit can be obtained.


We refer to u, π, φ as global parameters because they generalize to new data sequences.

the states z n are local to a specific sequence x n . We seek a distribution q over the unobserved variables that is close to the true posterior, but lies in the simpler factorized family q(•) q(u)q(φ)q(π)q(z).


Under relatively mild conditions, one may guarantee the existence of fixed points [13].

they may not be unique, nor are the results exact (the belief M i t does not converge to the true marginal).


Intuitively one would expect that, if there is node correspondence between the graphs, clustering based on graphon estimates would work better, because it aims to estimate the underlying probabilistic model for comparison.

in our experiments we found that a properly tuned NCLM matched the performance of NCGE.


Given A ∈ R n×d and y, the goal of SLR is to recover a sparse vector x that minimizes Ax − y The unconditional version of sparse regression can be shown to be NP-hard via a reduction to 3-set cover [14].

the problem has been studied heavily under a variety of assumptions such as incoherence [7], null-space property [8], restricted isometry property (RIP) or restricted strong convexity (RSC) [4,15].


In all cases, cascading the models is able to improve the robust error performance, sometimes substantially, for instance decreasing the robust error on CIFAR10 from 46.1% to 36.4% for = 2/255.

this comes at a cost as well: the nominal error increases throughout the cascade (this is to be expected, since the cascade essentially tries to force the robust and nominal errors to match).


The alpha-wealth has been used up fully, and those are the only rejections we are allowed to make with that batch of p-values.

for an internet company operating with motivation M2, it might be unacceptable to inform them that they essentially cannot run any more tests, or that they may perhaps never make another useful discovery.


The scheduled restart schemes we present here rely on a global sharpness hypothesis on the sublevel set defined by the initial point and are not adaptive to constant µ on smaller sublevel sets.

restarts on criterion that we present in Section 4, assuming that f * is known, adapt to the value of µ.


r = O(log n), it is hopeless to get any consistent estimator for the class D(α, C) since n −(1/ log n) = 1/e.

the ambient dimension d can increase exponentially fast with the sample size, which is a realistic scaling for high dimensional settings.


We see from the graphical representation in Figure 2 that z n is d-separated from x n . Thus when y n is observed, the posterior process is updated by using p (y n |f n ).

when the data point is unlabeled the posterior process must be updated by p (z n |f n ) which is easily computed as: The "effective likelihood function" for a single data point, L (f n ), therefore takes one of three forms: The constraint imposed by (1) implies that an unlabeled data point never comes from the class y n = 0.


In that equilibrium, H selects (1, 1) if θ ∈ [ 41 92 , 51 92 ].


This is useful for visualization [21,17,18,1], clustering [13], semi-supervised learning [2] and more.

in embedding approaches, the relation between a new point and the embedded points are less well-defined, and consequently these approaches are less suited for building generative models.


In practice, such information is not often available.

we can replace E m with a data-dependent local Rademacher complexity bound Êm , as in [7], which also satisfies (1), and satisfies (with high probability) Êm ≤ c ′ E m , for some constant c ′ ∈ [1, ∞) (see [13]).


For i = 1, 2, we define D i := (e f i , h i , x i,0 ) 2 T (C, C r ), and Note that, introducing the exponential discounting e is a way to construct a mathematically valid kernel to compare dynamical systems.

in a certain situation, this method does not work effectively.


Clearly, the original mixing matrix could not be reconstructed in any of the experiments.

interestingly, the latter two algorithms do indeed find an ISA up to permutation, which will be explained in section 3. theoretically speaking, it may only be applied to random vectors following the k-ISA blind source separation model, which means that they have to be mixtures of a random vector that consists of independent groups of size k. If this is the case, uniqueness up to permutation and scaling holds as noted above; however if k-ISA is applied to any random vector, a decomposition into groups that are only 'as independent as possible' cannot be unique and depends on the contrast and the algorithm.


In addition to the baselines already described, we also implement the dilated CNN.

the receptive fields size of a nine-layer dilated CNN is 512, and is insufficient to cover the sequence length of 784.


The overall loss for the network is defined as:  The proposed framework is able to generate diverse realistic outputs.

it does not require any supervisions during its training phase.


This direct linear programming approach experimentally yields a significant reduction in computation time over approximate value-and policy-iteration methods (sometimes reducing several hours to a few seconds).

the quality of the solutions produced by linear programming is weaker-usually about twice the approximation error for the same approximating class.


This algorithm is motivated by the observation that the Jacobian matrix (of derivatives) of the encoding function provides an estimator of a local Gaussian approximation of the density, i.e., the leading singular vectors of that matrix span the tangent plane of the manifold near which the data density concentrates.

a formal justification for this algorithm remains an open problem.


One important limitation of VAEs is the prior assumption that latent sample representations are independent and identically distributed.

for many important datasets, such as time-series of images, this assumption is too strong: accounting for covariances between samples, such as those in time, can yield to a more appropriate model specification and improve performance in downstream tasks.


The Places-CNN feature shows impressive performance on scene classification benchmarks, outperforming the current state-of-the-art methods for SUN397 (47.20% [21]) and for MIT Indoor67 (66.87% [4]).

the ImageNet-CNN feature shows better performance on object-related databases.


Provided that some agents contribute to the public good by cleaning up the aquifer, it is individually more rewarding to stay in the apple field.

if all players defect, then no-one gets any reward.


For example, in the Flash Fill system [Gulwani, 2011], this knowledge is explicitly specified by the system's creators.

neural program synthesis methods need to learn both the semantics of the DSL and how to synthesize programs in the DSL entirely from the training data.


[25,24] combined image classification, annotation and segmentation with a hierarchical graphical model.

these methods required considerable attention to each classifier, and considerable insight into the inner workings of each task and also the connections between tasks.


End point movement in small time steps is loosely approximated as having constant acceleration.

neural spike counts (which are typically measured in bins of 50 − 100ms) vary greatly from one time step to the next.


Indeed, almost all prior work performs computation proportional to the size of the data domain, which limits them to datasets with relatively few attributes.

we are able to process datasets with thousands of attributes, corresponding to domains of size 2 1000 .


The classification error rate of LR achieves 0.8, which is even worse than random guess.

roLR still achieves satisfactory classification performance with classification error rate around 0.4 even with λ → 1.


Previous studies have proposed image-based clutter measures that correlate with human search times and/or eye movements.

most models do not take into account the fact that the effects of clutter interact with the foveated nature of the human visual system: visual clutter further from the fovea has an increasing detrimental influence on perception.


It has previously been observed that environmental statistics can influence the neural tuning curves of sensory neurons [1,2,3,4,5].

most theoretical analysis has usually assumed the input stimulus distribution to be uniform.


As the appearance features typically take on real values, we first apply k-means clustering to the image features {a i } to build a visual vocabulary V. Thus a feature a i in the appearance space A can be represented as a visual word v, and we have While the topic prediction model in Equation 1 is able to capture regularly co-occurring patterns in the joint space of label and appearance, it ignores spatial priors on the label prediction.

i z spatial priors, such as spatial smoothness, are crucial to labeling tasks, as neighboring labels are usually strongly correlated.


We also study a convex relaxation for sparse SVD, based on the DSPCA algorithm proposed by [11] that encourages the singular vectors of the matrix to be supported over a sparse set of variables.

despite the increasing popularity of this method, we show that it is only guaranteed to yield a sparse set of singular vectors when the SNR is quite high, equivalent to element-wise thresholding, and fails for stronger scalings of the SNR.


In the case of the HUB experiments all classifiers perform similarly in both speaker verification and identification tasks with the exception of the SVM Fisher which performs significantly worse.

for the KING database, we can see that our KL based SVM kernels outperform all other classifiers in both identification and verification tasks.


Since the edges at each step are drawn iid given W , the graph sequence is edge exchangeable.

the corresponding graph measure G = i,j n ij δ (i,j) (where ) is not Kallenberg exchangeable, since the probability of generating edge {i, j} is directly related to the positions (i, j) and (j, i) in R 2 + of the corresponding atoms in G (in particular, the probability is decreasing in ij).


For our intended optimization routine, we are actually looking for the minimizer of an expected loss function L * (θ) = E x∈D L (θ, x).

in the parallel setting, we cannot investigate L * directly and we may only analyze it through L N . calculating the total loss function directly and exactly requires excessive inter-processor communication, which carries a huge computational burden as the number of processors increase.


Rules written by a human penalise undesirable combinations of notes, so that they will be filtered out when the best chord is chosen from all those compatible with the harmony already decided.

our model learns all its harmonic 'rules' from its training data.


Therefore, with su cient network capacity and optimization, the ensemble members will agree at observed data.

in regions of the space with little or no training data, their predictions will be determined by the generalization of their networks and priors.


Using this paradigm, we can easily deal with incomplete descriptions and errors in features and labels.

traversal to the use of more powerful classifiers, better image representations, such as SIFT [17] or GIST [21] have boosted recognition and categorization performance.


The problem of how many control questions to use is unlikely to yield a definitive answer, since real data are always likely to be more complicated than any model.

our results highlight several issues and provide insights and rules of thumb that can help crowdsourcing practitioners make their own decisions.


If one is interested in classification accuracy alone, without requiring deterministic guarantees, then online to batch conversion techniques combined with stochastic subgradient descent are a good choice [17].

while the dependence on is still Ω(1/ ) or worse [18], one gets bounds independent of n. as we pointed out earlier, these algorithms are applicable only when the empirical risk decomposes over the examples.


For problem of medium scale, ( 6) is not easier to solve than a linear system due to non-negative constraints, and thus an ALM is not preferred to IPM in the traditional sense.

for large-scale problem with m × n nnz(A), the ALM becomes advantageous since: (i) the conditioning of (6) does not worsen over iterations, and thus allows iterative methods to solve it approximately in time proportional to O(nnz(A)).


To summarize, the best known upper bound for optimizing with intermittent communication using a pure stochastic oracle is (20), which combines two different algorithms.

with active oracle accesses, SVRG is also possible and the upper bound becomes: Our main contributions in this paper are: (1) presenting a precise formal oracle framework for studying parallel stochastic optimization; (2) establishing tight oracle lower bounds in this framework that can then be easily applied to particular instances of parallel optimization; and (3) using the framework to study specific settings, obtaining optimality guarantees, understanding where additional assumptions would be needed to break barriers, and, perhaps most importantly, identifying gaps in our understanding that highlight possibilities for algorithmic improvement.


it emphasizes different aspects of real-world CPR problems.


More details about the block Lanczos is given in Appendix 6.1.

rSVD, which is equivalent to subspace iteration with a Gaussian random matrix, constructs a basis for A j 1 V 0 and then restricts A to this subspace to obtain the decomposition.


The magnitude of this factor is less trivial than it seems: since the algorithm increases the threshold by b t , it includes more hypotheses in the version space, which may cause the algorithm to query a lot more.

our analysis shows that the number of queries only increases by O(tb t ln t), i.e., ln t times the total number of ⊥'s received over t examples.


A pseudo code of the LCV procedure is summarized in Figure 1-(b) One of the potential limitations of CV in general is that it is not reliable in small sample cases since data splitting by CV further reduces the sample size.

in our CV procedure, the data splitting is performed over the test input samples, not over the training samples.


A standard technique for obtaining a mistake bound with respect to fairness violations would be to play a "halving algorithm", which would always act as if the unknown metric is at the center of the current version space (the set of metrics consistent with the feedback observed thus far) -so that mistakes necessarily remove a non-trivial fraction of the version space, making progress.

a standard technique for obtaining a diminishing regret bound is to play "optimistically" -i.e.


2 argmin F . The most popular algorithm for solving (1) is Stochastic Gradient Descent (SGD), which achieves statistically optimal O(1/ p N ) suboptimality in O(N ) time and constant memory.

in modern large-scale machine learning problems the number of data points N is often gigantic, and so even the linear time-complexity of SGD becomes onerous.


In some applications, annotators are required to be trained before identifying classes in data, and feedback from many annotators is aggregated to reduce labeling error.

many inexpensive approaches for collecting labeled data exist, such as data mining on social media websites, search engines, querying fewer annotators per instance, or the use of amateur annotators instead of experts.


The assumption that r k = N k /M k may seem rather strong.

it is essential as it justifies the decoupling equation ( 3) that enables a linear-time algorithm.


For instance, [3,10] use regular subsampling and [9,14,18] use random sampling based on compressed sensing.

they remain difficult to scale computationally, especially for large s and n. In this paper, we are interested in learning polynomials with s = O(2 δn ) for some δ ∈ (0, 1).


Figure 6 shows how using modules achieves higher training accuracy compared to the nonmodularized baseline.

in comparison to the language modeling tasks, this does not lead to improved generalization.


When the input is i.i.d., this is trivial as we can learn the best expert in O(log d) rounds and then follow its advice; since the expert is fair in isolation, this will guarantee vanishing non-discrimination.


Since J determines the information rate completely, we conclude that for any weakly-coupled network there is an equivalent Poisson network which conveys exactly the same information in the intermediate regime.

note that the the sufficient statistic ∆(r) is different in the Poisson and non-Poisson settings, since the f /f term linearly reweights the observed spikes, depending on how likely they were given the history; thus the optimal Bayesian decoder incorporates non-Poisson effects explicitly.


Consider corefTemplate in Figure 2, the neighbors of the template are Mention, Entity pairs.

the sufficient statistic is simply a Boolean based on the "distance" of the unrolled Mention from the canonical value of the Entity.


In neuroscience, the analysis of electrophysiological time-series data is largely centered around dynamic causal modeling (DCM) [5], where continuous state-space models are formulated based on differential equations that are specifically crafted around knowledge of underlying neurobiological processes.

dCM is not suitable for exploratory analysis of data, such as inferring unknown arousal levels, for two reasons: because the differential equations are driven by inputs of experimental conditions, and the analysis is dependent on a priori hypotheses about which neuronal populations and interactions are important.


Thus, the probability that an random element of À Ò is in a ball of radius « centered at one of ½ AE is at least AE´ ½ «µ Ò ½ .

since each ½ AE has distance at most « from , any element of an « ball centered at one of them is at most « • « far from .


Various first-order optimization algorithms such as gradient descent [42], stochastic gradient descent [27] and more recently variance-reduced stochastic gradient descent [46,3] have been proposed and analyzed for solving (1.1).

all these algorithms are only guaranteed to converge to a stationary point, which can be a local minimum, a local maximum, or even a saddle point.


On this trial, and the other "interval" trials, the concept learning model is certain that the correct concept is of the form numbers between m and n, because the observed examples rule out all the other concepts.

the model is not certain of the precise endpoints, such as whether the concept is numbers between 16 and 23, or numbers between 16 and 24, etc.


the overlap between the leading eigenvectors of the sample and population covariances [3].

the method as presented here is restricted to Gaussian data.


As reported in [1], AP does significantly outperform K-centers.

aP shows the unsatisfactory performance on the digit data where the manifold structures may occur due to that the styles of digits vary significantly.


This is interesting in and of itself since there are laminar matroids that are not cycle matroids.

we show that the more general DSFs share a variety of useful properties with decomposable functions.


In each epoch, only a constant number c 1 of turns is dedicated to exploration.

the estimation uses all the previous exploration phases, so that the number of samples for estimation grows linearly with time.


The algorithm is proved to converge almost-surely to a local saddle point.

the constraints are just implicitly considered by updating dual variables and the output policy may not actually satisfy the constraints.


Again, we find a significant (p < 0.005) correlation coefficient of -0.283 averaged over 10 runs.

this is a much weaker correlation than is found in the literature.


There are some studies on how to evaluate automatically generated summaries in the presence of multiple human-created annotations [21,22,23].

for learning, our goal is to generate one single ground-truth or "oracle" summary per video.


To tackle this challenge, we need to develop an appropriate machinery to check whether the value of c is already large enough for SVRG to decrease the objective value.

we cannot afford the cost for computing the objective value due to large n. To this end, we develop a "certificate" that can be easily verified and can act as signal for a sufficient decrease in the objective value.


2c attempts an unsafe action after some exploration.

algorithm 1 manages to safely explore a large part of the unknown environment.


Then the optimal coefficient vector would be It can be shown that r OLS is a biased estimator of r O , while r EO is an unbiased one.

the variance of r OLS is smaller than that of r EO .


The amount of this shifting is also known to the intended receiver of the message, who can decode the message by shifting back each letter in the encrypted message.

caesar cipher could also be broken by an unintended receiver (not knowing the shift) when it analyzes the frequencies of the letters in the encrypted messages and matches them up with the letter distribution of the original text [4, pp.9-11].


Such a model would learn to look at different parts of human body and its interactions with nearby objects.

it's notable that most existing action datasets, including [6,7,27,34,41,45], come with only frame or video level labels; and though [18,30] are designed for instance-level recognition, they are not applied as such.


Especially, PLML outputs multiple metrics which are similar to each other (tends to global learner's behavior) and only focus on first part of the alphabet, while MMLMNN by default only learns multiple metrics with the number of base metrics equaling to the number of classes.

results of UM 2 L OVS clearly demonstrate all 3 fields.


The particular stochastic processes we analyze are abstract.

they may be seen as models both for internally-generated neural processes, such as (spontaneous) network activity and local field potentials, and for sensory processes, in the form of externally-driven neural activity, or (taking a functional view) in the form of the stimuli themselves.


For most problems of interest, it is not efficient to compute this dense Hessian.

one can also differentiate the gradient-vector product to get a Hessian-vector product-this computation is usually not much more expensive than the gradient computation itself.


We notice that [16] also introduced the same regularization term τ /2 Π 2 F in their estimator.

our motivation is quite different from theirs.


First, we observe that the RANDOM approach tends to yield decent performance when the number of queries is very small.

as the number of queries increases, this simple approach loses its edge and often is not as effective as the other active learning approaches.


The gradient chains for Q u , in RIAL and Q, in DIAL, are based on the DQN loss.

in DIAL the gradient term for m is the backpropagated error from the recipient of the message to the sender.


They also define SP-LIME which summarizes a model by finding a set of points whose explanations (generated by LIME) are diverse in their selected features and their dependence on those features.

this does not address the difficulties local explanations have with global patterns because the individual explanations being chosen all are unaware of them.


As with any algorithm, there is a trade-off: DFacTo uses 3 times more memory than the Tensor Toolbox, since it needs to store 3 flattened matrices as opposed to a single tensor.

in return, our algorithm only requires two sparse matrix-vector multiplications, making DFacTo easy to implement using any standard sparse linear algebra library.