( 1) can be reformulated as a maximization for θ using max θ f (θ, w * (θ)).

typical GAN training only alternates two gradient updates w ← w − η w ∇ w f (θ, w) and θ ← θ + η θ ∇ θ f (θ, w), and usually just one step for each of θ and w in each round.


The heart data involves 6 variables giving rise to 2 6 = 64 clique candidates in total and a search space of 2 This illustrates the power of branch-and-bound type algorithms behind the solvers and their ability to prune the search space.

the econ dataset is based on 8 variables giving rise to a much larger search space 2 28 .


Ideally we would like to compute this whole a priori distribution of entropies, but this is quite difficult.

as noted by Wolpert and Wolf [6], one can compute the moments of P β (S) rather easily.


Here, we consider polynomial combinations of higher degree d ≥ 1 of the base kernels with non-negative coefficients of the form: Any kernel function K µ of this form is PDS since products and sums of PDS kernels are PDS [4].

note that K µ is in fact a linear combination of the PDS kernels the number of coefficients µ k1•••kp is in O(p d ), which may be too large for a reliable estimation from a sample of size m. Instead, we can assume that for some subset I of all p-tuples (k 1 , .


This property does not strictly hold for optimizers that use separate learning rates for individual parameters, like Adam [15] which we use in experiments, or when using momentum.

qualitatively we still find the same effect to hold.


In [14][15][16][17][18][19], analyze convex programs similar to the Programs 1.1 and 1.4 for the SBM and show that the minimum cluster size should be at least O( √ n) for successfully recovering the clusters.

the exact requirement on the cluster size is not known.


In the original GTEx eQTL study, no features were considered in the FDR analysis, corresponding to running the standard BH or SBH on the p-values.

we know many biological features affect whether a SNP is likely to be a true eQTL; i.e.


There are several works that show lower bounds on the quality of LSH hash functions [19,10,20,11].

those papers provide only a lower bound on the ρ parameter for asymptotic values of p 1 and p 2 , as opposed to an actual trade-off between these two quantities.


This seems much more restrictive than consistent matrix reconstruction that merely requires rN log N /|Ω| → 0 (Lemma 6, Appendix A).

this is due to the pessimistic nature of the error bound.


Like a standard multiple tree algorithm, the variable tree algorithm searches combinations of tree nodes to find valid sets of points.

we limit this search to just those points required to define, and thus bound, the models currently under consideration.


We find that object recognition performance of models B1 to B9 is improved compared to models A1 to A9, both on the distortions they were actually trained on (diagonal entries with red rectangles in Figure 4) as well as on a few of the distortions that were not part of the training data.

this improvement may be largely due to the fact that models B1 to B9 were trained on 200 epochs instead of 100 epochs as for models A1 to A9, since the accuracy of model B9 (trained & tested on uniform noise, 200 epochs) also shows an improvement towards model A9 (trained & tested on uniform noise, 100 epochs).


While other features such as "athlete" or "musician" might indicate that one person could be a friend of another, the geographic features could have extremely negative weights so that people who live far from each other are less likely to be friends.

the parameters for the non-geographic features would still be tied for all people, allowing us to make stronger inferences about how they influence the relations.


For this, we ran the trained detector on the training set to obtain the offsets and used the mean to compensate for the location changes.

we observed empirically that it did not help performance.


While the optimization ( 14) is convex, the running time of lasso is significantly longer than OMP unless A has some particular structure [10].

it is generally believed that lasso has superior performance.


Compared to the local polynomial derivative estimator in Figure 1b, the proposed estimator is slightly better in the interior for model (11).

both methods suffer from boundary effects.


Such an approach can be viewed as a pseudo-likelihood approximation of the full likelihood.

[1,30,10] propose a penalized likelihood approach to directly estimate Ω.


It has been shown that when using a characteristic kernel for the mapping [9], the properties of RKHS operators are related to statistical independence between input variables and allow testing for it in a principled way with the Hilbert-Schmidt Independence Criterion (HSIC) test [11].

the suitability of this test relies heavily on the assumption that i.i.d.


The time-consuming part of synthetic data generation is the creation of the mesh models of the objects.

there are many objects for which models are available on the internet, and can be used with only minor modifications.


We can form R with R u,v = r(u, v) and initialize the Laplacian of H using the formula given in (3) in Theorem 1.

this formula is quite unstable and generally yields an output which is far from a Laplacian even when R is corrupted by a small amount of noise.


Strictly speaking, this set is uncountable since b ij is continuous and arbitrary.

since we always select one bias parameter for each hypercut w ij , we do in fact end up with only M p M n classifiers.


used a global image descriptor [29] as an initial feature representation rather than pixels.

to avoid such hand-crafted features which may not be suitable for the task, and to scale to realistic sized inputs, models should take advantage of the pictorial nature of the image input.


A deep understanding of the value of control items may provide useful guidance for crowdsourcing practitioners.

a line of research has studied more advanced consensus methods that are able to simultaneously estimate the workers' performance and items' answers without any ground truth on the items, by building joint statistical models of the workers and labels (e.g., Dawid and Skene, 1979, Whitehill et al., 2009, Karger et al., 2011, Liu et al., 2012, Zhou et al., 2012.


BrownBoost is designed for noise tolerance, and it does well in the case of l = 5, but it also cannot handle the case of l = 20 and η > 0%.

directBoost order performs very well for all cases, showing DirectBoost order 's impressive noise tolerance property since the most difficult examples are given up without any penalty.


Then, for any bidding policy µ, R µ T (f ) ≥ (1/16 The proof of Theorem 2 is obtained by showing that, every time the bid is cleared, an incremental regret greater than /2 is incurred under the distribution with π = (1/2− ); otherwise, an incremental regret greater than /2 is incurred under the distribution with π = (1/2 + ).

to distinguish between these two distributions, one needs Ω(T ) samples, which results in a regret lower bound of Ω( √ T ).


The general theme is that the larger β is, the better the statistical properties of the maximumlikelihood estimator.

larger β also makes the distribution p θ,β less tractable, as q β (y | z) becomes concentrated on a smaller set of y's.


We further assume that the average number of non-zero elements of v i is d. In very large-scale problems, a single machine cannot hold all of the data in its memory.

we assume that a single node can hold a fraction of 1/s of the data in its memory.


Drawing inspiration from simpler dynamic Bayesian networks (DBNs) such as HMMs and Kalman filters, the proposed variational recurrent neural network (VRNN) explicitly models the dependencies between latent random variables across subsequent timesteps.

unlike these simpler DBN models, the VRNN retains the flexibility to model highly non-linear dynamics.


It is intuitive to directly resize all convolutional filters into matrices of the same dimensions and then apply k-means.

this simple resizing method increases the amount of the data that needs to be stored.


[26] showed global convergence and asymptotic superlinear convergence for Prox-QN methods under the assumption that the loss function is strongly convex.

this assumption is known to fail to hold in high-dimensional sampling settings, where the Hessian is typically rank-deficient, or indeed even in low-dimensional settings where there are redundant features.


It can be observed that when r = 0 and X is exactly Gaussian, Pearson,Spearman and Oracle can all recover the sparsity pattern perfectly.

when r > 0, the performances of Pearson significantly decrease, while Spearman is still very close to the Oracle.


They are thus viable for production settings where accessing c is expensive (requiring human labeling), impossible (requiring underlying transformations), or legally inadvisable (sharing protected data).

our method also produces a conditional decoder taking both c and z as inputs.


In the online setting, each sample is processed only once without storage, while in the distributed setting, one has several machines that can jointly fit the data into memory.

the real cases are often not as extreme as these two -there are usually machines that can fit part of the data, but not all of them.


However, this research is often applied to simplified datasets for demonstration purposes due to computation constraints, and are not aimed at improving the state-of-the-art.

we apply this perspective directly to the known state-of-the-art neural networks to show that this approach is now feasible and actually increases performance.


Traditionally, one would commit only this final representation to memory.

the Hierarchically Distributed Decision Theory stated that the intermediate results are also committed to some form of sensory memory (Figure Ib).


[15] applied the random walk with restart technique to the auto-captioning task.

their work is a supervised method requiring annotated caption words for the segmented regions in training images.


Our CPM also requires input and thus is also a type of conditional HMM.

the input is unobserved (but crucially it is shared between all replicates) and hence learning is unsupervised in the CPM model.


DMD finds approximations to the Koopman operator under the assumption that the state variables x span an invariant subspace.

they will not span an invariant subspace if the underlying dynamics are nonlinear.


Note that, larger mini-batch sizes produce lower errors here because it becomes closer to full-batch gradient and thus lower bias in SGD.

when the mini-batch size is as small as 10, the high error rate of 83.09% is close to a guess by majority rule -predicting the character (space) that has a largest proportion in the train set, i.e., 25, 499/153, 221 = 83.37%.


For comparison with [20,19] we evaluate our model following the set up described above and similarly, we have created dummy variables for those features that are categorical forming a total of 19 student-dependent features and 8 school-dependent features.

we note that school-descriptor features such as the percentage of students eligible for free school meals and the percentage of students in VR band 1 actually depend on the year the particular sample was taken.


when the number of dimensions is large, MSP and DSC outperform the other methods; this corresponds to the difficult regime of low signal to noise ratio.


One could argue that a log-Normal approximation to a Gamma-distributed variable is reasonable, although it is not accurate for small values of the shape parameter α i .

the most important implication is that we can now consider a Gaussian likelihood in the log-space.


Non-probabilistic classification schemes, such as SVMs, can handle traditional active learning by first establishing the confidence in the estimate of each label by using the distance from the classification boundary (margin) and then selecting the point that is closest to the margin.

it is fairly non-trivial to extend those approaches to tackle the active diagnosis and generalized information acquisition.


For example, setting δ = 1/n permits ( , δ)-DP mechanisms that always violate the privacy of a random individual [12].

there are other ways to specify that a random variable is mostly small.


It is a simple and effective procedure to combine many weak learners into a strong classifier.

most existing boosting methods were designed primarily for binary classification.


Finally, they use a standard L-BFGS solver for their inner problem, evaluating the criterion using additional sparse matrix software.

we enable Newton-Raphson by reducing it to Kalman smoothing.


Efficiency For small n, this approach is very fast ( 30ms per pair of images for n = 200 on a 3GHz PC).

higher quality results require n > 1000 observations which reduces the execution speed to a few seconds per image.


One limitation of our permutation-free explanation is that the argument only holds when the weights in Population EM 2 are initialized to be uniform.

the benefits of over-parameterization are not limited to this case.


We can then use an unsupervised learning method with the M reward functions as data points.

this approach would suffer from the sparsity of data, since each trajectory may not contain a sufficient amount of data to infer the reward function reliably, or the number of trajectories may not be enough for the unsupervised learning method to yield a meaningful result.


We adopt the CPM model proposed earlier [1].

instead of using upper confidence bound techniques, our work is motivated by another classic technique developed for MABs, namely that of forced exploration.


The feature space is typically induced implicitly by a kernel function, and linear PCA in the feature space is performed via the kernel trick.

due to the implicitness of the feature space, some extensions of PCA such as robust PCA cannot be directly generalized to KPCA.


Immediately from its definition, this function has the following properties: The first property is due to the facts that: (i) * is a non-negative cost function; (ii) T π B ,d+ * is a contraction mapping, which by the fixed point theorem [7] implies For the second property, from the above inequality one concludes that the Lyapunov function L * is a uniform upper-bound to the constraint cost, i.e., L * (x) ≥ D π B (x), because the constraint cost D π B (x) w.r.t.

policy π B is the unique solution to the fixed-point equation by construction, * (x) is an upper-bound of the cost-shaping term (x).


As mentioned in some of the above literature, the existing metrics for dynamical systems that have been developed are defined with principal angles between some appropriate subspaces such as column subspaces of observability matrices.

those are basically restricted to linear dynamical systems although Vishwanathan et al.


In principle, it is possible to use this theorem to prove central limit theorems in infinite dimensional settings, for example in kernel clustering where the associated reproducing kernel Hilbert space is infinite dimensional.

the required conditions become much less trivial, and actually fail to hold in some cases (see below for further details).


We have implemented the block-1 Hogwild algorithm.

in this scenario the algorithm diverges, which is certainly due to the fact that the spectral radius of M −1 Hog N Hog is greater than 1.


As an alternative to reward specification, imitation learning (Argall et al., 2009) and inverse reinforcement learning (Ng & Russell, 2000) instead seek to mimic expert behavior.

such approaches require an expert to show how to solve a task.


Neural Networks: One can constrain a neural network to be monotonic by restricting the network weights to all be positive [15,16,17,18,19].

this strategy significantly reduces expressibility [20].


Meanwhile, OG collects the Boolean signals (h k ) from MaxOracle during the greedy process (Line 5), and update estimators X(•) and N (•) according to those signals (Line 10).

maxOracle takes accessible arms A, estimators X(•), N (•), and counted time t , and returns an arm from A and signal h k ∈ {true, false} to instruct OG whether to update estimators for the following phase.


Also note that the most expensive step is in the first update for computing Σ t+1 yi , which if naively implemented would require an inversion of an L × L matrix.

this inversion can be computed easily using Sherman-Morrison-Woodbury formula, which in turn reduces the complexity of the update to O(K 3 + K 2 L).


The reasoning underlying both [19] and [20] is that square unfolding is better.

if we take the (ordinary) mode-k unfolding we can see ( 4) as an instance of information plus noise model (1) where m/n = n K−2 .


Similarly, the reverse correlation method does not give the correct RF, even in the simplest case where the input-output function (1) depends only on one projection.

vectors that span the RS are clearly special directions in the stimulus space.


Note that in reinforcement learning, the current reward is compromised by the rewards from intermediate states and future states.

in text generation, the generator G θ obtains the reward if and only if one sequence has been completely generated, which means no intermediate reward is gained before the sequence hits the end symbol.


This circuit produced behavior similar to STDP, implying it could be used in PEP.

it was sensitive to variability in the NMDA and potentiation thresholds, causing a fraction of the population to potentiate anytime the synapse received an input and another fraction to never potentiate, rendering both subpopulations useless.


Mental Images: Our methods build upon work to extract mental images from a user's head for both general objects [15], faces [23], and scenes [17].

our work differs because we estimate mental images in state-of-the-art computer vision feature spaces, which allows us to integrate the mental images into a machine recognition system.


The backbones are some feature extractors such as VGG 16 [47] and Resnet 101 [17].

the number of categories being considered usually is small: 20 for PASCAL VOC [10] and 80 for COCO [29].


There has been considerable progress in improving cooling efficiency, and best-practice physical designs are now commonplace in large-scale DCs [7].

on the software side, designing resource-efficient control strategies is still quite challenging, due to complex interactions between multiple non-linear mechanical and electrical systems.


This amounts to solving a classical transportation (or matching) problem for which very efficient solvers exist [19].

solving (7) using accelerated gradient algorithms requires solving a projection step on doubly stochastic matrices at each iteration [20].


We observe that the most probable regions are also lying over the track (black being more likely).

when sampling new trajectories using the learned density, we can see that, whereas the trajectories using our method are confined to the track, the GMM results in undesirable trajectories.


( 3) to marginalize over the space of possible worlds.


Previous work such as [7,18] have used fixed bin-size histogram or Parzen window methods for this purpose.

these methods do not generalize to high-dimensional data.


Boosting can be integrated into the CNN such that discriminative neurons are selected and activated in each iteration of CNN learning.

the boosting CNN (B-CNN) can overfit due Outputs of the FC layer are employed as input features and a subset of features (the blue nodes) are selected by boosting.


In other words, the approximate algorithm has no false negatives.

the algorithm overapproximates influence, so the algorithm can give a finding of "potential proxy use" when there are no proxies, resulting in a false positive.


Hence, we believe MNIST↔SVHN is a very challenging set-up and despite the huge visual differences, our algorithm results in accurate nearest neighbors.

figure 2 visualizes the example target images from webcam and their corresponding nearest source images from Amazon.


Since this is real data, we do not know the "ground truth" .

compared to the least squares method, our algorithm preserves more detail.


The observation may support the hypothesis that CNN based object detectors are highly over-parameterized.

when the size of dataset is much larger, it becomes much harder to outperform more complicated models.


[13] encode the 3d information of a single person inside a feature map forcing the network to output 3d joint positions for each semantic body joint at its corresponding 2d location.

if some joints are occluded or hard to recover, their method may not provide accurate estimates.


This experiment is an unusual example of BO as measurements can be obtained very quickly at frequencies up to 1 Hz.

the results are representative for only a couple of hours due to drift in the system.


While any linear program can be converted to an equivalent one in form (1), the margin can be exponentially small in the representation.

in practical applications the margin is usually a constant independent of the problem dimensions; a justification is given next.


We aim to embed the data points in as low-dimensional a space as possible in order to avoid the curse of dimensionality.

if the embedding dimension is too small, then distinct data points might be collapsed onto the same embedded point.


Bootstrapped DQN reaches peak performance roughly similar to DQN.

our improved exploration mean we reach human performance on average 30% faster across all games.


Similarly to STEVE, the target used is an unbiased linear combination of returns with minimum variance.

the Ω-return is not directly computable in non-tabular state spaces, and does n-step off-policy learning rather than learn a predictive model of the environment.


While in this paper we are not concerned with sequential learning, we have found it to be a good strategy to bootstrap a model when a large number of domains have to be learned.

the most popular approach to sequential learning, fine-tuning (section 2), is often a poor choice for learning shared representations as it tends to quickly forget the original tasks.


Moreover, missing value imputation can at most gauge the values of noisy covariates but inferring the latent confounders is the most critical for accurate causal inference.

the large number of covariates may include heterogeneous data types (e.g., continuous, ordinal, categorical, etc.)


's part-based models [6], and between different objects in 2D images [13,14].

a lot of valuable information about the shape and geometric layout of objects is lost when a 2D image is formed from the corresponding 3D world.


The most common approach to document categorization is to reduce the problem to a "flat" classification problem [13].

it is often the case that the topics are not just discrete classes, but are nodes in a complex taxonomy with rich inter-topic relationships.


Exact algorithms have been proposed for solving (24) (for instance, [18]).

the computational cost of these algorithms grows exponentially with respect to N which makes them impractical for our purposes.


Experiments with both artificial [12] and real [13] data have shown that starting from fixed, correct (or at least linguistically reasonable) structure, EM produces a grammar which has higher log-likelihood than the linguistically determined grammar, but lower parsing accuracy.

we additionally conjecture that EM over PCFGs fails to propagate contextual cues efficiently.


At a high level, all these results suggest that it is possible to leverage the structure to improve the SNR threshold at which the hypothesis testing problem is feasible.

computationally efficient procedures that achieve the minimax SNR thresholds are only known for a few of these problems.


The CCCP framework [23] was recently utilized in [22,25] to provide a local optimum solution by iteratively solving the latent variables H and the model parameter ω.

the CCCP does not address the or-nodes in hierarchy, i.e., assuming the configuration of structure is fixed.


Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property.

estimating and optimizing α-divergences require to use importance sampling, which may have large or infinite variance due to heavy tails of importance weights.


Preliminary results reported in [13] in a related context suggest that the resulting predictor can outperform predictors based on the individual scalar scores.

we will not pursue this idea further in this paper.


As in the synthetic experiments, spectral hashing appears to have an advantage over our method for extremely small code sizes, up to about 32 bits.

this low bit regime may not be very useful in practice, since below 32 bits, neither method achieves performance levels that would be satisfactory for real-world applications.


The theory of [1] only guarantees that this approach will achieve invariance (and discriminability) in the case of affine transformations.

many researchers have shown good performance of related architectures on object recognition tasks that seem to require invariance to non-affine transformations (e.g.


Multi-Frame SR. Baker and Kanade [2] extract optical flow to model the temporal dependency in video sequences for video SR. Then, various improvements [14,13] around this work are explored to better handle visual motions.

these methods suffer from the high computational cost due to the motion estimation.


Strehl and Littman [4] showed that in the discounted setting, efficiency in the sample complexity implies efficiency in the average loss.

average loss is defined in respect to the actually visited states, so that small average loss does not guarantee small total regret, which is defined in respect to the states visited by an optimal policy.


The modified MDP is equivalent to the original one in terms of dynamics, f (s, a).

we introduce additional action-states s a for each action in the original MDP.


Our work is rather different since the code/workload (as represented by the computation graph) is dynamically specified and must be executed rapidly, which precludes sophisticated statistic analysis.

we review some of the important related work here.


In fact, it has been shown in [1,2,11] that simple ad-hoc methods, and the greedy, SCoTLASS and SPCA algorithms, often underperform DSPCA.

the first-order algorithm for solving DSPCA, as developed in [1], has a computational complexity of O(n 4 √ log n), with n the number of features, which is too high for many large-scale data sets.


[9] proposed multi-stage algorithms to achieve the optimal strongly convex rate based on non-accelerated dual averaging methods.

the algorithms in [9] assume that φ(x) is a Lipschitz continuous function, i.e., the subgradient of φ(x) is bounded.


Second, the ZMP criterion does not permit rotation of the stance foot at the heel or the toe, which, however, can amount to up to eighty percent of a normal human walking gait, and is important and inevitable in fast biped walking.

sometimes dynamic biped walking can be achieved without considering any stability criterion such as the ZMP.


Probability estimation is one of the fundamental tasks in statistics and machine learning.

standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner.


The theoretical results suggest that the RDP approach may be impractical for large networks.

we can accelerate the algorithm and produce high quality solutions by making some changes, motivated by observations from our initial experiments.


For pred 1 ( (i)) = f 2 ( ) = i 1.1 , f 2 (i 1) f 2 (i) is monotonically increasing with i.

for pred 1 ( (i)) = f 1 ( ) = 1/i, f 1 (i 1) f 1 (i) is monotonically decreasing with i. Lemma 4 shows that the mistake bound (in terms of L NDCG ) of Predtron is better when pred 1 function is selected to be f 2 ( (i)) = i 1.1 (as well as for f 3 ( (i)) = i 2 ) instead of f 1 ( (i)) = 1/i.


[4] and [5] have proposed gene selection methods, which we call univariate ranking (UR) and recursive feature elimination (RFE) (see [14]), that can be combined with the 2-norm SVM.

these procedures are two-step procedures that depend on external gene selection methods.


In this experiment, Rasch appears to be the second-best method.

as our next experiment indicates, the success of Rasch hinges on the fact that the marginals of this experiment do not introduce many knots.


Hyperparameter estimation is the subject of many studies such as the "evidence framework" [4].

if the prior models the source poorly, no hyperparameters can be reliable [5].


The results show that the tree-based algorithm has an advantage in the beginning of the learning process.

the CE-Tree algorithm has problems finding a good policy in the 3-dimensional action-space, while the LAWER algorithm still performs well in this setting.


if we use the original CMAB framework, we need to set T i,t = T i,t−1 + 1{k i,t > 1}.


Sparse graph sequences are more representative of real-world graph behavior.

many popular network models (see, e.g., Lloyd et al.


On one  MovingMnist [33] DFN [19]& SVG [7] 10 inputs for 10 outputs 64x64 RobotPush [10] CDNA [10]& SV2P [3] 2 inputs for 8 outputs 64x64 Human3.6M [17] DrNet [8]& MCNet [34] 5 inputs for 10 outputs 64x64 Because the gradients back-propagated from them are to optimize different networks, which gets rid of balancing between these two loss functions.

sub-networks are designed dedicated for different objectives, e.g., the sampler is required to produce high quality proposals without requirement of motion accuracy, while the selector should be able to fully capture the motion information of previous inputs and select out proposals with high motion accuracy.


The responses of the central subregions matched the timing of the geniculate center.

the timing of the lateral subregions resembled more closely the timing of the geniculate surround (both peaked at 25-50 msec).


In particular, the automatic relevance determination (ARD) squared exponential kernel is often a default choice for Gaussian process regression.

sample functions with this covariance function are unrealistically smooth for practical optimization problems.


For any f , there exists With Theorem 5, we could reduce the feasible set of during the optimization by solving which the optimal solution is still equivalent to solving (2).

it is hard to solve the constrained optimization problem with backpropagation.


In current research, the effectiveness of a code matrix is determined primarily by the classification accuracy.

since many applications require accurate class membership probability estimates for each of the classes, it is important to also compare the different types of code matrices according to their ability of producing such estimates.


[5] evaluated their global self-similarity descriptor (GSS) on the simpler classification challenge on the PASCAL VOC 2007 dataset, while the object detection evaluation was performed on the ETHZ shape dataset.

we showed in [21], that including curvature already solves the detection task almost perfectly on the ETHZ dataset.


To interpret regression results we used the relative mean absolute deviation (Rmad), which is the quotient between the mean absolute distance of the function learned by the regression method and the mean absolute distance of the constant predictor that returns the mean value in all cases.

we can obtain some preference judgments from the ratings of the sessions comparing the rating of each product with the rest, one by one, and constructing the corresponding pair.


Correspondingly, the ideal input S for LSE should look like Figure 1 (c) because the underlying distribution of LSE is Gaussian.

the similarity matrix of real-world data often occurs differently from the ideal case.


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

knowledge of ρ is not required to run our MP variants.


Importantly they allow full Bayesian predictive distributions to be obtained, rather than merely point predictions.

in their simplest form GPs are limited by the nature of their simplicity: they assume the target data to be distributed as a multivariate Gaussian, with Gaussian noise on the individual points.


The limited feedback makes the BCO setup relevant to a number of applications, including online advertising.

it also makes the problem notoriously difficult and requires the learner to find a careful trade-off between exploration and exploitation.


3 by their expected values and we used the expected value of Si when computing the probability of activation of the hidden units.

we continued to use the stochastically chosen integer firing rates of the hidden units when computing the one-step reconstructions of the data, so the hidden activities cannot transmit an unbounded amount of information from the data to the reconstruction.


When using our reduction, they are always equivalent.

in [8] the choice max k∈{0,1} r(s i 1 |k) led to a bound on the performance of the policy in terms of the performance of the classifier.


Performing a first-order Taylor expansion of J( w + z) yields: In expectation, this becomes the gradient times a (diagonal) covariance matrix, and reduces to an unbiased estimate of the gradient, scaled by the learning rate and σ 2 , the variance of the perturbation.

this unbiasedness comes with a very high variance, as the direction of an update is uniformly distributed.


LTP occurs when a presynaptic firing precedes a postsynaptic one by no more than about 20ms.

lTD occurs when a presynaptic firing follows a postsynaptic one.


Let us define the weights of the output layer of the original classification network as W c , and the weights of the output layer of the adapted detection network as W d . We know that for a category i ∈ B, the final detection weights should be computed as W d i = W c i + δB i .

since there is no detection data for categories in A, we can not directly learn a corresponding δA layer during fine-tuning.


The proof above uses our assumption that the clustering function f is defined on the set of all distance functions on n points.

essentially the same proof yields a corresponding impossibility result for clustering functions f that are defined only on metrics, or only on distance functions arising from n points in a Euclidean space of some dimension.


On IU X-Ray dataset, HRGR-Agent achieves slightly lower BLEU-1,4 and ROUGE score than that of CoAtt [16].

coAtt uses different pre-processing of reports and visual features, jointly predicts 'impression' and 'findings', and uses single-image input while our method focuses on 'findings' and use combined frontal and lateral view of patients.


Contemporaneous results due to [25] show that for A 0 distributed according to the random orthogonal model, and E 0 with Bernoulli support, correct recovery occurs with high probability provided This is an interesting result, especially since it makes no assumption on the signs of the errors.

even for constant rank r it guarantees correction of only a vanishing fraction o(m 1.5 ) m 2 of errors.


This is not a surprising result, since sequences with three motions generally have more (inlying) point trajectories than sequences with two motions, thus the outlier rates for sequences with three motions are lower (recall that a fixed number of 100 false trajectories are added).

the KM method (column 3) is completely overwhelmed by the outliers-for all the sequences with outliers it returned a constant "3" as the number of motions.


The only known practical and theoretical way to achieve optimal rates in infinite Reproducing Kernel Hilbert Space (RKHS) is to use some form of cross-validation to select the step size that corresponds to a form of model selection [26,Chapter 7.4].

cross-validation techniques would result in a slower training procedure partially neglecting the advantage of the stochastic training.


Another major line of generative models of video analyzes the slowly changing features of visual input and proposes complex cells as such slow feature learners [6], [7].

these models are not expressive enough to encode visual motion and are more specifically designed to discover image dimensions invariant in time.


For datasets such as Covertype in which Recursive RLS-Nyström performs significantly better than uniform sampling, so does the accelerated method (see Figure 4b).

the performance of the accelerated method does not degrade when leverage scores are relatively uniform -it still offers the best runtime to approximation quality tradeoff (Figure 4c).


In general, the goal of classification is to predict the true label for an observed pattern.

patterns close to the decision boundary are misclassified with high probability.


Note that in the revised ConvLSTM network with a spatiotemporal memory in Figure 1, we replace the notation for memory cell from C to M to emphasize that it flows in the zigzag direction instead of the horizontal direction.

output Gate Forget Gate dropping the temporal flow in the horizontal direction is prone to sacrificing temporal coherency.


In Figure 3a, each convolution kernel is only used by one computation path.

the convolution kernel in Figure 3b is used by multiple times.


One way to alleviate this burden is to use the BB method, which replaces B t by a scalar matrix (1/η t )I.

one cannot choose a scalar η t such that the secant equation holds with B t = (1/η t )I.


Following earlier work [22], the dropout operator is applied only to non-recurrent connections (50% dropout on fully connected layers and/or 20% on input layer).


This might explains why only 5 movies are present in our " pareto front.

even in this case, the algorithm will produce a subset of the Pareto Front, made of uncomparable movies from popular genres.


Observe that y t v k−1 x t ≥ 0 implies r k ≥ 0 if and only if ρ k ≤ 1/(1 + y t v k−1 x t ).

if y t v k−1 x t < 0 then, in order for r k to be nonnegative, it suffices to pick ρ k ≤ 1.


Below, we examine the amount of reduction in sample complexity as a function of I s . For simplicity, we focus on a setting in which θ = 0 and γ = 1 2 , i.e., (1) is equal to 2n log n. We first consider the case of n 2 I s < 2n log n − 2m log m, i.e., (2) being equal to 2n log n − n 2 I s . In this case, sample complexity is reduced by n 2 I s . That being said, there is no asymptotical gain unless n 2 I s = Ω(n log n).

when n 2 I s = Ω(n log n), this reduction can be as significant as resulting in an order-wise reduction in sample complexity.


Therefore, the development of a tractable algorithm for NSG is important, and this is one of the goals of our work.

it was proven that the metric of NPG learning, F a (θ), accounts for the infinite time-steps joint distribution in the Markov chain M(θ) [19,1], while the metric of NSG learning, F s,a (θ) accounts only for the single time-step distribution, which is the stationary state-action joint distribution d θ (s)π(a|s;θ).


By combining these features with a classification mechanism directly in the same model, as in the conditional generative model (M2), we are able to get similar results without a separate TSVM classifier.

by far the best results were obtained using the stack of models M1 and M2.


In the node-wise sampling, the neighborhoods of each parent are not seen by other parents, hence the connections between the neighborhoods and other parents are unused.

for the layer-wise strategy, all neighborhoods are shared by nodes in the parent layer, thus all between-layer connections are utilized.


As shown in [20], FoBa requires that n = Ω(log(p)/(ρ 3 k+ β 2 min )) for high-dimensional consistent support recovery, where the choice of , which is greater than k, depends on the correlations in the matrix X.

the condition in (4.1), which reduces to n = Ω(log(p − k)/(ρ 2k β 2 min )), is weaker since 1/ρ 3 k+ < 1/ρ 2k for > k and p − k < p. This shows that if a sparse recovery algorithm can accurately estimate the true support, then SWAP does not introduce any false positives and also outputs the true support.


We assume that all views of a non-anomalous (normal) instance are generated using a single latent vector.

an anomalous instance is assumed to have multiple latent vectors, and its different views are generated using different latent vectors, which indicates inconsistency across different views of the instance.


In the case in which these constraints cannot be simultaneously satisfied, it is NP-hard to find arg min θ T (θ).

[1] the optimal value can be approximated.


Using this combined objective may be a good approach for practitioners.

no single objective was the best for all unfairness metrics, so it remains necessary for practitioners to consider precisely which form of fairness is most important in their application and optimize that specific objective.


Such a definition makes sense when the player by definition must select a strategy from some bounded set, for example a probability from the n-dimensional simplex, or a distribution on paths in a graph.

in contexts such as machine learning where any x 2 R n corresponds to a valid model, such a hard constraint is difficult to justify; while any x 2 R n is technically feasible, in order to prove regret bounds we compare to a much more restrictive set.


We presume no more objectivity in answering this question than we would have in judging the merits of our other children.

we believe that the level of musicality attained by our system is truly surprising, while the reliability is sufficient for live demonstration.


The computation of h m is an ERM operation, which can be performed efficiently whenever an efficient passive learner is available.


Our work supports the work of [14] by drawing connections between the metric used to perform local optimization and the ability of the training algorithm to find solutions that generalize.

we focus primarily on the different generalization properties of adaptive and non-adaptive methods.


We could use the mean-field approximation as in previous FAB approaches [9,8,12,13,22,21].

this approximation fails to capture the dependencies between hidden variables in SBN, as discussed in Song et al.


Their method securely aggregates local models and uses output perturbation to achieve differential privacy.

the noise scales inversely proportional to the smallest data set size of the m parties.


Removing edges between supervoxels that aren't spatio-color neighbors avoids spurious links.

this procedure also removes many genuine links due to high color variability (Fig.


[6] utilizes two SSCNets for RGB and  depth respectively and combines the outputs of two SSCNet branches by concatenation.

[6] directly processes low-resolution RGB scene surface in 3D space, resulting in losing lots of details.


Similar to the case of single-task learning, each training point creates a depression on the σ 2 T (x * , ρ) surface [9,13].

while each training point for task T creates a "full" depression that reaches the prior noise variance (horizontal dotted line at 0.05), the depression created by each training point for task S depends on ρ, "deeper" depressions for larger ρ 2 .


Looking at the results (reported using the EMA version of the classification output), we can see that the strongly coupled version performs well and the too loosely coupled versions do not.

a moderate decoupling seems to have the benefit of making the consistency ramp-up redundant.


Probabilistic approaches to computer vision typically assume a centralized setting, with the algorithm granted access to all observed data points.

many problems in wide-area surveillance can benefit from distributed modeling, either because of physical or computational constraints.


An estimate of the therapy outcome can assist physicians in choosing a successful regimen for an HIV patient.

the HIV clinical data sets suffer from several problems.


For the case when the noise is Gaussian, matrices constructed from higher order statistics (specifically, cumulants) can be used instead of the covariance matrix.

these matrices are not in general positive definite and thus the square root cannot always be extracted.


An interesting work is [15] which explicitly incorporates supervision in the policy evaluation phase of a policy iteration procedure that otherwise seeks to maximize task reward.

this approach only considers a greedy policy form that does not lend itself to being represented as a deep RNN, and has not been applied to structured output prediction.


In this model, firing rates in each neural state take a constant value.

actually in motor cortex, average firing rates and preferred direction change dynamically in motor planning and execution [4].


We observe that the proposed method outperforms all other by a wide margin, in many cases even when trained with fewer samples.

it can only be used when there are enough training samples to learn a dictionary, a limitation that does not apply to the other methods.


Importance sampling (IS) based approaches [16,23,8,5,10,22] are typically unbiased and strongly consistent, but despite recent progress tend to have high variance-especially if the evaluation policy is deterministic, as evaluating deterministic policies requires finding in the data sequences where the actions exactly match the evaluation policy.

in most real-world applications deterministic evaluation policies are more common-policies are typically to either amputate or not, rather than a policy that that flips a biased coin (to sample randomness) to decide whether to amputate.


Such a regularization can help uncover the structured sparsity, which is desirable for applications with some meaningful tree structures on the features.

the tree structured group Lasso is challenging to solve due to the complex regularization.


Unfortunately, wireless signal strength is a poor estimator of range, and active acoustic and GPS localization techniques are uneconomical in that they consume energy and require additional hardware.

sFS relies on environmental acoustic events such as hand claps, which are not generated by the sensor network.


According to the studies in [11], many existing pairwise ranking methods are, surprisingly, inconsistent with WPDL, even in a low-noise setting.

as we know, the pairwise ranking methods have been shown to work very well in practice, and have been regarded as state-of-the-art even today [15,16,17].


A straightforward way to prove it is by setting I 2 = V , so the problems reduce to standard influence maximization.


This quantity has no explicit dependence on the dimension of the approximation architecture.

comparable sample complexity results (eg.


A k-nearest-neighbour graph might link these, distorting the recovered coordinates.

evaluating the model without this edge (the correct graph) yields a higher variational bound (Fig.


In the discounted setting, several works have improved the bounds with respect to the number of states (Szita and Szepesvári, 2010) and the discount factor (Lattimore and Hutter, 2012).

these analyses focus on worst case bounds that do not scale with the hardness of the MDP, missing an opportunity to help bridge the gap between theory and practice.


[2017] introduce a modern max-margin technique with an approximate planner in the optimisation.

the max-margin approach has mostly been replaced by the max entropy IRL [Ziebart et al., 2008].


As one would expect, the amount of information transmitted per second about the stimulus details, or s, depends on the ensemble parameter 0": larger velocities allow a higher SNR for velocity estimation, and the system is able to transmit more information.

when we convert the information rate to bits/spike, we find that the system is transmitting at a constant efficiency of around 1.4 bits/spike.


Specifically, Kaiser and Cressie [20] assert in a Proposition of their paper that there is a valid joint distribution consistent with these Winsorized Poisson node-conditional distributions above.

in the following theorem, we prove that such a joint distribution can never exist.


Data-driven approaches to solving robotic tasks have gained a lot of traction in recent years.

most existing policies are trained on large-scale datasets collected in curated lab settings.


This is a direct consequence of the pruning effect, especially in the first layers.

there is no significant reduction in inference time when post-processing our model via a low-rank decomposition.


Classical theories of rational choice do not apply in such cases because they ignore information-processing resources, assuming that decision-makers always pick the optimal choice [10].

it is well known that human choice patterns deviate qualitatively from the perfectly rational ideal with increasing resource limitations.


Alternatively we could bound on the likelihood of a translation, marginalising out the derivation.

this bound cannot be maximised tractably when e is unobserved.


Using this scheme, SGD with floating gradients successfully trains AlexNet to similar accuracy, for mini-batch size of 256 and 512.

when mini-batch size is 1024, the top-1 accuracy drops 0.71% for the same reason as we point out in Section 4.1.


Therefore before subsampling we precondition the matrix by a Randomized Hadamard/Fourier Transform [1,4] and after conditioning, the probability of having high leverage points in the new design matrix becomes very small.

if we assume X to be random design and its rows are i.i.d.


At first glance, our work seems related to the multi-label classification literature, where the goal is to predict multiple labels for each input instance (e.g., text tags for images on Flickr).

the motivation and context of our work is fundamentally different.


This is expected since the features are specifically fine-tuned to the source domain before the adaptation starts.

the target domain features have no structure before adaptation.


Wang and Blei [15] explore truncation levels via a local collapsed Gibbs sampler, but samplers are slow to make large changes.

our births add many components at once and apply to any exponential family mixture model.


Moreover, RMHMC suffers from expensive inner iteration.

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


This phenomenon is due to the fact that we are using the Lipschitz assumption on F, which is a data-independent constraint on the scale of the trade-off between f (z 0 ) f (z) and d Z (z 0 , z).

for p > 1, one may also think of a similar data-independent (or, worst-case) constraint this holds only if f is constant, even in the simplest case Z ✓ R. The illustrative example presented in Section 2.2 implies that the minimax learning might be possible even when the functions in F are not uniformly Lipschitz, but there exists at least one smooth hypothesis (at least, except for the regime % !


If L is the squared loss, for G = {g 1 , g 2 } with g 1 (s) = s and g 2 (s) = s and H = {h} with h(s) = s, for odd T , sup g2G disc(s) 1/2.

the bound in terms of disc(s) is much finer and helps us select g such that disc(s) = 0 for that g. This example shows that even for simple deterministic dynamics our learning bounds are finer than existing ones.


The graph shows that the EVB-ICM algorithm reduces the VB free energy reasonably well over iterations.

for this artificial dataset, the convergence speed was quite slow once in 10 runs, which was actually trapped in a local minimum.


[33] introduced a joint framework for object segmentations, in which the segmentation benefits from the object detectors and the object detections are in consistent with the underlying segmentation of the image.

these methods still rely on the exhaustively searching to localize objects.


Covariance kernels have to satisfy the property of positive definiteness 5 , and the MI score I does not.

applying a standard transformation (called exponential embedding (EE) here), we arrive at EE becomes familiar if we note that it transforms the standard inner product x(1)' X(2) into the well-known Radial Basis Function (RBF) kernel 6 (4) 4When comparing X ( l) , X ( 2) via the inner product, we are not interested in correlating their features uniformly, but rather focus on regions of high volume under Pm e d . 5 K is positive definite if the matrix (K(X(k ll , X(k 2 »)hl ,k2 is positive definite for every set {x(1 ), ... , X (K ) } of distinct points.


A previous study found that Knowledge Gradient (KG), which approximates the relative action values of exploiting and exploring to deterministically choose the best option on each trial [25], is the best model among several decision policies [4] (not including softmax).

in a later study, softmax was found to explain human data better than KG [11].


As a result, flat methods on such datasets face unbalanced classification problems which results in smaller error ratios; hierarchical classification should be preferred in this case.

for hierarchies such as the one of IPC, which are relatively well balanced and do not suffer from the rare categories phenomenon, flat classification performs at par or even better than hierarchical classification.


Therefore a combination of the two can solve the fundamental flaws of both methods.

a key design issue is how to implement a backward greedy strategy that is provably effective.


Across values of λ, λ = 1 performs best, save for Q * (λ) where λ = 0.5 obtains slightly superior performance.

is highly sensitive to the choice of λ (see Figure 1, left, and Table 2 in the appendix).


Moreover, we show that this family of estimators has several well known estimators as special cases for certain choices of the output space and its metric.

our main emphasis lies on the problem of regression with manifold-valued input and output which includes the multivariate Euclidean case.


The effectiveness of the pruning strategy relies on the principle that if the absolute value of a weight in a CNN is sufficiently small, its influence on the output is often negligible.

these methods tend to disregard the properties of larger weights, which might also provide opportunities for compression.


Note that by allowing θ = 0 in the above condition we can capture a full spectrum of functions.

a broad family of functions can have a sharper upper bound, i.e., with a non-zero constant θ in the above condition.


Thus, in the set {u} ∪ X there are k+1 points all of distance greater than 2OPT from each other.

then two of these points v, v ∈ ({u} ∪ X) must be assigned to the same center v * in the optimal solution.


12 Considering the phase-disparity model, R have different variances depending on d, and are usually not independent of each other, the sum cannot be modeled by a χ 2 −distribution.

we can compute the Fisher information for the two implied binocular simple cells instead.


As long as the similar conditions are satisfied, the framework and theoretical results hold for any general exponential family embedding model as well.

proving these conditions is quite challenging from the probability perspective.


SKI works by providing accurate and fast matrix vector multiplies (MVMs) with kernel matrices, which can then be used in iterative solvers such as linear conjugate gradients for scalable GP inference.

evaluating the marginal likelihood and its derivatives, for kernel learning, has followed a scaled eigenvalue approach [12,13] instead of iterative MVM approaches.


For any edge e ∈ E, we define N S,e as the number of nodes in V \ S it is relevant to, and define P S,e as the conditional probability that e is observed given S, ( Notice that N S,e only depends on the topology of G, while P S,e depends on both the topology of G and the probability weight w. The maximum observed relevance C * is defined as the maximum (over S) 2-norm of N S,e 's weighted by P S,e 's, As is detailed in the proof of Lemma 1 in Appendix A, C * arises in the step where Cauchy-Schwarz inequality is applied.

note that C * also depends on both the topology of G and the probability weight w. C * can be bounded from above only based on the topology of G or the size of the problem, i.e., L = |V| and |E|.


Our FS algorithm is essentially the same as the subsampling algorithm proposed by [4].

our theoretical analysis of it is novel, and furtheremore they only consider it in fixed design setting with Hadamard preconditioning.


Substantial data support a temporal difference (TO) model of dopamine (OA) neuron activity in which the cells provide a global error signal for reinforcement learning.

in certain circumstances, OA activity seems anomalous under the TO model, responding to non-rewarding stimuli.


Equation ( 1) is computationally highly intractable and its dual form is usually utilized [25]: where the supremum is taken over all Lipschitz functions f : Ξ → R, i.e., functions that assign a value to a sequence of events (points) and satisfy |f (ξ) − f (ρ)| ≤ ξ − ρ for all ξ and ρ.

solving the dual form is still highly nontrivial.


As in recent methods [12], we build on the observation that the Newton direction computation is a Lasso problem, and perform iterative coordinate descent to find its solution.

the naive approach has an update cost of O(p 2 ) for performing each coordinate descent update in the inner loop, which makes this resume infeasible for this problem.


This modification is not a heuristic, in that it still applies the exact SVRG algorithm.

at best it can only cut the runtime in half.


We have also successfully run BA on the CIFAR-10 data set (boat and horse images) which contains 10,000 instances and we believe that our algorithm can scale to much larger datasets.

training DHL on such larger samples did not terminate as it is based on a costly QCQP.


One possible route is to initialize the weights ✓ to ↵.

before the policy behaves reasonably, the noise injected into the policy for exploration (when using stochastic policy gradients) can cause poor initial performance.


Recent work has focused on learning grounded cooperative communication protocols between agents to solve various tasks [29,8,24].

these methods are usually only applicable when the communication between agents is carried out over a dedicated, differentiable communication channel.


It can be noticed that the linear model (Linear) reaches performances which are in some cases better than RNN without pre-training.

it is important to notice that while it achieves good results on the training set (e.g.


Knowing u it is possible to tune η to have a O( u √ T ) bound, that is optimal [1].

eG has a regret bound of O( √ T log d), where d is the dimension of the space.


They just use a 'uniform' discretization of the domain.

the zooming algorithm of [7] adapts to the smoothness of µ (more arms are sampled at areas where µ is high).


We can conclude that ψ implements the η-function in a biophysically plausible way.

ψ does neither explicitly specify η's multiplicative operation, nor its exponential function exp(•).


As shown in Figure 2, bottom n ′ th margin is a multimodal function, this algorithm with ǫ-relaxation is very sensitive to the choice of n ′ , and it usually gets stuck in a bad coordinatewise point without using ǫ-relaxation.

an impressive advantage is that this method is tolerant to noise, which will be shown in Section 3.


Additionally [Scaman et al., 2018] needs a boundedness constraint for the input problem.

cOLA can handle non-smooth and non-strongly convex objectives (A) and (B), suited to the mentioned applications in machine learning and signal processing.


With noise vectors {η t }, {ξ t }, the system's time evolution is governed by the following equations: If the dynamics A, B, C, D are known, then the Kalman filter [Kal60] is known to estimate the hidden state optimally under Gaussian noise, thereby producing optimal predictions of the system's response to any given input.

this is rarely the case -indeed, real-world systems are seldom purely linear, and rarely are their evolution matrices known.


For ReLU networks, p(q ⇤ ) = 1/2, and we see that max and 2 JJ T grow linearly with depth and dynamical isometry is unachievable in ReLU networks, even for critical orthogonal weights.

for hard tanh networks, p(q ⇤ ) = erf(1/ p 2q ⇤ ).


We will exploit this when we study some interesting special cases of the general problem.

in general, it is not possible to infer the losses for functions such that s t,i < s(f ) i for some i (cf.


A common objective function in traffic control is the average vehicle travel time.

it is impossible to identify a particular car in the system, let alone what its travel time was.


This indicates that after initialization the network tends to almost always predict the same (typically wrong) class, which is then corrected with a strong gradient update.

the network with BN does not exhibit the same behavior, instead positive gradients are distributed throughout all classes.


It is known that the greedy algorithm leads to a 1/2-approximation for the submodular social welfare maximization problem (SWM) [11], and this problem admits a 1 − 1/e-approximation in the offline setting [24], which is tight [19].

for the online setting, the problem does not admit a better than 1/2-approximation algorithm unless P= NP [12].


To call x ′ a successful "adversarial example", a natural definition would compare the predicted label h(x ′ ) with some other "anticipated answer".

what h(x ′ ) is exactly compared to is where various definitions of adversarial examples diverge.


If one only knows the initial condition of a diffusion, then it is straightforward to simulate a sample path of the process.

simulating a sample path conditional on both initial and final conditions is a challenging problem.


We do not discuss it in this paper, because our method can be combined with many techniques, which select a model after obtaining the estimators.

we should note that some famous methods such as AIC and MDL, which are based on statistical asymptotic theory, cannot be applied to mixture models because of the unidentifiability of the parameter.


The slightly limiting factor of this theorem is that k x must be c 0 -universal, which often can be tricky to verify.

most standard kernels-including all radial, non-constant kernels-are c 0 -universal (see Sriperumbudur et al., 2011).


Vanialle particle filters exhibit non-zero error even with 100,000 samples.

it is important to notice that these results were obtained using simulated data and a hand-tuned loss function approach.


In order to combine the few scores available in a sparse input matrix, a multilayer CNN would require very large filters or many layers to diffuse the score information across matrix domains.

our diffusion-based approach allows to reconstruct the missing information just by imposing the proper amount of diffusion iterations.


Long-term bistable synapses are a good technological solution for weight storage.

the maximum and minimum weight limits in bimodal STDP already act as natural attractors.


Traditionally, the multilayer perceptron is used to optimize such hierarchical models based on a discriminative criterion that models P (y|x) using a error backpropagating gradient descent [2,3].

when the architecture is deep, it is challenging to train the entire network through supervised learning due to the large number of parameters, the non-convex optimization problem and the dilution of the error signal through the layers.


In particular, they showed that the bridge penalty can be obtained by mixing the Laplace distribution with a stable distribution.

zou and Li [23] proved that both MCP and SCAD can not be cast into this framework.


[35] develops a novel way to split each word into sub-word units which is widely used in neural machine translation.

the low-frequency sub-word units are still difficult to train: [31] provides a comprehensive study which shows that the rare (sub)words are usually under-estimated in neural machine translation: during inference step, the model tends to choose popular words over their rare alternatives.


(2011), the sample mean is adopted to estimate µ (k) 's, and CLIME.RC is adopted to estimate Ω = Σ −1 .

we adopt the Catoni's M-estimator to estimate µ k 's, and EPIC is adopted to estimate Ω.


One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization.

in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings.


Isomap recovers the manifold for the error-free cases (left).

all-pairs shortest path can "leak" through AC and CB, resulting a significant change in the embedding.


Figure 1: Graphical Model for the sticky HDP-HMM (setting κ = 0 recovers the HDP-HMM) The hyperparameter α governs the variability of the prior mean across the rows of the transition matrix and γ controls how concentrated or diffuse the probability mass of β will be over the states of the transition matrix.

in the HDP-HMM we have each row of the transition matrix is drawn as π j ∼ DP(α, β).


The VB estimator (the magenta solid curve) is zero when V ≤ 1, which means exact sparsity.

fB (fully-Bayesian or rigorous Bayes; blue crosses) shows no sign of sparsity.


There has been extensive work on submodular optimization (both approximate and exact minimization and maximization, see, e.g., [8,9,10,11]).

we are unaware of previous work that addresses the general problem of probabilistic inference in Bayesian submodular models.


Importantly, g j , and therefore gj , depend only on w j , u j and v j , so a three-dimensional quadrature will suffice.

using similar arguments to those in [7] more efficient alternatives exist.


Previously both approaches [3,4,6,36] have been studied.

for high DoF manipulators sampling based approaches [4,6] maintains tractability of the problem, hence we take this approach.


In Section 5, randomly initialized SGD solved one example with a 100% success rate over 1,000 trials, despite the presence of spurious local minima.

it failed with a consistent rate of ≈ 6% on another other example with an RIP constant of just 1/2.


For example, if a dataset has one billion features (D = 10 9 ), we can simply generate a "permutation vector" of length D = 10 9 , the memory cost of which (i.e., 4GB) is not significant.

it would not be realistic to store a "permutation matrix" of size D × k if D = 10 9 and k = 500; instead, one usually has to resort to approximations such as universal hashing [5].


• In the main result, the augmented neuron can be viewed as a skip connection from the input to the output layer.

this skip connection is not critical, as the same result also holds if we add one special neuron to each layer of a fully-connected feedforward neural network.


The empirical risk minimization (ERM) problem in (4) can be solved using state-of-the-art methods for minimizing strongly convex functions.

these methods never exploit the particular property of ERM that the functions are drawn from the same distribution.


They use the Gaussian distribution to model the learning instances of each class.

the strong model assumptions might easily be very inflexible for many learning problems.


Our exact global VB solver (EGVBS) provides the global solution of a non-convex minimization problem by using the homotopy method, which solves the stationary condition written as a polynomial system.

our approximate global VB solver (AGVBS) finds the roots of a polynomial equation with a single unknown variable, and provides the global solution of an approximate problem.


These options could potentially give better diversity of various samples from the family, and thus better uncertainty estimates; exploring them further is a promising direction for future work.

we found that these methods degraded the accuracy of the base models.


To address this issue, inexact techniques, including sub-sampling techniques, have recently been proposed in the Euclidean space [35,36,37,38,39].

no work has been reported in the Riemannian setting.


Many machine learning algorithms iteratively transform some global state (e.g., model parameters or variable assignment) giving the illusion of serial dependencies between each operation.

due to sparsity, exchangeability, and other symmetries, it is often the case that many, but not all, of the state-transforming operations can be computed concurrently while still preserving serializability: the equivalence to some serial execution where individual operations have been reordered.


The contributions of these directions will cancel each other and a large step will be taken in that direction.

the function will probably also change fast in that direction (because of the high curvature), and the step is too large for the local quadratic approximation we have considered.


therefore, we expand Equation 1 as follows, using the independencies represented by the directed graphical model in Figure 1  the summation inside the log makes it difficult to learn the parameters.


In practice, this means a discriminator might quickly learn to reject all samples that don't lie on V T n (sequences of one-hot vectors) and give meaningless gradients to the generator.

it is easily seen that the conditions of Theorem 1 and Corollary 1 of [2] are satisfied even on this non-standard learning scenario with X = T n . This means that W (P r , P g ) is still well defined, continuous everywhere and differentiable almost everywhere, and we can optimize it just like in any other continuous variable setting.


val a = 1 + { (10 + (10 + 100)) + 1000 } = 1121 In this way, the program is still written in direct style (with shift and reset operators).

the automated transformation will reorganize it into CPS format, realizing delimited continuations.


A VAE imposes a prior density p(z), such as z ∼ N (0, I), and uses a KL-divergence regularizer to align both posteriors p E (z|x 1 , y 1 ) and p E (z|x 2 , y 2 ) to it, The overall objective is to minimize L rec + L KL , whose opposite is the variational lower bound of data likelihood.

as we have argued in the previous section, restricting z to a simple and even distribution and pushing most complexity to the decoder may not be a good strategy for non-parallel style transfer.


It is worth noting that when α = (s log d/n) 1/4 , we still have (n 3 s log d) 1/4 uncorrupted labels.

our lower bound (along with the upper bound shown in Theorem 3.2) indicates that the information contained in these uncorrupted labels are buried in the noise, and cannot essentially improve the detection quality compared with the unsupervised setting.


Several authors have proposed to smooth the LP with entropy terms and employ variants of coordinate minimization [7,26].

the convergence rates of these methods have not been analyzed.


we replace n 2 with k 2 which may be much smaller.


Intuitively, different classifiers provide different "expertise" in making certain distinctions that can inform the classification task.

as we discuss in Section 2, most of these methods use a fixed procedure determined at training time to apply the classifiers without adapting to each individual test instance.


The prior work [21] achieved some success in entropy estimation using symmetric stable random projections.

even after aggressively exploiting the bias-variance tradeoff, they still need to a large number of samples, e.g., 10 6 , which is prohibitive in both time and space, especially considering that in streaming applications the pseudo-random numbers have to be re-generated on the fly, the cost of which is directly proportional to the sample size.


When we design the detail structure of the GAN, we adopt Gated Recurrent Unit (GRU) [10], a state-of-the-art RNN cell, as the basic network of G and D. It is worth noting that, others RNN variants can also be used in this work, such as the Long Short-Term Memory (LSTM) [21] cell.

the time lags between two consecutive valid observations vary a lot due to data incompleteness, which makes traditional GRU cell or LSTM cell not applicable to our senario.


We see that CUR and GL-REG perform similarly.

(since CUR is a randomized algorithm, on every run it gives a different result.


The rate of decay is related to the variance of this Gaussian.

if we take one standard deviation as the effective receptive field (ERF) size which is roughly the radius of the ERF, then this size is as we stack more convolutional layers, the theoretical receptive field grows linearly, therefore relative to the theoretical receptive field, the ERF actually shrinks at a rate of O(1/ √ n), which we found surprising.


Define r b0 = log 2 1 + 1 2+3L/b0 and we have When there are multiple functions and the median partition is performed on pooled data, the partition might not happen at the empirical median on each subset.

as long as the partition quantiles are upper and lower bounded by α and 1 − α for some α ∈ [1/2, 1), we can establish results similar to Theorem 2.


For example, if P X1 is a uniform distribution over a unit cube in q dimensional Euclidean space, then h(r) = min(1, r) q , and our error bound becomes meaningful for n ≥ (L 2 /ρ) q/2δ .

if P X1 is supported over finitely many points, then h(r) = min x∈supp(P X 1 ) P X1 (x) is a positive constant, and the role of the latent dimension becomes irrelevant.


This symmetry can be observed in the frequency representations of the examples in Figure 1(b).

since we seek to optimize over parameters embedded directly in the frequency domain, we need to pay close attention to ensure the conjugate symmetry constraints are enforced upon inversion back to the spatial domain (see Subsection 2.2).


This perturbation forms the shape of the spike, with the spike shapes varying across neurons as well as across different spikes of the same neuron.

each neuron has its own characteristic distribution over shapes, and we let ✓ ⇤ i 2 ⇥ parametrize this distribution for neuron i.


Some applications, like ranking images by semantic relevance to a given image query are known to be non-symmetric when based on human judgement [15].

in some applications symmetry or positivity constraints reflects a prior knowledge that may help in avoiding overfitting.


Algorithm ROBUST-LRA (Figure 1) outputs a low-rank matrix.

it is possible to output a low-rank factorization without any loss in efficiency.


Conversely, since the 1/f yi (x i ; ✓) term is absent in its gradient, MAE treats every sample equally, which makes it more robust to noisy labels.

as we demonstrate empirically, this can lead to significantly longer training time before convergence.


Beginning with ζ M,t (see definition in Fig.

1), repeated application of bridge sampling alone could in principle arrive at an accurate estimate of {ζi,t reducing the variance sufficiently to provide useful estimates of the log partition function would require using a relatively large number of samples at each temperature.


This observation leads us to consider and rigorously analyze a bias-corrected PCR method, which we ultimately show is consistent in fixed n settings, if σ 2 → 0 and d → ∞.

it will also be shown below that ŷpcr is inconsistent in one-shot asymptotic regimes.


Only then estimates are updated and a new policy is calculated.

since all states in the same interval I j have the same confidence intervals, finding the optimal pair Mk , πk in ( 4) is equivalent to finding the respective optimistic discretized MDP M agg k and an optimal policy πagg k on M agg k . Then πk can be set to be the extension of πagg k to S, that is, πk (s) := πagg k (I(s)) for all s. due to the constraint on the bias even in this finite case efficient computation of M agg k and πagg k is still an open problem.


Deep reinforcement learning algorithms have been shown to learn complex tasks using highly general policy classes.

sparse reward problems remain a significant challenge.


We validated our model on both synthetic and real medical datasets to confirm the superiority of proposed feature level set embedding under our joint learning framework.

there is still room for improvement of our model.


Exact inference is intractable in this model.

expectation propagation offers an approximate alternative.


Unfortunately, we cannot use the algorithm A 2 .

due to the randomness we have added, we can argue that algorithm A 2 is quite close: Lemma 3.


Thus, in expectation, and modulo a small additive term, Ψ n decreases monotonically.

the amount of decrease at the nth time step can be arbitrarily small when Ψ n is close to 1.


As discussed in [15], ACCPM has an overall complexity is O(n 4 log(1/ε) 2 ) for finding an ε-optimal solution.

this method needs to use interior methods at each iteration which would be slow for large scale datasets.


Second, all 3 states are fully utilized in the weight quantization.

for the activation quantization, TTQ doesn't present good bipolar distribution as the original FP data.


FQI is inherently an offline method -given historical data, the algorithm estimates the optimal policy.

fQI can also be used for online learning.


This type of result was known for the square loss.

we develop new techniques that let us prove such hardness results for any loss function satisfying some minimal requirements on the loss function (including the three listed above).


In this special tree case the maximum likelihood estimator is tractable and is tantamount to finding a maximum weighted spanning-tree.

it is also known that in the case of general graphs with cycles, maximum likelihood estimators are intractable as they require computation of the partition function of the underlying GM, with notable exceptions of the Gaussian GM, see for instance [9], and some other special cases, like planar Ising models without magnetic field [10].


Although SSMs have an illustrious history [24], their stochasticity has limited their widespread use in the deep learning community, as inference can only be exact for two relatively simple classes of SSMs, namely hidden Markov models and linear Gaussian models, neither of which are well-suited to modeling long-term dependencies and complex probability distributions over high-dimensional sequences.

modern RNNs rely on gated nonlinearities such as long short-term memory (LSTM) [16] cells or gated recurrent units (GRUs) [6], that let the deterministic hidden state of the RNN act as an internal memory for the model.


We consider first the problem of computing optimal recommendation sets given the system's uncertainty about the user's true utility function w. Given belief state θ, if a single recommendation is to be made, then we should recommend the option x * (θ) that maximizes expected utility EU (x, θ).

there is often value in suggesting a "shortlist" containing multiple options and allowing the user to select her most preferred option.


GP regression assumes a GP prior over functions, where K is a covariance matrix whose entries are given by a covariance function, The simplest way to extend a GP to deal with multiple outputs is to assume that, given the inputs, the outputs are independent.

for correlated output dimensions, this is a poor approximation.


12) requires samples of x from the out-of-domain distribution p out (x).

the true out-of-domain distribution is unknown and samples are unavailable.


We don't know whether it is a proper scoring function.

it equals the matrix entropic loss when X is a dyad.


The consistent part of t IN is an effective cue for items that followed the initial presentation of the probe item (open symbols, Figure 1c).

recovery of the state of context that was present before the probe item was initially presented is a symmetric cue (filled symbols, Figure 1).


To handle intractable inference, research in this area has developed new approximation methods that are fast and effective.

theoretical analysis of the performance of such approximations is not well developed.


If there were no bandwidth limitation, the stimulus could be decoded just from this initial transmission.

the bandwidth limitation results in coarse, or noisy, principal neuron transmission, an issue we will return to later.


The target-domain support set-the k instances of each of the n classes in the target domain-are used merely for comparison to query (to-be-classified) instances.

weight adaptation determines model parameters using both source and target domain data.


Naturally the problem is non-convex and is in fact NP-hard in general, and hence the above algorithm might not even converge.

by restricting the noise in the bags to a class of "nice" distributions, we can show that the above algorithm converges to the global optima at a linear rate.


The low AUC of the proposed model indicates that it does not consider singleview anomalies as anomalies.

the AUC of the one-class SVM (OCSVM) was high because OCSVM is a single-view anomaly detection method, and it leads to low multi-view anomaly detection performance.


In recent computer science research [18] [13][3] [19], machine learning methods have been applied for fMRI data analysis.

in these approaches information on the connectivity and interactivity between brain voxels is discarded and brain voxels are assumed to be independent, which is an inaccurate assumption (see use of statistical maps [3] [19] or the mean of each fMRI time interval [13]).


In particular, the robust return of π is min ξ ρ(π , ξ) = −9, while the optimistic return of π B is max ξ ρ(π B , ξ) = +10.

solving (2) will return the optimal policy since: min ξ ρ(π , ξ) − ρ(π B , ξ) = 11 − 10 = −9 − (−10) = 1.


In different perspective, [3,5] describe the optimal posterior, but unfortunately there is no efficient sampling procedure for this posterior model.

our work explores posterior models which allow efficient sampling.


By a simple application of the union bound, it is clear that the asymptotic probability of the Type I error will be lim n→∞ P H0 (A n ) ≤ α.

if the alternative holds, there exists some m with |m| ≤ M for which V (h, Z m ) = n −1 S m,n converges to a non-zero constant.


We can see the house value increases with more rooms and decreases as the crime rate increases.

when the crime rate is low, smaller sized houses (4 or 5 rooms) seem to be preferred.


In the 'path update' stage, fewer than .01% of proposals were accepted.

the coloured noise expansion method used N = 7 Gaussian inputs with a linear correction and was able to approximate the posterior accurately.


The relative risk of the plugin estimator is L Note that the sign of E depends on the nature of the error ε n , so PLUGIN could be either better or worse than ORACLE.

oRACLEPLUGIN is always better than PLUGIN.


The estimated environment noise parameters are then used to compensate noise effects in the feature or model space for recognition of noisy speech.

it is well-known that noise statistics may vary during recognition.


K 1 is just the FLG kernel k κ FLG induced from the base kernel κ between the lowest level subgraphs: 2.

for = 2, 3, . . . , L, K is the FLG kernel induced from K −1 between G (v) and G (v ): Definition 5 defines the MLS kernel as a kernel between different subgraphs of the same graph G. if two graphs G 1 and G 2 share the same base kernel, the MLS kernel can also be used to compare any subgraph of G 1 with any subgraph of G 2 .


Adapting this to make a distance measure, One drawback with this measure is that it implicitly assumes that all c CCA vectors are equally important to the representations at layer L 1 .

there has been ample evidence that DNNs do As the signal to noise ratio decreases, the unweighted mean underestimates the shared structure, while the projection weighted mean remains largely robust.


When agent i fixes a Markov policy π i , the game is an MDP for agent j.

if agent i's policy is not Markovian the resulting game is not an MDP on the original state space.


As in [7], we can choose λ = √ n or λ = n to obtain decays rates log n √ n or log n n respectively, where the latter has a fixed non-decaying gap term (b − a) 2 /2.

unlike [7], in our proof both cases are achievable with η = 1, i.e., for the variational algorithm.


It is impossible to perform the full non-linear computation of extracting an angle from the population activity I in a single linear operation S I ¦I .

in a regime in which a linear approximation holds, the one factor can represent the systematic covariation in the activity of the population coming from the single dimension of angular variation in the input.


The original formulation of the method was for a finite domain.

simulated annealing can be generalized straightforwardly to a continuous domain because the Metropolis-Hastings algorithm can be used with almost no differences on discrete and continuous domains The main difference is that on a continuous domain the equilibrium distributions are specified by probability densities.


Specifically, in multi-label classification there are multiple possible labels for each instance and the goal is to predict as many of them as possible.

in our setting there is a single ground-truth label for each instance and the learner makes multiple guesses, all of which are evaluated against that single ground-truth.


Swimmer-5 Swimmer-3 Swimmer-3 Figure 3: Left: For a 3-link swimmer, with relatively simple dynamics, the compared methods yield similar results and possibly a slight advantage to the purely model-based SVG (1).

middle: as the environment model's capacity is reduced from 20 to 10 then to 5 hidden units per state-dimension subnetwork, SVG(1) dramatically deteriorates, whereas SVG(1) shows undisturbed performance.


Consequently, rounding can be done only after every K steps (with a reasonably large K); in this case, nonzero coefficients have sufficient time to go above the threshold θ.

if K is too large, then in the training stage, we must keep many more nonzero features in the intermediate steps before they are rounded to zero.


As one would expect, our experiments indicate that the parsing performance of the grammatical bigram model is not as good as that of state-ofthe-art parsers; however, its performance in Experiment II suggests that it may be useful in domains where partial accuracy is valuable and large amounts of unlabelled data are available.

to realize that potential, the model must be improved so that its performance in Experiment III is closer to that of Experiment II.


The pipeline adopted is otherwise unchanged from the previous dataset.

we did not apply pooling, and instead coded the whole 429 dimensional vector with a dictionary with 2000 and 8000 elements found with OMP-1, with the same parameter α as in the vision tasks.


the sequence), and sent the result to the RNN.

a fully end-to-end approach to pre-miRNA identification we would need to learn even the secondary structure from the input sequences.


In fact, if f is supermodular (α ≡ 1) and for = k, we recover the 1 − e −1 ≈ 0.63 guarantee from [18].

for an approximately supermodular function (ᾱ < 1), the result in (9) shows that the 63% guarantee can be recovered by selecting a set of size = ᾱ−1 k. Thus, α not only measures how much f violates supermodularity, but also gives a factor by which the cardinality constraint must be violated to obtain a supermodular near-optimal certificate.


Clearly, both z-static trees degrade in accuracy over time, and they do so on both legitimate and spam IPs.

the accuracy of the dynamic tree does not degrade over this period.


The online weak learning condition imposes minimal assumptions on the asymptotic accuracy of learners, and obviously it leads to a solid theory of online boosting.


We use the same discriminator, generator, and reconstructor architectures as in the previous section.

the previous mode collapsing metric is inappropriate here, owing to CIFAR's greater diversity.


That is, because Shannon information does not make any assumptions about the code, it is not always apparent how information should be best extracted from the responses: just because information is 'there' does not mean we know how to get at it.

using a simple approximation for the decoding distribution, q(y|r) (e.g.


Thus, the constraint µ L 8 n is satisfied when λ 8ξR n . In low-dimensional settings, the optimal regularization parameter is of the form C/n [29] where C is a scalar constant, and may thus violate the constraint.

the improvement with respect to regularization parameters of the form λ = C/ √ n is known to be asymptotically negligible, and in any case in such low-dimensional settings, regular stochastic or batch gradient descent may be efficient enough in practice.


1 k times can only achieve finite sample rate of Õ( p 1/m), while the one in (3) achieves Õ( p 1/km).

the constants max i2[k] i (in Corollary 1) and ↵ (in Thm.


Obviously, to find an optimal threshold θ, access to the entire joint distribution is needed.

this is not the main problem here, since in the next section, we will show that only a polynomial number of parameters of the joint distribution is needed.


Typical inference algorithms for DGMs are in the amortized form like that in Section 2.3.

this approach cannot leverage the conjugate structures in latent variables.


This is not practical because every module must explore in order to learn.

we can approximate it by decreasing the exploration of each module, making its policy less stochastic and more greedy.


Next, we wish to go beyond proportionality and determine the precise relationship between bias and discriminability under the power-law efficient coding framework described above.

any optimization of Fisher information, including ours, doesn't prescribe a method for selecting a parametric encoding distribution p(y | x) associated with a particular power-law efficient code, that is, a distribution with Fisher information allocated according to J(x) = k p(x) q .


In practice this point will be a minimum because any maximum would represent an unstable equilibrium.

unlike VMP we have no guarantee to decrease KL(q||p) at every step, and indeed we do sometimes encounter convergence problems which require damping to fix: see Section 7.


Factored models offer a more natural and compact way of parameterizing complex decision processes.

not all CMDP models and related factorizations are equally suitable also for the purpose of optimization.


The constant Q can be considered to represent the second moment of the "gradient noise" in ∇J i (x k ).

therefore, the second moment of ∇J i (x k ) can be bounded above as Under Assumptions 1, 2, and 3, the iterates of CDSGD satisfy ∀k ∈ N: In Lemma 2, the first term is strictly negative if the step size satisfies the following necessary condition: in latter analysis, when such a condition is substituted into the convergence analysis, it may produce a larger upper bound.


To reduce the computational complexity, Greengard and Strain proposed the Fast Gauss Transform (FGT) [5], using two expansions, the far-field Hermite expansion and the local Taylor expansion, and a translation process that converts between the two, yielding an overall complexity of O(M + N ).

due to the expensive translation operation, O(p d ) constant term, and the box based data structure, this method becomes less effective for higher dimensions (e.g.


At each iteration, a quadratic approximation to the loss is used as a surrogate functional with the regularization term added to induce joint functional sparsity.

a technical difficulty is that the approximate quadratic problem in each iteration is weighted by a non-diagonal matrix in function space, thus a trivial extension of the algorithm in (Ravikumar et al., 2007) for sparse binary nonparametric logistic regression does not apply.


In principle, one could use arbitrary bipartite graph G for task allocation.

as we show later in this paper, random regular graphs are sufficient to achieve order-optimal performance.


To solve this problem, a regularization term can be introduced [11], while it is not easy to optimize the regularization parameter for this term.

we optimize parameters of the similarity (kernel) function.


Knowing the final program exit status (crashed or successful) leaves us in a classification setting.

our primary goal is that of feature selection [2].


Incorporating R y into training significantly alleviate this issue -an augmented C would resolve G's confusion.

it still makes mistakes in some confusing classes, such as 3 and 5.


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

labels in strongly clustered points clearly contribute to the overall cost and changing their label will alter the alignment significantly.


As to the space complexity, both algorithms proposed in [Ouyang et al., 2017b;Agrawal and Jia, 2017] need to store counts of state and action visitations.

dS-PSRL uses a model independent schedule and as a result does not need to store such statistics.


Note that the joint and conditional histograms of the synthesized samples have similar transition of spatial dependencies as the separation increases (column 1,2 and 3), suggesting that the FoGSM accounts well for pairwise joint dependencies of coefficients over a full range of spatial separations.

the dependencies between subbands of different orientations and scales are not properly modeled by FoGSM (column 4 and 5).


observations (x 1 , y 1 ), ..., (x n , y n ), 1 Generally one has to introduce an additional scale parameter σ and allow rescaling of the residuals via ri/σ, to preserve parameter equivariance [3,4].


In terms of the evaluation criteria, we first adopt the pixel-wise evaluation criteria commonly used by previous works [6,28].

as mentioned in [11], such metrics mainly evaluate pixel-wise depth and normal offsets, but do not well reflect the quality of reconstructed structures over edges and planar surfaces.


As a result, it requires linear update time and quadratic memory, instead of the exponential time and memory requirements of the Bayes filter.

we give two caveats regarding our method: it is approximate, and it does not maintain probabilities.


The performance of RankSVM seems insensitive to the level of truncation for NDCG.

roBiRank, which uses non-convex loss function to concentrate its performance at the top of the ranked list, performs much better especially at low truncation levels.


To be precise, there is an one-to-one mapping between the set of weights on which BN(z) is invariant and a point on V(1, n), but not on G(1, n).

the proposed method interprets each weight vector as a point on the manifold only when the weight update is performed.


This can significantly reduce MR scanning time.

according to structured sparsity theory, the measurements can be further reduced to O(K + log n) for tree-sparse data instead of O(K + K log n) for standard K-sparse data with length n. few of existing algorithms have utilized this for CS-MRI, while most of them model the problem with total variation and wavelet sparse regularization.


The buyer b t depends on the full loss vector `t : assuming that we can see the full `t would not lead to a meaningful reduction for MAB.

our construction of ⌫ t is such that each posted price is associated with a single action.


In a detailed study on AMS-based broad-band SNR estimation [11) it was shown that harmonicity which is well represented in AMS patterns is the most important cue for the neural network to distinguish between speech and noise.

harmonicity is not the only cue, as the algorithm allows for reliable discrimination between unvoiced speech and noise.


In terms of the linear algebra, the spectral expansion of K is dominated by a few large eigenvalue eigenvectors, we will call this the "PCA-like" scenario.

in situations where f varies more rapidly, a shorter lengthscale kernel is called for, local relationships between nearby points become more important, which the landmark point method is less well suited to capture.


However, the total score of this trajectory is still only 0.0603, making the direct path the more likely one.

if t = 2, then the path through y becomes more likely by a score of 0.0546 to 0.0451.


The creator of the SSL model claims that the model avoids variables that could lead to discrimination [4] this is the case then we would expect to see only weak proxies if any.

the C&C dataset contains many variables that are correlated with race, so we would expect to find strong proxies in a model trained with this dataset.


As our method does not have access to valuable labeled data, one might expect that our method is severely disadvantaged and should not perform on the same level.

with unlabeled data and sequence autoencoders, we are able to obtain 16.7%, ranking second amongst many other methods that have access to a much larger corpus of labeled data.


The fact that no permitted set can have a forbidden subset represents a constraint on the possible computations of symmetric networks.

this constraint does not have to be viewed as an undesired limitation.


copies of the same pair of random variables.

hypercontractivity coefficient tensorizes, i.e, mutual information is additive, i.e., Tensorizing quantities capture the strongest relationship among independent copies while additive quantities capture the sum.


equivalent to random guessing) for the purposes of conditional estimation tasks.

eRG models are not suitable for application to the large-scale setting.


There are several approaches for learning communication in MARL including DIAL [4] , CommNet [23], BiCNet [19], and Master-Slave [8].

information sharing among all agents or in predefined communication architectures these methods adopt can be problematic.


This means that it could be better for an algorithm to output k � < k elements if the goal is to maximize sum-min(•).

this non-monotonicity is not too serious a problem, as the following lemma shows (proof in the supplement, Section A.1).


The formal guarantees parallel those of the GLM-TRON algorithm.

the rates achieved are somewhat worse, due to the additional difficulty of simultaneously estimating both u and w. Theorem 2.


For example, [14] that we use here, obtains an average of 66% correct hand detection (comparing favorably to other state-of-the-art methods) in the general setting experiments, when both the person and the background are unseen during part detector training.

as shown in [14], average 85% part detection performance can be achieved in more restricted settings.