sample of size n from a distribution P ∈ N d . There exists a universal (numerical) constant c such that Given centralized access to the full mn-sized sample, a reasonable procedure would be to compute the sample mean, leading to an estimate with mean-squared error σ 2 d mn , which is minimax optimal.

theorem 2 shows that to achieve an order-optimal mean-squared error, the total number of bits communicated must (nearly) scale with the product of the dimension d and number of machines m, that is, as dm/ log m. If we ignore logarithmic factors, this lower bound is achievable by a simple procedure: each machine computes the sample mean of its local data and quantizes each coordinate to precision σ 2 /n using O(d log(n/σ 2 )) bits.


The distribution of dishes sampled by those imaginary customers reflects user relevance feedback.

the updated expectation of the relevance vector has a bias towards user preferences.


In practice, however, the parameter matrices of this model might not have low rank.

the resulting approximations yield some loss of accuracy and, more importantly, will typically not correspond to the most compact networks.


Therefore the solution of the (s, ρ)-trajectory-based short-sighted SSP only chooses the action a c to move the car.

also, since m is even, every state s used by SSiPP for generating (s, ρ)-trajectory-based short-sighted SSPs has l s ∈ N. for even values of m, i.e., for ρ ∈ (0.5 i+1 , 0.5 i ] and i ∈ {1, 3, 5, . . . }, trajectory-based SSiPP always chooses the actions a c to move the car to l c , thus avoiding the all dead-ends.


By Lemma 15, it follows that is η -mixable, and from Theorem 11, is (η −1 S)-mixable.

substituting Φ for η −1 S in Theorem 14 implies that (η /η − 1) S is convex on ri ∆ k . η ≤ η , and since from Theorem 7 η ≤ η , we conclude that η = η .


This means high accuracy solutions can be achieved, as demonstrated in Appendix B.

under the conditions of Theorem 2, generically in C, RTR converges to global optima.


Indeed, any point in feasible set of state-action frequencies may be achieved by such a stationary policy [5].

alternative learning schemes may be applicable to this problem.


Let α t = t. Assume K = R n . Algorithm 2 is actually the case the x-player uses MIRRORDESCENT.

xT is an O( 1 T 2 )-approximate optimal solution of min x f (x) by Theorem 2 and Corollary 1.


The current state-of-the-art model for predicting the activity of V4 neurons uses the output of middle layer neurons in a CNN previously trained without any information about the responses of V4 neurons [23].

we used a pre-trained CNN (GoogLeNet) to obtain the predictive feature embeddings.


For instance, on Wikipedia1k, training one binary classifier takes 12.35s on average, and inference with one classifier (for the whole test dataset) takes 3.18s.

bR requires about 206 minutes (1000 × 12.35s) for training and 53m for testing on the whole test set.


On the other hand, notice that if we tighten the nonnegativity constraint to X kl ≥ , the objective function of (12) will always be finite.

we can simply modify the optimization of ( 12) the objective function to become infinity, as: The following result shows that with a sufficiently small , the constrained optimization problem in (13) has a unique global optimal solution that affords a closed-form and intuitive interpretation.


By Newton's law, a 0-mass particle can achieve infinite acceleration and has infinitesimal response time to any force acting on it.

the particle is "locked" on the force field (the gradient field) of the potential (f ) -the velocity of the particle is always proportional to the restoration force acting on the particle.


This would then imply that X ∈ X c . To prove the claim, observe that for i = m + 1, . . . , n, both sides of ( 24) are equal to 0.

moreover, since Xk ∈ X c , Propositions 4.2 and 4.3 give it suffices to show that for ǫ > 0 sufficiently small, Towards that end, fix an index i = 1, . . . , m and consider the three cases defined in Section 4.1.1: Case (A).


The following holds with probability at least 1 − δ.

for any n ≥ 1, This implies, for all n ≥ 1, the final hypothesis returned by Algorithm 1 after seeing n unlabeled data has roughly the same error bound as a hypothesis returned by a standard passive learner with n labeled data.


EEG data from Brain-Computer Interface experiments are highly challenging to evaluate due to noise, nonstationarity and diverse artifacts.

bCI provides an excellent testbed for testing the quality and applicability of robust machine learning methods (cf.


Better calibrated uncertainties produce smaller gaps beween model confidences and actual accuracies, shown in green bars.

the perfect calibration when the confidences exactly matches the actual accuracies: .


In our learning setting, the agents share the same observations of previous plays.

we take the pre-image to be the most recent m joint actions appended by the number of steps played so far.


This algorithm, also known as ν-method, uses an accelerated gradient descent step, which is faster than L2 Boosting because we only need √ t iterations to get the same solution as the L2 Boosting would get after t iterations.


Note that unlike k-clustering functions that optimize common clustering objective functions, heuristics that aim to find clusterings with low loss for these objective functions do not necessarily make meaningful k-clustering functions.

such heuristic's failure to satisfy certain properties does not preclude these properties from being axioms of clustering, but rather illustrates a weakness of the heuristic.


Let N denote the set of all pairs, and let N k denote the set of first k pairs in the random order.

since each pair in N is treated equally, N k is a random subset of N of size k. k i=1 (a γ(i) /σ x ) 2 is equivalent to take the total sum of (a i /σ x ) 2 with i from 1 to d and divide it by d/k.


Then, setting D L D R equal to DAB, we obtain the solution , where the subscript f denotes the retained singular value and vectors.

the only modification to the method in the previous section is to replace the estimation of A and B in ( 18)-( 21) with the global solution V f Λ −1 f Λ F V T f . this method allows us to avoid the alternating optimization for finding A and B, which potentially can get stuck in undesired local minima.


If f d (z) is that estimate, an equivalent representation of the data term is g 1 (w) = ED ∇ w Eq w (Z) f D (Z) where D is uniform over subsets of data.

one can define an unbiased estimator by using one of the techniques above (to cope with Eq w (Z) ) on a random minibatch D (to cope with ED).


Label propagation assumes that data points (nodes) connected in a graph should have similar labels.

the label estimation heavily depends on edge weights in a graph which represent similarity of each node pair.


While the generator benefits from being able to blend pixels at object boundaries, multiplying real images by these fractional values causes the discriminator to learn that mid gray is 'real' (i.e., we push the answer towards the midpoint 0 of the normalized [−1,1] pixel space).

we threshold the learned attention map for the discriminator: where t new and s new are masked versions of target sample t and translated source sample s , which only contain pixels exceeding a user-defined attention threshold τ , which we set to 0.1 (Figure 3 in the supplemental material justifies such choice).


Furthermore, the system has to perform real-time computations to promptly choose which image to show the user in the next round.

it is critical for a practical system to have a time complexity sublinear in N . One naive approach is to select a subset of arms ahead of time, such as volumetric spanners [19].


Using dynamic programming, one can compute the optimal value function of M, but the time and space required to do so grow fast with the number of states n [7,8].

the use of KBRL leads to a dilemma: on the one hand, one wants to use as many transitions as possible to capture the dynamics of M, but on the other hand one wants to have an MDP M of manageable size.


Initial results show that in field L, temporal patterns give at least % extra information.

single central auditory neurons can provide an informative representation of naturalistic sounds, in which spike timing may play a significant role.


This choice is made to strengthen our result: it would 'survive' the discovery of an algorithm that would use very specific properties of cliques (or even of random dense graphs) to detect their presence.

the analysis of our reduction is more technically complicated.


Laplacian regularization encourages nearby data points to have similar latent representations (e.g., assignments) and is widely used in spectral clustering [32,26] as well as in semi-supervised and/or representation learning [2].

the model can handle non-convex (or manifold-structured) clusters, unlike standard prototype-based clustering techniques such as K-means.


In the example of Düsseldorf and Hamburg, the car-license-plate cue would yield that Düsseldorf (D) is larger than Hamburg (HH), whereas the soccer-team cue would correctly favor Hamburg.

how successful a lexicographic strategy is in a comparison task consisting of a partial ordering of cue profiles depends on how well the cue ranking minimizes the number of incorrect comparisons.


The directed edge from node (i; j) to node (p; q) will be assigned a weight w 1 ((i; j); (p; q)) , d((i; j)jj(p; q)) F (i p; j q), where is a free parameter of our algorithm 2 .

the weight of the edge from node (i; j) to node (p; q) is proportional to their dissimilarity and to their closeness in the domain of M . Note that the edge in the opposite direction has exactly the same weight.


However, we are given a set of demonstrated trajectories, which presumably originate from some optimal expert policy distribution π E1 that optimizes an unknown reward function R E1 .

by trying to estimate the reward function R E1 and optimizing the policy π θ with respect to it, we can recover the expert policy.


This is because when each item A ij is kept with probability p ij A 2 ij , the result-ing entry B ij in the sample matrix has magnitude .

if an extremely small element A ij is accidentally picked, the largest entry of the sample matrix "blows up".


This connection is rather intuitive, as the collapsing issue is a clear sign of low entropy.

to avoid collapsing and increase coverage, we consider explicitly increasing the entropy.


We fit the model by maximizing the log-posterior probability of the correct labels D averaged over the data and noise samples: In practice, the expectation over the noise distribution is approximated by sampling.

we estimate the contribution of a word / context pair w, h to the gradient of Eq.


Partially dichotomized Gaussian model Another simple possibility to obtain a joint distribution of continuous and binary variables is to take multivariate (latent) Gaussian distribution for all variables and then dichotomize those components which should represent the binary variables.

a binary variable b i is set to 1 if the underlying Gaussian variables is greater than 0 and it is set to 0 if the Gaussian variable is smaller than 0.


In total, each subject performed 16 blocks.

in each of the 10 stimulus × code conditions, there were a total of 32 letter presentations or 2304 stimulus events.


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

at training time we provide the learner with only one example at the time (or a small mini-batch), in the form of a triplet (x i , t i , y i ).


For a given set of parameters from the AdEx model, we want to reproduce the exact same behavior with our hardware neuron.

a simple two-steps procedure was developed to translate biological parameters from the AdEx model to hardware parameters.


A direct comparison with the reported results in the literature for C. diff risk prediction is difficult because of the differences in the studies mentioned above.

to measure the added value of considering the temporal dimension, we implemented the standard approach as represented in the related literature of classifying patients based on their current or average state and applied it to our data set.


This already is an optimal universal Hanoi solver.

within 1 additional day OOPS was able to solve the remaining 27 tasks for up to 30, reusing the same program £© d# x x " again and again.


But this is impossible without strong modeling assumptions; any rating is just as likely to be a true rating as due to the system.

we make strong, but plausible assumptions about a RS.


The Jacobian (∂p θ /∂θ) is a linear map Θ → X .

for a given x , ∂p θ ∂θ T α is the integral w.r.t.


This separation implies that the partition function can be computed in lower dimensional pieces As a result, the computation is exponential only in the size of the subsets α ∈ A.

we can also estimate the partition function with lower dimensional random MAP perturbations, E γ [max xα\x β {θ α (x α ) + γ α (x α )}].


Note that f (x, y, l) is the probability that a random walker starting at x stops at y with exactly l steps, which satisfies P z2V f (x, z, l) = 1.


In this framework, ideally, we can find the optimal "aggregated clustering" even if only a minority of the input clusterings are good enough.

we only need to specify an appropriate range of the input parameters, rather than the optimal values, for the underlying clustering algorithms.


In CP, observations about likes only update the t vector of movies and observations about acted only update the h vector.

what is being learned about movies through observations about acted does not affect the predictions about likes and vice versa.


In addition, a detailed comparison between the linear model and real neurons shows characteristic differences indicating that tangential neurons usually operate in the plateau range rather than in the linear range of the EMDs [2].

our study can only give a hint on what might happen at small image velocities.


Inserting (2) into (5) results in Since an appropriate cost function used in ( 1) is non-negative and monotonically decreasing, C [y i F (x i )] is always negative and R(i) is non-negative according to its definition in (6).

we can define our empirical data distribution as D(i) is always non-negative based on definitions of cost function in (1) and R(i) in (6).


In addition, by executing this operation, we can recover h 1 .


Suppose that there are sufficient training data.

the posterior distribution of all parameters are usually highly peaked.


By correlating the input signal and encoding redundant information, the channel signal to noise ratio (SNR) can be balanced to reduce the vulnerability of those independent channels with low SNR.

the overall L 2 performance is improved at the cost of transferring a suboptimal amount of information.


Some existing methods can solve it, but not efficiently.

in this subsection we will derive a new efficient algorithm to solve this optimization problem with global convergence proof, where we employ an iteratively reweighted method [18] to deal with the non-smooth regularization terms.


Recall that δ is the depth (distance from a hidden node to its closest observed nodes), θ min is the minimum (absolute) edge potential and η = dmax dmin is the ratio of distance bounds.

theorem 1 (Structural Consistency and Sample Requirements) Under (A1)-(A5), the probability that the proposed method is structurally consistent tends to one, when the number of samples scales as for learning Ising models on locally tree-like graphs, the sample complexity is dependent both on the minimum edge potential θ min and on the depth δ.


Even the realizable case, while commonly described as "solved" via the Perceptron algorithm or linear programming (LP), is not straightforward: The Perceptron's runtime is quadratic in the inverse-margin, while solving the consistent hyperplane problem in strongly polynomial time is equivalent to solving the general LP problem in strongly polynomial time [Nikolov, 2018, Chvátal], a question that has been open for decades [Bárász and Vempala, 2010].

an unconditional (i.e., infinite-precision and independent of data configuration in space) polynomial-time solution for the consistent hyperplane problem hinges on the strongly polynomial LP conjecture.


Moreover, we are guaranteed to be (|V |+|E|) -close to a dual optimal solution if no direction of descent is found in ∂ q(λ).

we are able to get out of corners and efficiently reach an approximated dual optimal solution.


Let V l be a vector field on the manifold M l . For each point x l i , let V x l i denote the value of the vector field V l at x l i .

recall the definition of vector field, V x l i should be a vector in the tangent space T x l i M l . we can represent it by the coordinates of the tangent space T x l i M l as Let f l be a function on the manifold M l . By abusing the notation without confusion, we also use f l to denote the vector is, V l is a d l n l -dimensional big column vector which concatenates all the v l i 's for a fixed l. Then for each task, we aim to compute the vector f l and the vector V l . In this section, we introduce multi-task vector field learning (MTVFL).


The number of ls (cluster indices) that hold this condition is limited to a certain finite number.


For f (λ) = λ 2t and L = D −1 W , we get the Diffusion Map [25].

f (λ) function has one-to-one correspondence relationship with spectral dimension reduction techniques.


Suppose we have a set of base kernel functions {k m } M m=1 (or base kernel matrices {K m } M m=1 ).

an ensemble kernel function k (or an ensemble kernel matrix K) is then defined by the learned model from binary-class data {(x i , y i ∈ ±1)} will be of the form: Optimizing both the coefficients {α i } N i=1 and {β m } M m=1 is one particular form of the MKL problems.


This implies g(L ) < g(L), which contradicts the assumption that L is the labeling from the max flow algorithm.

there is no better path in terms of f () than that associated with the result of the max flow algorithm.


[19] have empirically shown that unsupervised learning of visual features can obtain a more general and effective representation.

in this paper, we focus on learning a fast approximation of sparse coding in an unsupervised manner.


From here we can see that if we let L go to infinity and set k(n) = λ −n , 0 ≤ λ ≤ 1, then we obtain the λ-return estimator in equation ( 4), since .

λ-return (as used in the TD(λ) family of algorithms) is the maximum-likelihood estimator of return under the following assumptions: 1.


We now replace each occurence of Pu-+ c in P(d) by 1 -LaEA\{ c }Pu-+ a .

since uc never occurs in d and Pu-+x ~ pv-+x, the u --+ x Fisher score entry for a document d becomes tf( ux, d) The Fisher kernel is subsequently defined to be k(d,d') = UJrIUd', where Ud is the Fisher score vector with ux-component a~n P( d) and I = Ed[UdUdTJ .


ImageNet-5k, JFT [16], OpenImages [18]), different structures in the underlying network (e.g multi-scale features [20,26], deformable convolutions [8], heavier heads [28], anchor sizes, path aggregation [22]), test time augmentations like flipping, mask tightening, iterative bounding box regression etc.

we compare our results with SNIP [33], which is a recent method for training object detectors on an image pyramid.


Then, for any positive integer k, the β-mixing coefficient of the stochastic process Z is defined as Z is said to be β-mixing if β(k) → 0.

it is said to be algebraically β-mixing if there exist real numbers β 0 > 0 and r > 0 such that β(k) ≤ β 0 /k r for all k, and exponentially mixing if there exist real numbers β 0 and a sequence of random variables is mixing when the dependence of an event on those occurring k units of time in the past weakens as a function of k. Our generalization bounds will be based on the following measure of the complexity of a class of functions.


Then, by construction, for any y ∈ ∆ l , we have To see how C can be used to compute Q w (z, s), we note first that the states of C can be identified with pairs (q A , q B ) where q A is a state of A, q B is a state of B, and the transitions are obtained by matching a transition in A with one in B.

for any z ∈ ∆ q and s ∈ [l], let E z,s be the set of transitions of C constructed by pairing the transition in A ((z 1:q−1 , s − 1), z q , ω(z, s), (z 2:q , s)) with a transition in B: Note that, since C is deterministic, there can be only one transition leaving a state labeled with z q .


In [5], it was shown that the eigenfunctions and eigenvalues of (4) can be approximated as φ j (x i ) ≈ √ N e ji , λ j ≈ λj N , where e ji denotes the ith element of the jth eigenvector.

hence, the mapping (4), can be approximated as the mapping is based on the eigenspectrum of K. The feature space data set may be represented in matrix form as Φ N ×N = [Φ(x 1 ), .


The literature indicates the difficulty of defense evaluations.

our goal is to ensure the lower bounds on the size of adversarial perturbations that can deceive networks for each input.


We use models trained on MNIST-ROT to report evaluation results on this dataset, to show the advantage of unsupervised invariance induction in cases where certain z are not annotated  in the training data.

information about these z cannot be used to train supervised invariance induction models.


For the JFA problem, if we stack the matrices then the problem reverts to the FA problem.


Following standard variational inference methodology, [1] we obtain the evidence lower bound of a GP-SSM augmented with inducing points In order to achieve tractability, we use a variational distribution that factorizes as where q(u) and q(x) can take any form but the terms relating to f are taken to match those of the prior (3).

the difficult p(f t |...) terms inside the log cancel out and lead to the following lower bound L(q(u), q(x),θ) = −KL(q(u) p(u)) + H(q(x)) + x q(x) log p(x 0 ) where KL denotes the Kullback-Leibler divergence and H the entropy.


We denote the solution obtained in the th iteration as w ( ) .

in the ( + 1)th iteration, due to the concavity property of we can bound the second term in problem (5) as follows in the ( + 1)th iteration, we need to solve a weighted version of problem (1): According to [14], the MM algorithm is guaranteed to converge to a local optimum.


That is, Self-infolTIlation characterizes the raw likelihood of the specific n-dimensional vector of ROB values given by X . p(X) in this case is based on observing a number of n-dimensional feature vectors based on patches drawn from the area surrounding X .

p( X) characterizes the raw likelihood of observing X based on its surround and -l og(p(X)) becomes closer to a measure of local contrast whereas entropy as defined in the usual manner is closer to a measure of local activity.


However, due to its intractability, we must seek different means of comparison.

we plot the probability of the most likely non-presented odor (red); the average probability of the non-presented odors (green), and the probability of guessing the correct odors via simple template matching (dashed; see Fig.


the update rule for the new objective function is simply Note that we follow a popular practice of adding an additional entropy regularization term H, which was first proposed by [18] to help the agent escape from local optimal at the beginning of the training process.


However, for the applications we are interested in, comprising sequences of large-scale images, it is critical from a practical standpoint to avoid processing all samples simultaneously; we require a procedure that is both low in memory use and yields fast inference.

we propose a new scheme for gradient descent that enables Monte Carlo gradient estimates in a distributable and memory-efficient fashion.


There is a natural logarithmic dependence on p and a linear dependence on the average degree parameter c. Finally, the dependence on α can be explained as follows: any α-walk-summable model is also β-walk-summable for all β > α.

the class of β-walk-summable models contains the class of α-walk-summable models.


A standard corpus of labelled ground truth data for the beat-tracking problem does not exist.

we labelled a relatively small number of songs for evaluation of our algorithm, by listening to the songs and pressing a key at each perceived beat.


But to formally quantify this phenomenon, we appeal again to Definition 3.2 as we seek a worst-case (adversarial) notion of robustness.

we can quantify the stability of an explanation generation model f expl (x), by estimating, for a given input x and neighborhood size ✏: where for SENN we have f expl (x) := ✓(x), and for raw-input methods we replace h(x) with x, turning (5) into an estimation of the Lipschitz constant (in the usual sense) of f expl .


The righthand side of ( 11) is bounded from below by 1, which is approached whenever one or more columns in some Φ * are similar to φ * (i.e., coherent).

even the slightest amount of curvature (or strict concavity) in h can lead to the inequality being satisfied when highly coherent columns are present.


Since our proof goes through Lemma 1, it also yields a policy regret bound against the ⇡ ramp (⋅) class.

this result is directly comparable to the Õ(T p+1 p+2 ) bound of Cesa-Bianchi et al.


In the case of the MoGnet, we used the same number of Gaussian mixture models as HMM's in the Alphanet, each with the same number of hidden states.

it has fewer parameters, because it is lacking the transition probabilities of the HMM.


If the bandwidth is very low, then it is more efficient to simply find all source points x i that influence a target y j and perform exact evaluation for those source points.

if n s source points are within the cut-off radius of y j , then the time to build the structure is O(N log N ) and the time to perform a query is O(n s log N ) for each target.


Typically, X 0 is not in C K , and we are not interested in X 0 , but in how far it is from X.

as Theorem 2 below will show, the optimum value in (SS Km ) determines this distance, measured in Frobenius norm, and  K. if the value K is small enough, it implies that no good clusterings of the data can differ more than K from X(C).


We assume that the baseline method knows that content-unrelated annotations do not appear in any document.

the precision of the baseline method is always one, because the number of false positive samples is zero.


Unlike the standard Independent Component Analysis where we use observed data to estimate the hidden sources, in LICA the "observed data" for ICA are actually task parameters.

they are latent and themselves need to be learned from the training data of each individual task.


Obviously, a reward which precedes an action in an rollout, can neither be caused by the action nor cause an action in the same rollout.

when inserting Equations (2) into Equation ( 5), all cross-products between r t and ∂ θ log π(a t+δt |s t+δt , t + δt) for δt > 0 become zero in expectation [10].


one can disregard the matrix D and dual variables ∆ when solving the optimization in Theorem 7.


The average resulting cost (ie the average resulting difference from the log probability under exact inference) is m j d v log units.

the ACh-based approximation performs well, and much better than purely bottom-up inference.


Specifically, we impose the rank-1 expansion H = Kc k=1 u :k v T :k , where u :k and v :k are column vectors (thus their outer product is a rank-1 matrix), each of them is modeled here by a Gaussian distribution: and K c is the number of such rank-1 matrices such that K c < min(K l , K r ), i.e., H is low-rank.

to motivate this model, consider the representation we may also express X = ΨΦ T , with Ψ ∈ R P ×Kc and Φ ∈ R N ×Kc ; the kth column of Ψ is defined by Lu :k and the kth column of Φ defined by Rv :k . Consequently, the low-rank assumption for H yields a low-rank model X = ΨΦ T , precisely as in [17,18].


While Type II displays invariance to W -and D-like transformations, Type I methods do not.

we examined two dictionary-standardization methods for Type I.


While each view differs in its implicit human-designed splitting criterion, all separate some classes from others, thereby lending (often complementary) discriminative cues.

rather than commit to a single representation, we aim to inject pieces of the various taxonomies as needed.


Similarly, we can construct classification tasks exhibiting the manifold assumption, the cluster assumption, or their conjunction, but without the MFS.


However, Figure 1(b) shows that, in terms of the statistical error |||Σ * − S (t) ||| ∞ , µ = 1 performs similarly to the other smaller µ's.

we show that significant computational efficiency can be gained with little loss of statistical error.


In other words, we require v y 2 should be larger than all the length of the other capsules.

we can minimize the following negative logarithmic softmax function to train the capsule subspaces and the network generating x through backpropagation in an end-to-end fashion.


We use the following simple upper bound B ss (τ ): Here, λ = λ/ α √ Ω for any λ and α.

sampling from the dominating hazard function B ss (•) reduces to straightforward sampling from a Weibull with a smaller scale parameter λss .


The human mind faces the same challenge.

solutions to the algorithm selection problem can inspire models of human strategy selection and vice versa.


Cosegmentation uses the observation that while global histograms of images of the same object (in different backgrounds) may differ, the histogram(s) of the respective foreground regions in the image pair (based on certain invariant features) remain relatively stable.

one may perform a concurrent segmentation of the images with a global constraint that enforces consistency between histograms of only the foreground voxels.


For the sake of brevity, the standard Perceptron algorithm is called FO ("First Order"), the Second-order algorithm is denoted by SO ("Second Order"), while the Higher-order algorithm with norm parameter p and ρ k = c/k is abbreviated as HO p (c).


Specifically, the class of polynomial networks of constant depth t is contained in the class of multivariate polynomials of total degree at most s = 2 t . This class can be represented as a d s -dimensional linear space, where each vector is the coefficient vector of some such polynomial.

the class of polynomial networks of depth t can be learned in time poly(d 2 t ), by mapping each instance vector x ∈ R d to all of its monomials, and learning a linear predictor on top of this representation (which can be done efficiently in the realizable case, or when a convex loss function is used).


Our model is the first among those using discrete latent variables which challenges the performance of continuous VAEs.

we get very good reconstructions like regular VAEs provide, with the compressed representation that symbolic representations provide.


The actual dependence of the performance on the discount factor may be non-trivial, and therefore hard to predict based on simple bounds.

the most practical approach is to first predict an improving discount factor based on the theoretical predictions, and then use line search to find a discount factor that ensures good performance.


However, we show that the lattice filter model explains several existing observations in vertebrate and invertebrate visual systems and makes testable predictions.

we believe that lattice filters provide a convenient abstraction for modeling temporal aspects of visual processing.


Indeed, given W ∈ R d×m , K-means aims to decompose it in the form W = µE ⊤ where µ ∈ R d×r are cluster centers and E represents a partition.

given E, µ is found by minimizing min µ W ⊤ − Eµ ⊤ 2 F . a natural strategy outlined by [9], is to alternate between optimizing µ, the partition E and the weight vectors W . We now show that our convex norm is obtained when minimizing in closed form with respect to µ and relaxing.


This is because as the learning proceeds, the networks will eventually try to fit noisy data (which tends to have larger losses compared to clean data).

we need to ignore them by not updating the networks parameters using large loss instances [2].


During this period, since the noise is too small compared to the large magnitude of the gradient, the update is dominated by the gradient, and the influence of the noise is negligible.

the ODE approximation is reliable before it enters the neighborhood of the optimum.


Further, we desire scheduling approaches that do not depend on the details of SelectBatch, but work well for any reasonable implementation.

rather than directly optimizing regret for a specific SelectBatch, we consider the following surrogate criteria.


This essentially means that our functionals satisfy a stronger form of differentiability called Fréchet differentiability [7,36] in the L 2 metric.

we can write all derivatives in terms of the densities, and the VME reduces to a functional Taylor expansion on the densities (Lemmas 9, 10 in Appendix A): This expansion will be the basis for our estimators.


The gradient with respect to α j is g j = ∂C ∂αj = t h t q tj − λsign(α j ) with q tj the value of the j-th output neuron with input x t . This means that if, for a given j, we have | t h t q tj | < λ, moving α j away from 0 can only increase the cost.

the right quantity to consider is (| t h t q tj | − λ) + .


The best model fit from 200 random restarts (lower bound of −2.24 × 10 4 , no crossvalidation, results not shown) only used 3 out of the 8 possible states (the other 5 states had a probability of less than 0.5 %).

in this example, the best lower bound is achieved by a model with correct, and low, complexity.


It seems surprising that even an approximate solution can be obtained in seconds in a space of hundreds of dimensions.

we would like to investigate why these point-based algorithms work well, whether there are sub-classes of POMDPs that are computationally easier, and whether there are alternative measures that better capture the complexity of POMDP planning for point-based algorithms.


This decomposes into n independent problems, which simply identify the best predictor for each datapoint according to the current hinge-losses, i.e.

: Given {ρ i,m }, optimization over W decomposes into M independent problems, one for each predictor, which are equivalent to single-output SSVM learning problems: each subproblem in 10c can be optimized using using any standard technique for training SSVMs.


In practice, this function can capture resource constraints that limit how many actions an agent can execute in parallel.

the transition probability distribution in practice may be defined over a much smaller subset than the power-set of primary actions (e.g., in the grid world example in Figure 3, the power set is > 100, but the set of concurrent actions is only ≈ 10).


The objective is to find feature weights that maximize the likelihood of asking the human-produced questions.

we want to optimize where D = {d (1) , ..., d (N ) } are the questions (translated into programs) in the human data set.


Therefore, applying Theorem 3 with appropriate η * , one gets .

when φ(C) ⊆ {0, 1} d , the LDOMD algorithm with the above choice of F gives a better regret bound than both Hedge/Naïve OMD and FPL; in fact the performance of LDOMD in this setting is essentially optimal, as one can easily show a matching lower bound [3].


It is not possible for an element of H f (ρ; c, k) ∪ H f (ρ; c, k) to have all centers far from B 0 , since otherwise the cost is larger than c. (Concretely, "far from" means at least 4c/r 1 away; note that this term appears in the definitions of B and C in Theorem 3.2.)

at least one center lies near to B 0 ; this reasoning was also the first step in the k-means consistency proof due to k-means Pollard [1].


samples y n , the RankTest(y n ; ξ, η, 1) is structurally consistent under (A1)-(A3) with probability at least 1 − δ.

remarks: the rank test is also applicable for graphical model selection.


Here and in the following, we denote by a i: and a :i the i-th row and column of a matrix A, respectively (both are column vectors).

each x d: represents the time series of one of the D factors whereas w :d is a vector of loadings which are spatially distributed.


N ) denotes the normal density with mean µ N and variance σ 2 N , and µ N is asymptotically normal with mean θ 0 and variance σ 2 N . Here the maximum in the above expression is well-defined and unique.

under these conditions, the information maximization strategy works, and works better than the i.i.d.


We now re-write the MAP loss above in a manner that allows us to show the existence of an O(r 2 )-dimensional convex, calibrated surrogate.

in particular, we can write by Theorem 3, for the r(r+1) -dimensional surrogate ψ * MAP : {0, 1} r × R r(r+1)/2 → R+ and pred * MAP : R r(r+1)/2 →S r defined as we have that (ψ * MAP , pred * MAP ) is � MAP -calibrated.


Now ρ (x, Q ) ≤ h + 2r ≤ 4r + 2r since the if-clauses were not entered if we got to the end of the iteration.

q is an r-packing of B(x, 8r), and therefore max |Q| ≤ 2 8d .


In contrast, CMS has only logarithmic update cost, which is desirable, but local CMS summaries cannot be combined (since they are not reducible).

even if CMS is known to be faster than FA, it is not a suitable option in distributed setting.


Indeed, although the original paper [1] proposes to model the document length as L|λ ∼ Poisson(λ), this is never used in practice and, in particular, the parameter λ is not learned.

in the way that the LDA model is typically used, it does not provide a complete generative process of a document as there is no rule to sample L|λ.


Essentially, the SCMS algorithm detects the ridges of the kernel density estimator (KDE).

the SCMS algorithm requires a preselected parameter h, which acts as the role of smoothing bandwidth in the kernel density estimator.


The hierarchical-grained case denotes that, the transition among super-classes is discrete (e.g., aquatic mammals and flowers) and impossible, while the transition among sub-classes is continuous (e.g., aquatic mammals contain beaver, dolphin, otter, seal, and whale) and possible [32].

human cognition can mask invalid class transitions (i.e., aquatic mammals flowers), and highlight valid class transitions (i.e., beaver ↔ dolphin).


It is easy to see that recovering a pairwise tensor T = Pair(A, 0, 0) is equivalent to recover the matrix A from a subset of its entries.

the recovery problem of pairwise interaction tensors subsumes matrix completion problem as a special case.


These sources, such as news articles and web texts, are created by a writer to communicate information to a reader, where the writer and reader share substantial domain knowledge.

the texts tend to be concise and mention the minimum information necessary for the reader to draw the correct conclusions.


In [8], the LSE function is expanded as a second order Taylor series around a point ϕ ϕ ϕ, and an upper bound is found by replacing the Hessian matrix H(ϕ ϕ ϕ) with a fixed matrix , where C * = C − 1, I C * is the identity matrix of size M × M and 1 C * is a M -vector of ones.

similar to [16], we have: where ϕ ϕ ϕ m ∈ R C * is a vector of variational parameters.


For any > 1 and r > 1, suppose m tasks are assigned according to a random ( , r)-regular graph drawn from the configuration model.

if µ > 0, ˆ rα 2 β 2 > 1, and rα > 1, then for any t ∈ {±1} m , the estimate ti = sign(x i ) after k iterations of Algorithm 2 achieves the average error rate is bounded by The second term, which is the probability that the resulting ( , r) regular random graph is not locally tree-like, can be made small for large m as long as k = O( √ log m) (which is the choice we make in Algorithm 1).


In particular, changes in stimulus statistics such as luminance, contrast and spatio-temporal correlations can generate adaptation lasting seconds to tens of seconds [5,28,14].

we additionally explored adding feedback over longer timescales to the convolutional network.


We make this statement precise in Theorem 4.1.

it is only when ζ ≥ 1 that the parameter γ d plays a role in the performance of SWAP.


But then we cannot recommend that item to the user again!

the only way to learn about a user's preferences is through collaboration, or inferring from other users' ratings.


Because of the discretization of optical variables (OVs) in our simulation, increasing ∆t stim translates to an overall smaller number of jumps in OVs, but each with higher amplitude.

we say ψ(t) ≡ V (t) if and only if g exc and g inh are defined with the last equation.


In the extreme case, when α → 0+, the l α norm approaches the Hamming norm (i.e., the number of non-zeros in the vector).

there is the natural demand in science and engineering for dimension reductions in the l α norm other than l 2 .


For some reason, when the 100/100 kept the hand on track, it was less likely to do overshoots than the 100/50 case, which is why the average PT and success rate is better.

we conclude that the faster module are more influential over motor control.


The subunit model describes a receptive field as the linear combination of nonlinear kernel responses that spatially tile the stimulus.

the contribution of each localized patch of stimulus (of a size equal to the subunit kernel) is the same, up to a scale factor set by the weighting used in the subsequent pooling stage.


By rounding that fractional solution (for instance via randomized Pipage rounding [15]) we obtain a set whose utility is at least 1 2 of the optimum solution set of size k. We note that randomized Pipage rounding does not need access to the value of f . We also remark that projection onto P k can be done very efficiently in O(n) time (see [18,34,35]).

such an approach easily scales to big data scenarios where the size of the data set (e.g.


We use the following lemma to quantify this term.

3) There is a function f such that for any z, for a large d, and D  d, the ratio of the variance of ORF and RFF is Var(K ORF (x, y)) Figure 2(a) shows the ratio of the variance of ORF to that of RFF when D = d and d is large.


In the primal, we have 4n constraints (including ξ ≥ 0 ) instead of the 2n constraints in the SVM.

solving RMM as a standard QP has the same order of complexity as the SVM.


This is because scalar ambiguities show up in m between ℓ and ℓ ref due to light attenuation, between x(n) and κ(n) due to the shading factor s(n), and in the observed image v(n) itself due to varying exposure settings.

the performance metric typically used is the angular error cos −1 between the true and estimated illuminant vectors m and m. Database For training and evaluation, we use the database of 568 natural indoor and outdoor images captured under various illuminants by Gehler et al.


8 includes a potentially vector-valued stepsize η.

notice however that scaling w ← λw will have no affect on the values of z, z * or y * and hence on v. if we also scale η ← λη, then the sequence of discrete states z t , z * t , y * t will not be affected either.


Unpacking the Lemma, the LHS in Equation 7represents the object minimised by some suitable loss for class-probability estimation.

since g is affine, we can use any convex, differentiable ϕ, and so can use any suitable class-probability loss to estimate η. Lemma 2 thus implies that producing η by minimising any class-probability loss equivalently produces an r as per Equation 6that minimises a Bregman divergence to the true r. Theorem 1 provides a reduction from density ratio to multiclass probability estimation.


Real biological systems however are much more robust and flexible than current artificial intelligence mostly due to a much more efficient representations used in biological systems.

unsupervised learning algorithms that capture more sophisticated representations can provide a better understanding of neural information processing and also provide improved algorithm for signal processing applications.


Thus V (r, p 1 )/V (r, p 0 ) = F (γ −1 (r)) = 1 − 1/γ −1 (r) is strictly increasing on I , as desired.

as we have now established that F satisfies Conditions 1-3, Proposition 2 gives us a weight function λ : R → R >0 such that for all y ∈ Y, the map r → λ(r)V (r, y) is strictly increasing on R. fixing r 0 ∈ R, the loss L(r, y) = r r0 λ(r )V (r , y)dr is convex in r for each y ∈ Y, as noted by Rockafellar [19,Theorem 24.2].


From an intuitive point of view this is justified by the fact that π θ (•|s) is a probability distribution.

for all s ∈ S the probabilities π θ (a|s) must sum up to 1, removing |S| degrees of freedom.


However, most inverse optimization algorithms are designed specifically in batch setting, where all the data is available in advance.

there has been rare use of these methods in an online setting suitable for real-time applications.


One of the strengths of query expansion is its potential for solving the vocabulary mismatch problem by finding different words to express the same information need.

we can also require a minimal level of aspect coverage.


The influence of the cross-terms (UWS T and SW T U T ) is addressed later.


In terms of convergence, recent work [15,16] reveals that simultaneous SGD has faster convergence and achieves better performance than the alternative one.

we propose to apply SGD and update all parameters simultaneously in the training graph according to the total loss, which is the sum of each head's loss as well as regularization Ω(θ).


4 Uncorrelated feature learning via exclusive group LASSO Motivation It is known that in Lasso-type (including elastic net) [24,32] variable selection, variable correlations are not taken into account.

some strongly correlated variables tend to be in or out of the model together.


TP = N + , FP = 0, TN = N − , and FN = 0, giving: Let v [t] denote the best solution found until iteration t, i.e., According to the prior model, containing too many rules penalizes the model due to the large complexity.

to hold a spot in the model, each rule needs to make enough "contribution" to the objective, i.e., capturing enough of the positive class, to cancel off the decrease in the prior.


For an increasing exploration budget per tree and an increasing number of trees, the approximate action values of action a and b obtained by aggregation converge to 1 3 1 1−γ and 1 2 1 1−γ , respectively.

the decision rule will select action b for a sufficiently large budget, even though a is the optimal action.


2) uses a layer-specific GMM with K l components, so the dimensionality of each FV is 2K l d l , which, considering that FVs are computed densely, might be too large for practical applications.

we decrease FV dimensionality by projection onto h l -dimensional subspace using a discriminatively trained linear projection W l ∈ R h l ×2K l d l . In practice, this is carried out using an efficient variant of the FV encoder (Sect.


Note that the zero pattern of the G adjacency matrix coincides with the zero pattern of the concentration matrix.

the estimation of this graph G from k random samples of X is equivalent to the covariance selection problem.


Besides, the local regions of the bird in each image are annotated with locations by experts.

we can either directly extract the local image features using the ground-truth location annotations or indirectly extract the local image features using the SPDA-CNN framework [31] to detect the important regions followed a sub-network that uses a 3×3 ROI to pool each region for a 512-d feature.


We will then show that the score functions developed in the previous section is an asymptotically consistent estimator of the p-values.

it will follow that the strategy of declaring an anomaly when a test sample has a low score is asymptotically optimal.


This update rule uses a diagonal scaling (D γ|β +�I) −1 , which is independent of j β and Θ.

while one could directly use the update (17), in implementation, we propose to replace (17) with an adaptive coordinate-wise gradient descent algorithm (e.g.


Essentially, EGS suggests that x/y determines the availability of discriminative statistics in the environment.

the limitation is on learning, not on performance.


This indicates that the optimal rate of convergence is achieved.

the stochastic binary search adapts to the curvature of different functions and yields the optimal local minimax complexity, as given by our benchmark.


It is quite prominent that (i) a small norm of a column vector corresponds to a strongly correlated feature, and (ii) there is only one feature which carries most of the dependencies between the sources.


As shown in [12, Theorem 1] and [27, Theorem 2.1], the optimal estimator corresponding to any τ -divergence ambiguity set always coincides with the Bayesian estimator for the nominal distribution P = N d (µ, Σ) irrespective of ρ.

in stark contrast to the setting considered here, the size of a τ -divergence ambiguity set has no impact on the corresponding optimal estimator.


This problem is especially challenging for ranking distributions for which the order of two items is hard to elicit (because many entries of P are close to 1/2).

we again relax the goal of the learner and only require it to find a ranking r with the following property: There is no pair of items 1  i, j  M , such that r ⇤ i < r ⇤ j , r i > r j and p i,j > 1/2 + ✏.


Note that this learning-free scheme is fundamentally different from existing feed-forward networks that require learning with pre-defined styles and fine-tuning for new styles.

our approach is able to achieve style transfer universally.


( 10) can be further simplified and written as, We expand the norm in the above equation and obtain that, The set M t consists of indices of instances which were incorrectly classified.

thus, y t j (ω t • x t j ) ≤ 0 for every j ∈ M t . ∆ t can further be bounded from below as follows, where for the second inequality we used the fact that the norm of all the instances is bounded by R. To recap, we have shown that on trials for which the prediction is imperfect , while in perfect trials where no mistake is made ∆ t = 0.


In this formulation, the H 2 cost can be written as a Frobenius norm and the H ∞ constraint reduces to a linear matrix inequality.

the inner optimization can be equivalently written as a semidefinite program over O(F i (n 2 + np)) decision variables.


This leads, however, to an inconsistency in the objective function and gradient at the beginning and at the end of the iteration, which can be detrimental to quasi-Newton methods.

we seek to find a fault-tolerant variant of the batch L-BFGS method that is capable of dealing with slow or unresponsive computational nodes.


Let i 0 = K 0 = ∅ and 1 {•} denote the indicator function.

denoting DRIP's Gaussian parameters as θ, the likelihood is thus The only stochastic variables in the model are i t and δ t , where all other random variables are either observed or deterministic given the sequences i 1:T and δ 1:T . we may equivalently write p(s|x, θ) = p(i 1:T , δ 1:T |θ).


To gain intuition about the scaling of these random variables, consider the following: Proposition 5 Suppose that, for at least an 0(1) fraction of the features i (i = 1, ... ,n), it holds true that IP(Xi = 11Y = T) -P(Xi = 11Y = F)I ::::: 'Y for some fixed'Y > 0 (or IJLi ly=T -JLi ly=FI ::::: 'Y in the case of continuous inputs).

then as long as the class label gives information about an 0(1) fraction of the features (or less formally, as long as most of the features are "relevant" to the class label), the expected value of IlGen, oo(X) I will be O(n).


Our proposal produces a V * that has rows that are entirely zero, and it is motivated by the following two observations about CUR.

first, following from the definition of the leverage scores (3), CUR chooses columns of X based on the norm of their corresponding rows of V k . it essentially "zeros-out" the rows of V k with small norms (in a probabilistic sense).


For traditional categorization tasks the same 1-hot vector in the output will always map back to precisely the same hidden unit activities in a given layer.

this kind of naive TP may have difficulties when different instances of the same class have different appearances, since it will attempt to make their representations identical even in the early layers.


This result essentially says that the modulus of continuity measures the size (in fact, the larger half-width) of the the "flat set" where the magnitude of the subderivative is smaller than ✏.

see Figure 1 for an illustration for the class of symmetric functions f For the asymmetric case That is, the size of the flat set depends on the flatter side of the function.


The main complexity in each iteration is on computing Wx (t) .

the total computational complexity for MPGM is less than O(M N 2 ), where N = n 2 is the length of vector x (t) and M is the maximum iteration.


In the negative case, some performance is lost as a consequence of the mixing process, that persists even for infinite sample sizes 1 If the mixing matrix is known, a conceptually simple strategy to solve the partial label problem consists of estimating posterior partial label probabilities, using them to estimate posterior class probabilities and predict y.

since we can define vectors p(x) and η(x) with components p i = P {z = b i |x} and η j = P {y j = 1|x}, to write (2) as p(x) = M(x)η(x) and, thus, where a first condition to estimate η from p given M is that the conditional mixing matrix has a left inverse (i.e., the columns of M(x) are linearly independent).


When performing conditional independence tests or evaluating score functions, statistical errors occur more frequently as the dimensionality of a dataset increases, unless the sample size also increases at an exponential rate (resulting from the so-called curse of dimensionality).

until reliable methods for resolving conflicting information from input PAGs are developed, ION and similar algorithms will not in general be useful for higher dimensional datasets.


Note G G is not a desirable solution to R, because it is improper to assign a high correlation to two words simply because of their high co-occurrence; the two words may be not closely related as judged by the maximum-margin criterion.

it is important to search for the optimal word-correlation matrix R in addition to the maximum discovered in Eqn.


Thus, following the approach introduced in [11], we look for a function Then, the ranking function f : R d → R can be simply defined by f (x) = F (x, 0).

as we have already constructed a set of preference judgments P J, we can specify F by means of the restrictions we have a binary classification problem that can be solved using SVM.


If our analysis produces very different results for slightly different training data, the biological conclusions are unlikely to be meaningful.

we want genes that are assigned to nearby nodes in the tree, to be close together also in hierarchies learned from perturbed data sets.


As suggested by Jaakkola and Haussler [2], the Fisher kernel may be combined with additional transformations.

we evaluated the standard kernels for both setups.


However, all linear approaches have a fundamental shortcoming -the space of images, which is highly non-linear and thought to form a manifold, may not be well represented by a linear subspace.

lin-ear approaches to correlate the fMRI data with the EEG data may not capture any low dimensional manifold structure.


The only source of randomness comes from the realization of the Brownian.

being correct means that among all possible realizations of the Brownian motion, there is a subset of measure at least 1 − ε on which OOB outputs an estimate M ε which is at most ε-away from the true maximum.


1(d)), our GenDeR is much better than 'MF'.

we conclude that 'MF' performs comparably with or slightly better than our GenDeR in terms of diversity, at the cost of sacrificing the relevance of the entire ranking list.


In particular, Equation 1 is equivalent to EBRW's mean response (averaged over many trials) with decision threshold bounds placed γ units away for the starting point for evidence accumulation.

gCM with a low value of γ can be viewed as a limited capacity model, whereas GCM with a high value for γ converges to the predictions of an infinite capacity model.


From Lemma 1 we know that EXTRACTSVD returns an SVD that reconstructs to A's projection onto V (i.e., A = AV V T ).

we have only to show that mcSqErr in the terminal iteration is an upper bound on the error ||A − A|| 2 F with probability at least 1 − δ.


Our main contribution is an algorithm that also achieves O(nk) in the general case and O(n log k) in the convex case by exploiting the following key fact -the dynamic programming method always runs in time linear in the sum of possible x i values over all x i .

our goal is to limit the range of values by using properties of the f i functions.


Clearly, the number of breakpoints of h is at most n. Throughout the execution of SPLIT(Q 1 , Q n ), the algorithm computes a supporting k-partition at most once for each k ∈ {1, . . . , n}.

fINDPARTITION is called at most 2n times in total.


For example, consider the case where m = n + 1 and Rank(Φ) = n, implying that Φ has a null-space dimension of one.

any feasible solution to y = Φx can be expressed as x = x + αv, where v ∈ Null(Φ), α is any real-valued scalar, and x is any fixed, feasible solution (e.g., the minimum norm solution).


Then Z(θ) = 2c M ∈Ω ij∈M w ij where we have used the fact that all the new weights have a value of one.

the partition function is a sum over the weights of perfect matchings in G PM .


This gives the optimization problem: S X `V The choice of the constant 1 in the right hand side of ( 4) is arbitrary but not important, and changing it to any other positive constant 7 results only in S being replaced by 7 f S . Also, this problem has an objective that is linear in the parameters S , and both of the constraints are also easily verified to be convex.

the optimization problem is convex, which enables us to derive efficient, local-minima-free algorithms to solve it.


Indeed, the first step is due to the spherical symmetry of the hash family, the second step follows from the above discussion about replacing a random orthogonal matrix with a Gaussian one and that one can assume w.l.o.g.

that p = e 1 and q = αe 1 + βe 2 ; the last step is due to the independence of the entries of u and v. proving Theorem 1 reduces to estimating the right-hand side of (1).


The proposed method operates under a semi-supervised setting, in which both labeled training and unlabeled testing data are incorporated to form the intrinsic geometry of the sample space.

the violating samples or feature values are identified as sample-outliers or feature-noises, respectively.


[10] found that random forests had the best accuracy of all the classifiers in the study (neural networks with many layers were not included).

random forests can be considered a gold standard to which compare competing classifiers.


The variancecovariance matrix of Z under q is already known in closed from from E[ Z ] and (5).

computing ∂/∂φ j of (19) exactly is mechanical.


Due to the sub-sampling the kernel regressions do not contain too many kernel centers and the compact support of the kernel ensures sparse kernel matrices.

efficient regression and evaluation is guaranteed.


Documents in a corpus share the same set of K topics, but each document uses a mix of topics unique to itself.

topic models are a relaxation of classical document mixture models, which associate each document with a single unknown topic.


For instance, for k = 0, the sub-importances of X 2 and X 5 are positive, while all others are null, which means that only those two variables are ever selected at the root node, hence masking the others.

this also means that the importances of the remaining variables is biased and that it actually only accounts of their relevance when conditioned to X 2 or X 5 , but not of their relevance in other contexts.


Hence, quality guarantees for max-sum fixed points are good whenever: (i) the cycles in the MRF do not share any variables; and (ii) the smallest cycle in the MRF is large.

our result confirms and refines the recent results obtained for single-cycle MRFs [11].


We start by defining τ = ε/(q + 5), where ε is the error bound found in Theorems 1 and 2.

τ is simply a multiple of ε, which we can think of as an arbitrarily small positive number.


This can be explained by Theorem 2 because the local incoherence of a block diagonal entry is given by µ ij = n 2 rK 2 , where K is the corresponding cluster size, and hence the error corruption probability should satisfy 1 2⇢ ij > C 0 p n K log n for correct recovery.

a larger cluster can resist denser errors.


Assumption 1 means that items in position k > K are never clicked.

the algorithm never needs to actually compute the blocks P td where min I td > K because items in these blocks are never shown to the user.


Compared with network quantization and sparse connections, channel pruning removes both channels and the related filters from the network.

it can be well supported by existing deep learning libraries with little additional effort.


state s(t), action a(t), and reward r(t), as follows.

if the subject starts from a state s(t) and comes back to the same state after k steps, the expected cumulative reward V(t) should satisfy the consistency condition (3) for each time t of the data file, we calculated the weighted sum of the rewards acquired until the subject returned to the same state and estimated the value function for that episode as The estimate of the value function V(t) at time t was given by the average of all previous episodes from the same state as at time t ( ) ( ) where {t 1 , …, t L } are the indices of time visiting the same state as s(t), i.e.


For another thing, applying the previous methodology onto problem (5) does not lead to an tractable reformulation either, mainly because the objective function Ω ψ( dP1 d(P1+P2) )d(P 1 + P 2 ) is not separable in P 1 and P 2 , but depends on the density on the common support of P 1 and P 2 .

as argued in Section 4, in the least-favorable distribution the probability mass of the two distributions cannot be transported arbitrarily, but are linked via their common support.


The partition of the support to bins allows some relaxation of the TV notion.

instead of the TV, it may be interesting to consider the L 1 as a similarity distance on the measures after discretization.


We remove these assumptions when presenting experimental results.

our analysis uses a simplified model of the analog multipliers given by: where o is the multiplier output, x and w are the inputs, γ x and γ w represent the input offsets, and a x and a w are the multiplier gains associated with each input.


With the additive model assumption (no overlapping groups), the individual functions depend on their specific variable groups only, i.e., X (j) .

f j (x (j) ) can be optimized independently on a lower dimensional subspace.


(a) Removing the convolutional structures of the gates Given the local spatiotemporal features of the 3DCNN block, it can be considered that the 3DCNN block has paid attention to the noticeable spatial regions where there is valuable spatiotemporal information.

the ConvLSTM block can just focus on the spatiotemporal feature fusion along with the recurrent steps.


Second, the operation that must be performed on each trace is the same-a multiplication by λ.

tD(λ) need only store the sum of the return estimates from each state, rather than having to store each individually.


Moreover, the shortcuts are undetermined due to its multimodality.

the characteristics of a given task ought to be considered to determine the model structure.


Importantly, while the observations are assumed to be reliable indicators for relative preference ranking, their numerical scores may be quite deviant from the ground truth low rank preference matrix.

we aim at addressing preference completion under the following generalizations: 1.


SwitchLDA is an extension of CI-LDA to give emphasis or de-emphasis to specific languages for each topic.

switchLDA may represent multilingual topics more flexibly; however, it still has the drawback that the dependencies between languages are relatively weak.


the only parameters are the coefficients of the filter k. The most common choice is exponential, f (z) = exp(z), corresponding to the canonical 'log' link function for Poisson GLMs.


In other words, we hypothesize that similar points from two pointsets should also have neighboring points which are similar.

for each point we define a neighborhood of the point and weight the similarity between each pair of points with the similarity between their neighborhoods.


By the above lemma, we have F (x t ) − F (x) ≤ Lϵ as long as ∥z t − z∥ ≤ ϵ.

it suffices to show quadratic convergence of ∥z t − z∥ to guarantee F (x t ) − F (x) double its precision after each iteration.


PLP was designed to extract speaker-independent features from speech [4].

by using PLP and a variant such as RAS TA-PL P, we were able to train our classifiers to recognize letters and digits independently of who spoke them.


In light of what we know about the statistics of the visual input, however, this would be very surprising: Natural images are known to exhibit complex higherorder correlations which are extremely difficult to model yet being perceptually relevant.

if we assume that retinal ganglion cells do not discard the information underlying these higher-order correlations altogether, it would be a very difficult signal processing task to remove all of those already within the retinal network.


This is a constraint non-convex quadratic optimization problem in the number of hidden units which is too complex to be solved in each EM iteration.

we perform a step of the gradient projection algorithm [14,15], which performs first a gradient step and then projects the result to the feasible set.


That is, and by B S (i, σ), the probability that this classifier makes exactly Now, approximating the binomial by relative entropy Chernoff bound [Langford, 2005], we have, for a classifier f : As also shown in [Laviolette and Marchand, 2007], since m j = m m−j and kl(R S (f ) R(f )) = kl(1 − R S (f ) 1 − R(f )), the above inequality holds true for each factor inside the sum on the left hand side.

in the case of sample compressed classifier, ∀(z i , σ) ∈ K and ∀S ∈ (X × Y) m : Bounding this by δ yields: Now, consider the quantity in the probability in Equation 3 as the bad event over classifiers defined by a compression set i and an associated message string σ.


This, in turn, implies that p(x) must be degenerate, concentrated on the points x where I is maximal.

instead of finding optimal distributions p(x), we need only find optimal inputs x, in the sense of maximizing the conditional information between θ and y, given a single input x: .


We additionally display results obtained on the more challenging ImageNet dataset in Table 2 which shows similar impact for our methods.

the main point arising from our results is that, in contrast to previous conception, there is no inherent generalization problem with training using large mini batches.


Stochastic gradients can be computed faster than their batch counterparts, allowing more frequent updates.

in Algorithm 1, any stochastic estimator ∇f (x k−d k ; ξ) of the gradient may be used, as long as then, in Algorithm 2, the stochastic mini-batch estimator where ξ i are IID, may be used in place of ∇f any increasing batch size m k = Ω((k + 1) −α ), with α ∈ (0, 1), conforms to Assumption 3.


It is immediately obvious that using the above lemmas to compute N requires no extra memory other than storing M r , which contains at most nnzc(X 2 ) ≤ Ω X non-zero entries.

we completely avoid the intermediate data explosion problem.


Second, any overlapping region between co-occurring visual patterns is likely to cover a part (but not the full) of the object of interest.

they can be used to generate mis-localized positives as informative hard negatives for training (see white boxes in Figure 3), which can further reduce localization errors at test time.


But if f differs significantly from f * then the variance in the left hand side of ( 9), as well as the value of D, will be large.

if we take the variance in the left hand side of ( 9) as a measure of distance between f and f * then the hypothesis spaces with large and small D can be visualized as shown in Figure 1.


When the above equation is satisfied, the residual is equal for both policies.

we can change policies at such points without violating any of the LARS-TD invariants.


In the next section, we generalize this estimator into one that does not require prior knowledge of µ and can handle non-linear feedback.

suppose now that we have the same setup as in the previous section, except that now feedback has a non-linear dependence on the prediction: i ) for some arbitrary function f . For example, in the case of a linear predictive model ŷ = w • x, this kind of feedback could arise if we have feature feedback x i to the above predictions, we only affect the feedback term f (•): by adding artificial noise ⌫ (t) i , we are able to cancel out the nuisance terms, and isolate the feedback function f that we want to estimate.


On the other hand, the variational framework we have described accounts for these findings by showing that decision-making using approximate densities leads automatically to reward-modulated probabilistic beliefs.

the apparent inconsistency with statistical decision theory may be an artifact of rational responses to the information-processing constraints of the brain.


Section 3 for a brief discusssion) also has a large impact on the time needed to solve (1) using the dual problem.

it is of high interest to know how many support vectors one can expect for a given classification problem.


Intuitively, a foveated clutter model that takes into account target search should score very low when the target is in the fovea (near zero), and very high when the target is in the periphery.

an observer should find a target without difficulty, achieving a near perfect hit rate in the fovea, yet the observer should have a lower hit rate in the periphery given crowding effects.


Note that this is identical to the one spanned by ϕ(x 0 ), .

. . , ϕ(x τ −1 ), whose corresponding Krylov matrix is given by if we denote a set of τ orthogonal bases of the Krylov subspace by q 1 , .


This is obvious for u 1 , v 1 / ∈ [ω, 1 − ω] 2 , because C θ1 is a copula.

straightforward but tedious algebra shows that ∀u 1 , v 1 ∈ (ω, 1 − ω) 2 : C θ1,θ2,ω is continuous and has density almost everywhere on [0, 1] 2 and is therefore 2increasing.


Our method is based on the assumption that the combined data including x and y for an expert are usually distributed locally in the combined d + 1 dimensional space.

clustering methods such as k-mean can be used to cluster data, one cluster for one expert.


Our reduction strategy brings inter-dependency between the pairs containing the same observation and its true class in the original training set.

we derive new generalization bounds using local fractional Rademacher complexity showing that even with a shift in the original class distribution and also the inter-dependency between the pairs of example, the empirical risk minimization principle over the transformation of the sampled training set remains consistent.


Thus we can identify the family (ψ n1,...,n d ) with the one dimensional Fourier basis with frequency T d λ , which means that the condition number ρ = 1 for this curve.

for a d-dimensional function f , sparse in the Fourier basis, it is sufficient to sample along the curve induced by g to ensure that V C is invertible.


end for ESCB with time horizon T has a complexity of O(|M|T ) as neither b M nor c M can be written as M y for some vector y ∈ R d . Assuming that the offline (static) combinatorial problem is solvable in O(V (M)) time, the complexity of the CUCB algorithm in [10] and [11] after T rounds is O(V (M)T ).

if the offline problem is efficiently implementable, i.e., V (M) = O(poly(d/m)), CUCB is efficient, whereas ESCB is not since |M| may have exponentially many elements.


Cortex is segmented, then each cortical hemisphere is inflated to obtain a smooth surface, which is projected to the sphere, S 2 , represented by a discrete spherical mesh M s = {p k ∈ S 2 ; 1 ≤ k ≤ N v /2}.

the two cortical hemispheres are hence modeled by the disjoint union S = S 2 S 2 , represented by the corresponding disjoint union of mesh points M = M s M s . Anatomical cortical features, such as cortical curvature, are functions D a : S → R Na sampled on M . our analysis is restricted to cortex only.


of lower likelihood, then it is downweighted.

beta divergence allows to construct robust estimators as samples with low likelihood are downweighted (see also M-estimators [28]).


edge-exchangeable random graph sequences allow for a wide range of sparse and dense behavior.


Because we can guarantee that our models are drawn from the true posterior over models, this approach is a standard Monte Carlo approximation of the expectation.

we can apply the central limit theorem to state that the estimated expected rewards will be distributed around the true expectation with approximately normal noise N (0, σ 2 n ), where n is the number of POMDP samples and σ 2 is a problem-specific variance.


Even if a generative model can capture some of these features, an inversion of the model using Bayes' rule very rapidly becomes analytically and computationally intractable.

generative modelers make compromises to allow for trainability and applicability of their generative approaches.


We make predictions for each user and report the averaged results.

we make accurate predictions by observing users in the early stage.


The proposed projection approach is designed to be applicable to any probabilistic model.

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


Other groupings include type of occupation and education level as well as ethnic proportions.

overall our method captures sensible relationships.


The reason that we make such an assumption can be intuitively explained with the observation, once one arbitrary matrix is given, human cognition can certainly describe its structure, e.g., diagonal or tri-diagonal.

there must be a function that can implement the mapping from s to its structure s o .


Instead of introducing such an exponential discounting, our idea to construct a mathematically valid kernel is considering the limit of the ratio of kernels defined via finite series of the orbits of dynamical systems.

we do not need to introduce the exponential discounting.


We also show that using multiplicative forests, we can efficiently calculate the ML parameters.

we can calculate the maximum change in log likelihood for a forest modification proposal, which gives us the best iterative update to the forest model.


Interband intermodulation sources can be discerned, as long as the product does not fall into the testing band.

the STI allows for standard AI-frequency band weighted SNR effects, MTF-time domain effects, and some limited measurements of nonlinearities.


The prevalent training framework in machine learning, Empirical Risk Minimization [51], does not guarantee performance when tested on a different data distribution.

it is important to develop new training methods that can generalize to different input distributions, or new methods that can reliably detect covariate shift [52].


Modelling only the tail of the density via (4) requires moving beyond strictly proper composite losses: from Proposition 2, all such losses have the same Bayes-optimal solution, up to a transformation.

we will construct suitable alternate losses via the weight function representation of a proper composite loss: every such loss with invertible link Ψ can be written [Reid and Williamson, 2010, Theorem 6] where the (generalised) function w : [0, 1] → R≥0 is the weight, and 01 is the cost-sensitive loss minimising equivalently minimises a mixture of cost-sensitive losses for various cost ratios, whose relative importance is determined by w; see Buja et al.


Much of the applied research has focused on modeling the bottom-up aspect of selective attention.

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


Proposition 1 suggests that it suffices to prove Theorem 1 if we find a dual certificate Y that satisfies the dual certificate conditions ( 9)- (12).

the second step is to construct Y via the golfing scheme.


Table 1 demonstrates that the relevant neurons identified by VBLS coincided at a very high percentage with those of the baseline results, while PLS, stepwise regression and LASSO regression had inferior outcomes.

in general, VBLS achieved comparable performance with the baseline study when reconstructing EMG data from M1 neurons.


We thus look for two constants c 0 and c 1 = 0, such that, for all values of f (x) + b, there exists a value 0 ≤ p(1|x) ≤ 1 such that The system (6) has a solution over the whole range of possible values of f (x) + b if and only if c 0 = log(2) and c 1 = 0.

the SVM optimization problem does not implement the MAP approach to Gaussian processes.


The surprise can also be expressed as the absolute value of the residual |y i − pi |.

local case-control sampling is equivalent to influence-based sampling under the approximation that there is no effect due to the regression design.


However, the algorithm would also work with any other prior, so if it were known a priori that certain values in the grid were of special importance, they could be given larger prior mass.

a more advanced analysis demonstrating that only a subset of learning rates could potentially be optimal (in the sense of minimizing the regret R η T ) would directly lead to factors of improvement in the algorithm.


The symbolic ordering extracted on one iteration will serve to constrain the model's interpretation of the anagram on the next iteration.

the feedback forces the model down one path in a solution tree.


More precisely, the weight w ij associated with the edge ij in a graph will be the result of an appropriate composition of a feature vector x ij (observed) and a parameter vector ✓ (estimated from training data).

in practice, our input is a vector-weighted bipartite graph G x = (V, E, x) (x : E 7 !


In words, X i and Z i have the same distribution conditioned on the event .

the probability in the lemma above can be written as where Z i are bounded in [0, r] with probability 1.


That is, if we denote by g 1ℓ (r, ℓ) the ℓ-th row of the output of the denoiser, we assume that for a vector-valued function φ(•) that is the same for all rows.

the ℓ-th row output g ℓ (•) depends only on the ℓ-th row input.


Because control-based exploration maintains the sampling area in the control space, the sampling is almost uniform in the parameter space at around s = 0, where the agent visits frequently.

the parameter-based exploration may realize more efficient sampling than the control-based exploration.


in the supplement, it follows that d = σ 2 0 / Σ 0 2 ≥ tr(Σ 0 )/ Σ 0 ≥ 1.

assuming that the sample size satisfies m ≥ (6C ) 4 dβ, then, dβ/m ≤ 1/(6C ) 4 < 1, and by some algebraic manipulations we have that For completeness, a detailed computation is given in the supplement.


By considering a cost function c : Ω S × Ω T → [0, ∞[, Monge's formulation of the OT problem is to find a transport map T : Ω S → Ω T (also known as a push-forward operator) between two probability measures µ S on Ω S and µ T on Ω T realizing the infimum of the following function: When reaching this infimum, the corresponding map T is an optimal transport map.

it associates one point from Ω S to a single point in Ω T . the existence of this map is not always guaranteed, as when for example µ S is a Dirac and µ T is not.


• In terms of computing, (2) requires O(n 2 ) memory to store the W matrix, which is typically dense unless making further structural assumption.

a standard solver will be hard to scale beyond 30, 000 players.


Note that even if two pixels are assigned to the same vertex, they will have different features after reprojection.

gCU is likely to preserve the spatial details of the signal.


Therefore in a good round, we see at least (L − f (S))/2 increase in value of S. In other words, the gap L − f (S) is reduced by a factor of at least 2 in each good round.

since f only takes integer values, once L − f (S) becomes less than 1, we know that f (S) ≥ L. there cannot be more than log 2 L good rounds.


Every fixed point of the system (1) is called an equilibrium of the system, and they correspond to the critical points of the function f . Unless f is a quadratic function of the parameters, the system described by ( 1) is either a nonlinear system or a hybrid system that switches from one dynamics to another over time.

the system (1) can exhibit behaviors that are typically observed in nonlinear and hybrid systems, such as convergence to an orbit but not to a fixed point, or dependence of convergence on the equilibria and the initialization.


This is expected as the Mean-Field method makes an extreme approximation.

cross-validation is more appropriate for the Mean-Field method.


We note that following a GCG scheme has another practical benefit: the rank of the intermediate solutions starts from a small value and then gradually increases, while the starting solutions obtained from existing first-order methods are always of high rank.

gCG is likely to find a lowrank solution faster, especially for large size problems.


With these considerations in mind, we suggest that our model variability should induce temporal dependencies across timesteps.

like DBN models such as HMMs and Kalman filters, we model the dependencies between the latent random variables across timesteps.


Decoder and encoder networks each consisted of two convolutional layers (kernel size 3 × 3) with sigmoid activation functions, each of which had a stride of two (both conv and conv transposed).

a training sample with a size of 28 × 28 is downsampled to 7 × 7, and then upsampled to 28 × 28.


On the other hand, Marg k is exactly the wavelet space W k−1 of the Bi-CMRA generated by ν 0 = {(n)} of Example 2.

when p is q-sparse, noting that d (n−1,1) = n−1, by using the methods of the previous section, we can find its projection to each of these spaces in just O(n 4 q) time.


Figure 1: Algorithm of the Multinomial Particle Filter.

where α y is the y'th element of α and n y is the number of occurrences of y in the essence of this problem lies in how to detect a change point given the data up to time t, a change point problem in discrete space.


Since both UML and Kinship data have no attributes in basic entity types, composite entities become more important to model.

we suspect that the MRC model achieves better performance because it can perform clustering on two-argument predicates which corresponds to composite entities.


In fact, each (i, j) entry of the low rank matrix L can be associated with a local incoherence parameter µ ij , which is less than or equal to the global parameter µ, and then the allowable entry-wise error density can be potentially higher than that characterized based on the global incoherence.

the total number of errors that the matrix can tolerate in robust PCA can be much higher than that characterized based on the global incoherence when errors are distributed accordingly.


In other work, entropy was generalized to partitionings by interpreting partitionings as probability distributions [20,21].

entropy emerges as an important statistic for our problem, but new definitions will be needed for quantifying information in feature allocations.


Ideally, all preferred items are ranked above the quantile and non-preferred ones ranked below.

the loss or generalization error of a hypothesis h : X !


To shape the behavior, a very narrow initial state distribution and termination conditions are used in the benchmarks.

the learned policies become highly trajectory centric -i.e.


However, ML criteria are non-discriminative modeling techniques for estimating generative models.

they suffer when model assumptions are inaccurate.


To train SGAN, we draw inspirations from the recently proposed adversarially learned inference framework (ALI) [5], and build two adversarial games to drive I, G to match the true joint distributions p(x, z), and C, G to match the true joint distribution p(x, y).

sGAN can be seen as a combination of two adversarial games and two collaborative games, where I, G combat each other to match joint distributions in the visible space, but I, C, G collaborate with each other to minimize a reconstruction error in the hidden space.


These studies conclude that the (asymptotic) information content of unlabeled examples decreases as classes overlap.

1 the assumption that classes are well separated is sensible if we expect to take advantage of unlabeled examples.


Consider a graph-structured pattern drawn from an Ising model or the GGM with weight matrix W of the hierarchical block form as depicted in Figure 2.

if = 2 − (1−β) ∀ ≤ γ log 2 p+1, for constants γ, β ∈ (0, 1), and = 0 otherwise, then the noise threshold for consistent MSE recovery (R if we take advantage of the network interaction structure, it is possible to tolerate noise with variance that scales with the network size p, whereas without exploiting structure the noise variance needs to decrease with p, as discussed in the introduction.


Assume the PSM scoring function ψ(s, x) is that of Didea (i.e., Equation 1) where the emission function f θτ (s(i)) has uniform weights The full proof of Theorem 2 may be found in [15].

didea's scoring function effectively serves to lower bound XCorr.


Note that if we were to assign one unique point of the Z space to each dataset sample, then a neural network could learn to memorize the dataset by mapping each selected z ∈ Z to its corresponding real sample (we have introduced N disjoint component in Z space in this case), however this is not how GANs are modeled.

the memorization issue is not of concern for common GANs and our proposed models (note that this argument is addressing the very narrow case of dataset memorization, not over-fitting in general).


Many more-or-less heuristic methods for non-linear manifold discovery are based on the idea of preserving the geometric properties of local neighbourhoods within the data, while embedding, unfolding or otherwise transforming the data to occupy fewer dimensions.

algorithms such as locally-linear embedding (LLE) and Laplacian eigenmap attempt to preserve local linear relationships or to minimise the distortion of local derivatives [1,2].


In our problem formulation, however, changing c t to c t may change the decision set D t to a possibly disjoint D t , making that notion ill-defined.

when we discuss the impossibility of regret-minimization under standard differential privacy in Section 5, we revert back to a fixed action set A with an explicit per-round context c t . In this work, in addition to formulating the definition of JDP under continual observation, we also present a framework for implementing JDP algorithms for the contextual linear bandit problem.


Shapes are represented by unlabeled point sets of arbitrary size and a background component is used to handle occlusion, local dissimilarity and clutter.

unlike many shape matching techniques, our approach can be applied to shapes extracted from real images.


Unfortunately, such an analysis of individual parameters or units quickly becomes intractable in the presence of very deep networks.

currently, one of the most popular compression approaches amounts to extracting low-rank approximations either of individual units [28] or of the parameter matrix/tensor of each layer [14].


For example, symmetrized K-nearest-neighbor (K-NN) graph is a popularly used similarity input.

similarity matrices in real-world clustering tasks often look like Figure 1 (a), where the non-zero entries are much sparser than the ideal case.


The following functional with respect to r is called the free energy: In the last equation, the first term is the Kullback-Leibler (KL) distance from the trial distribution to the Bayes posterior, and the second term is a constant.

minimizing the free energy (4) amounts to finding the distribution closest to the Bayes posterior in the sense of the KL distance.


In particular, when p = 1, we have the following guarantee: We note that ROBUST-PCA yields a smaller additive error than ROBUST-LRA by a factor of n/d, but at the expense of an additional multiplicative factor of log 2 (d).

in settings where OPT k (A) is small (e.g.


[37] YOLOv2 [24] ‡ 53.97 ---Hinami and Satoh [10] Query-Adaptive RCNN [10]  multi-channel input.

the number of forwardings to infer is significantly decreased.


We will focus on the algorithm in its basic form, where the domain W equals R d . The existing analysis of SVRG ( [11]) assumes stochastic iterations, which involves sampling the data with replacement.

it is natural to consider whether a similar convergence behavior occurs using without-replacement sampling.


We will show that both conclusions holding simultaneously implies the desired result.

observe that for any E ∈ E\{E 0 }, BIC γ (E) > BIC γ (E 0 ), which yields the desired result.


2001), and can be viewed as similar in spirit to belief propagation in probabilistic inference, and thus complements the recent work of (Vickrey and Koller 2002), who explored a junction tree approach.

as for probabilistic inference, we have at least two promising general-purpose approaches to equilibria computation in graphs.


We are also able to guarantee that the bound on the model's treewidth grows by at most one at each iteration.

our method resembles the global nature of Chow and Liu [5] more closely than the thin junction tree approach of Bach and Jordan [2], while being applicable in practice to any desired treewidth.


Even with the application of various correction factors, the AI does not predict intelligibility in the presence of some time-domain distortions.

the Modulation Transfer Function (MTF) has been utilized to measure the loss of intelligibility due to echoes and reverberation [4].


(With a slightly stronger complexity-theoretic assumption, it follows that obtaining an approximation even within an exponential factor is impossible.)

while previous results established that there was at least a computational barrier to going from factored MDP parameters to good policies, here we show that the barrier is actually representational, a considerably worse situation.


The variable H was the keystone for the conditional independence assumptions in this network.

the marginal distribution over the remaining variables has almost no structure: each }j depends on all the Xi'S, and the }j's themselves are also fully connected.


Analyzing the results of those experiments, it is apparent that the actual disagreement percentages between the dynamic decision output and the decision made by the complete committee are significantly lower than the specified target α.

more queries are made than the ones that are actually needed.


[5]), and hence we suggestively call it the hypergraph Laplacian.

we develop algorithms for hypergraph embedding and transductive inference based on the hypergraph Laplacian.


(This is a consequence of the nonnegativity constraint on the feature vectors: for all examples % and feature components Q .)

the nonnegativity constraints on the mixture weights and basis functions are enforced by these multiplicative udpates.


For any λ > 0 and a given partition where Θ * is the optimal solution of (1) and Θ is as defined in (2).

if a partition {V c } k c=1 satisfies the assumption of Theorem 1, Θ and Θ * will be the same, and the last step of Algorithm 1 is not needed anymore.


Intuitively, if kernel k cannot result in high MMD distance M k (P, Q) when P 6 = Q, Mk (P, Q) has more chance to be smaller than c ↵ .

then we are unlikely to reject the null hypothesis H 0 with finite samples, which implies Q is not distinguishable from P. instead of training g ✓ via (1) with a pre-specified kernel k as GMMN, we consider training g ✓ via which takes different possible characteristic kernels k 2 K into account.


This is similar to the previous example; only weight of the formula is different.

substituting this new weight, IPP output by Algorithm 2 will have objective function n x n y w 1 r + n x n y w 1 (1 − r)s and two constraints 0 ≤ r ≤ 1 and 0 ≤ s ≤ 1.


Theorem 2 The isd posterior with β = 1/2 is marginally consistent for Gaussian distributions.

proof 2 Start by integrating over x N : Assume the singleton prior p(θ N ) is uniform and integrate over θ N to obtain: Consider only the right hand integral and impute the formula for the Bhattacharyya affinity: In the (white) Gaussian case A(θ) = θ T θ which simplifies the above into: Reinserting the integral changes the exponent of the pairs of Bhattacharyya affinities between the (N − 1) models raising it to the appropriate power λ/(N − 1): we get the same isd score that we would have obtained had we started with only (N − 1) data points.


Even if downsampling is not possible through dedicated hardware, for most object detection schemes, the image must be downsampled to form an image pyramid in order to search for the object at different scales.

we can run the early stages of such a pipelined detector at the low resolution versions of the image and throw out large regions of the high resolution versions.


Under certain assumptions in [1], and the restrictions: η = O(1), and γ is large enough, the algorithm in [1] requires log p λ 2 samples, which is matched by the first term in our lower bound.

the algorithm in [1] is optimal, for the setting considered.


The algorithmic aspects of the problem have only been started upon in this work.

it remains to find out what is the computational complexity of the studied problem.


With a particular choice of adaptor, based on the Pitman-Yor process [1,2,3], simple context-free grammars specify distributions commonly used in nonparametric Bayesian statistics, such as Dirichlet processes [4] and hierarchical Dirichlet processes [5].

many nonparametric Bayesian models that have been used in computational linguistics, such as models of morphology [6] and word segmentation [7], can be expressed as adaptor grammars.


However, our updates use samples rather than the expected value, so an action a t that is actually worse could, due to stochasticity in the environment, result in a TD error that suggests it is advantageous.

the gradient estimates are influenced by the stochasticity of the transition function P and reward function R. If P or R is very stochastic, the same s, a pair will result in seemingly random TD errors, which manifests as large variance in δ t ψ st,at samples.


After an inference has been made, feedback is given about whether a decision was right or wrong.

the order-learning algorithm has information about which cues were looked up, whether a cue discriminated, and whether a discriminating cue led to the right or wrong decision.


Continuing with the same notation, we show now that Note that, if we apply Bayes' law recursively, Thus, and so forth.

what we wish to prove is ( ) or, rearranging, Note that, given the stipulated relationship between p( ) on each processing iteration and p( | u G ) on the previous iteration, With this in mind, we can rewrite the left hand side product in (17) as follows: Note that, given (18), the numerator in each factor of ( 19) cancels with the denominator in the subsequent factor, leaving only p(u G | *) in that denominator.


Even if it does converge, in mixed extensions of finite games (where each agent's action set is a probability simplex over a finite number of actions), the limit can assign positive weight only to strictly dominated actions.

establishing joint convergence to Nash equilibria under no-regret learning algorithms (OGD included) for a broad and meaningful subclass of games has been a challenging ongoing effort.


This means that if (3) is not injective, then the maximum risk is attained for P = Q, i.e., distinct distributions are not classifiable.

the injectivity of ( 3) is of primal importance in applications.


For example, the property tester rejected more than 95% of the ANN indices that are between 0.005-far and 0.01-far from being a 10-NN graph for c 1 = 0.01, c 2 = 5. depends heavily on the cost incurred otherwise.

we compare the property tester against the minimum cost that every algorithm that uses an ANN index must invest before it can employ it or even just draw conclusions about its quality: the build time of the index.


Furthermore, the conventional training of log-linear models is a strictly convex optimization problem.

the global optimum of the training criterion is unique and no other local optima exist.


But such data structures would require non-uniform memory access patterns, limiting their efficiency on GPU architectures.

we modify the algorithm to use ordinary finite integers.


Note that in Euclidean space, the exponential map is an addition operation, Exp(µ, z) = µ + z.

our model coincides with (1), the standard PPCA model, when M = R n . We develop a maximum likelihood procedure to estimate the parameters θ = (µ, W, Λ, τ ) of the PPGA model defined in (3).


However, the unknown mixing matrix C has potentially n 2 elements (for n sources and n detectors).

we need to evaluate two delayed correlation matrices M and M with two different time delays defined as to get enough information about the mixing process [10].


(This follows from [12] and the fact that the clique-partition number of G equals the chromatic number of its complement.)

with computational constraints, one cannot hope to obtain a bound better than Õ( √ kT ).


The weights β j are in turn generated by a Dirichlet distribution centered around π with a degree of variability determined by α.

π acts as the group-level expected value of the subjectspecific weights.