Then the number of rounds T that SMILE takes to achieve (up to a constant factor) the same number of matches M * T as the Omniscient Matchmaker drops significantly.

when S in SMILE has the form (n 2 log n)/ M , where M is the value returned by Phase 0, we have the following result.


On CIFAR-100 data, we have observed significant speed-up.

the evolutional dropout achieves relative improvements over 10% on the testing performance and over 50% on the convergence speed compared to the standard dropout.


2 Existing Trainable Iterations: Lack Generalizations and Guarantees We review existing training based iterative methods for model optimization.

most learning and vision tasks can be formulated as the following regularized optimization model: where f denotes the loss term and g is related to the regularization term.


Specifically, MAML performs the following optimization: where φ i is used to denote the parameters updated by gradient descent and where the loss corresponds to negative log likelihood of the data.

in the case of supervised classification with inputs {x j }, their corresponding labels {y j }, and a classifier f θ , we will denote the negative log likelihood of the data under the classifier as L(θ, D) = − (xj ,yj )∈D log p(y j |x j , θ).


The three average linkage distance functions are all trying to minimize something very much like our cost function.

ward's measure of the distance between two clusters is exactly the increase in k-means cost occasioned by merging those clusters.


The new method enables users to incorporate prior knowledge of the expected size of clusters into the clustering process.

the cost function of the new method is defined as the sum of the inter-cluster similarity and a regularization term that measures the relative size of two clusters.


In fact, as was shown in [BC17], the sample complexity with an unknown domain size is significantly different.

[BC17] gave a generalized uniformity tester with expected sample complexity O(1/( 6 p 3 )) and showed a lower bound of Ω(1/ p 3 ).


Let B be a d q × k matrix whose columns form an orthonormal basis of V . Thus, we have The condition that xS = (1 ± ) x simultaneously for all x ∈ V is equivalent to the condition that the singular values of B T S are bounded by 1 ± .

by Lemma 2, for m ≥ (2 + 3 q )/(( /k) 2 δ), with probability at least 1 − δ, we have the squared singular values of B T S are bounded by 1 ± , implying that the singular values of B T S are also bounded by 1 ± .


We then normalize the row so that each row has 1 norm equal to 1.

we get new normalized cost matrix where t + e r ) plays the role of weight.


We would like to note that this condition with s 2 < 1 is satisfied by many practically used kernels such as the Gaussian kernel.

it is satisfied if the kernel is smooth so that H r,k is included in a Sobolev space W 2,s2 [0, 1].


In the feature selection setting, existing methods for FDR control utilize the p-values produced by an algorithm for evaluating feature importance, under the null hypothesis that the feature is not relevant.

for each feature, one tests the significance of the statistical association between the specific feature and the response either jointly or marginally and obtains a p-value.


In this paper, we have proposed the DENN, a neural network architecture constructed to study the advantage that the dendrite tree structure of biological neurons might offer in learning.

we apply DENNs on supervised machine learning tasks.


Finally, it is important to stress that the -LDP guarantee established in Theorem 4 is not a panacea, and in particular it is a weaker guarantee provided in a much more challenging setting than just the -LDP guarantee across all users that we provide for a single round of data collection (an easier setting).

while LDP across all population of users is resilient to any attack based on auxiliary information, LDP across a sub population may be vulnerable to such attacks and additional levels of protection may need to be applied.


In addition, it covered much more ground during exploration than LTA, one of the few existing competitor models able to function in unbounded environments.

the EB-CRP-PIG model evenly explored a large number of environmental states.


[2015] proved that target propagation can be at most as good as back-prop, and in practice an additional back-propagation for fine-tuning is often needed.

the good-old back-propagation is still the most effective way to train a differentiable learning system such as neural networks.


We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices.

as one application, we provide a different route from the recent result of Duchi et al.


Other weight constraints would produce no clear differences in the following results.

we constrained the norm of the weight as .


Therefore, we can also require a minimal level of aspect coverage.

we may require more than just that terms are balanced evenly among all query terms: we may care about the absolute level of support that exists.


Theorem 2 Let x q q−1 ≤ a for q ∈ (1, 2] for any x ∈ X and f * ∈ F. Under Assumptions 1-2, for q ∈ (1, 2], by taking λ = σ 2 = O(n − q 4q+3 ), we have: with confidence at least 1 − δ.

for q = 1 and x ∞ ≤ a, choosing λ = σ 2 = ( ln p n ) 1 7 , we have: with confidence at least 1 − δ, Here C 1 , C 2 is a constant independent of n, δ. Theorem 2 shows that the excess risk of R(f * ) − R(f z ) → 0 with the polynomial decay and the estimation consistency is guaranteed as n → ∞.


Practical classification problems usually involve corrupted labels.

let {(x i , z i )} n i=1 be n independent data points, where x i ∈ R d is the covariate vector and z i ∈ {0, 1} is the uncorrupted label.


The methodology presented here is an attempt to sidestep the whole issue of mixing by permitting the independent particles to be stuck in modes, but then considering them jointly when estimating.

instead of using a time average, we estimate using a weighted ensemble average.


We use the COMPAS recidivism prediction dataset compiled by ProPublica [8], which comprises of information about all criminal offenders screened through the COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) tool in Broward County, Florida during 2013-2014.

for each offender, it contains a set of demographic features (gender, race, age), the offender's criminal history (e.g., the reason why the person was arrested, number of prior offenses), and the risk score assigned to the offender by COMPAS.


A principled way to tackle this problem is to use Bayesian inference.

we first compute the posterior distribution over the model parameters, p(θ|D N ) ∝ p(θ) N i=1 p(y i |x i , θ), where D N = {(x i , y i )} N i=1 , x i ∈ X D is the i'th input (where D is the number of features), and y i ∈ Y is the i'th output.


Thus, we cannot assume that the data comes from a fixed distribution over the IP address space; the algorithm needs to adapt to dynamic nature of the malicious activity, and track these changes accurately and quickly.

we must consider not only an online sequence of examples but also a changing target function.


To guarantee uniqueness, we require Σ T T to be invertible.

let C min = λ min (Σ T T ), we require C min > 0.


The noise variance has some low intrinsic level , which under ¦ ¡ -but not ¦ ¨is increased by some fraction © of the vibrational energy ¤ .

¥ ¦ £ ¦ ¡ ¨¤ E¦ ¢ ¦ T£ ! )


For simplicity, we define only two such matrices, for potentiation, M + , and depression, M − , respectively, and then map different activity patterns to these events.

we assume Fusi's cascade model [14] 4 and three possible mappings (Fig.


In our sampling scheme, we sample a fixed number of example queries for each possible query DAG structure.

given a DAG structure with E edges-specified by a vector d = [d 1 , d 2 , ..., d E ] of node out degrees, which are sorted in topological order [42] -we sample edges using the following procedure: First we sample the query target node (i.e., the root of the DAG); next, we sample d 1 out-edges from this node and we add each of these sampled nodes to a queue; we then iteratively pop nodes from the queue, sampling d i+1 neighbors from the ith node popped from the queue, and so on.


We follow the same procedure as RootSIFT-HQE [43] method, by replacing RootSIFT with our learned HardNet++ descriptor.

we use: (i) weighting of the votes as a decreasing function of the Hamming distance [44]; (ii) burstiness suppression [44]; (iii) multiple assignments of features to visual words [34,45]; and (iv) QE with feature aggregation [43].


After weighting, resampling and reproducing, the hypothesis particles are propagated forward according to the prior statistical distribution on how the scene variable tends to progress.

p(x t |x t−1 ) yields a proposed hypothesis about the stimulus at time t + 1 based on the existing hypothesis which is defined at t and earlier times.


We consider the simplified case of a state space comprised of all the parameters relevant to the task.

the state space includes the identity of the previous action, an indicator as to whether a reward is available in the food magazine, and, as necessary, the number of LPs since the previous reinforcement (for FR) or the elapsed time since the previous LP (for RI).


the following is true: each permutation has at least one edge that is different from all the others.


We were able to reject the null hypothesis for the measures complexity, femininity and masculinity, but failed to do so for attractiveness, ethnicity and prototypicality.

we observed a significant negative correlation (r = -0.3067) between stimulus complexity and reconstruction accuracy.


It is also an interesting venue of research to see whether a similar analysis can be done with those activations.

for Leaky ReLU we briefly explain how the proof would divert from ours in Section Sup.2.


However, it turns out that the partition resolution increases slowly (compared to our method which will be introduced in the next section) with the number of mixtures.

much larger number of Gaussians will be needed and this will result in a Fisher vector whose dimensionality is too high to be handled in practice.


The value of α is tuned such that the upper bound is minimized.


A bandit strategy would play an arm I t ∈ K at each time step t and observe a sample from θ It .

its goal is to maximise the sum of expected rewards after n time steps the objective is to be competitive, in expectation, against an oracle that plays an optimal arm all the time.


Or, stated differently, they do not guarantee any specific properties of the relation P except being reciprocal.

p does not necessarily obey any type of transitivity property.


3, from P 1 to P 5 , similarities are measured from low-level feature such as color, texture to high-level feature such as object.

p t is able to identify fine-grained similarities among pixels belonging to coarsely labeled objects, such as figures for nodes 1, 6 where table mat and painting are highlighted when they are labeled as table and background respectively.


We derive an upper bound on the Rademacher complexity R n (F nn , µ).

as we explain next, our upper bound is tighter than directly applying the existing bounds in [8,22].


This algorithm models the semibandit feedback as linearly related to the query-document features and learns this relationship, while selecting composite actions using an upper-confidence bound strategy.

the algorithm maintains a weight vector ✓ t 2 R d formed by solving a ridge regression problem with the semibandit feedback y t (a t,`) as regression targets.


In the abstract game, this combined strategy might become part of an equilibrium and hence the abstract strategy would make occasional mistakes.

abstraction does not necessarily preserve strategy domination.


We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints.

we develop two general approaches for an important subproblem -identifying phrase structure.


R, where F is a (discrete or continuous) set of predictors f : X !

y, and we write the empirical risk on the sample (X, Y ) and the generalization error on distribution D as The PAC-Bayesian theory [24,25] studies an averaging of the above losses according to a posterior distribution ⇢ over F. it provides probably approximately correct generalization bounds on the (unknown) quantity f ) and some other parameters.


Recent work has made progress on analyzing the mixing time of Gibbs sampling, but there are still major limitations to our understanding.

most results are only for specific models or for random scan.


Let f (x) = f, x for any f ∈ F and x ∈ X .

consider the sequence of constraints {C t } T t=1 given by consider the case of a Euclidean-norm restriction on the moves.


The rank of T is the minimum m such that the above equality holds.

the CP decomposition represents T as a sum of rank-1 tensors.


We thereby answered a crucial question in the study of (automated) mechanism design: how to relate the performance of the mechanisms in the search space over the input samples to their expectation over the underlying-unknown-distribution.

for a fixed class of auctions, we determine the sample complexity necessary to ensure that with high probability, for any auction in that class, the average revenue over the sample is close to the expected revenue with respect to the underlying, unknown distribution over bidders' valuations.


The notion of a closed map proves useful when analyzing the step ĥk ∈ H(f k ) in the SD algorithm.


The trick (similar to [9]) is to aggregate the lifted cost-shifting terms and multiply the result with the ground unary terms.


Let V h : H → H be the operator corresponding to h via such isometry.

we show that the SELF definition is satisfied with V = V h and ψ(y) = k(y, •) ∈ H for any y ∈ M. we have V ≤ V HS = h H⊗H , with V HS denoting the Hilbert-Schmidt norm of V . Step If Y is compact and geodesically convex, then it is diffeomorphic to a compact set of R d . By using this fact, we prove that any function in C ∞ (Y ×Y), the space of smooth functions on Y ×Y, admits an extension in C ∞ 0 (M×M) the space of smooth functions on M × M vanishing at infinity (this is well defined since M is diffeomorphic to R d , see ??


Our theory predicts important systems-level aspects of memory from synaptic-level constraints.

by optimizing our dual system solely for memory recall we also predicted non-trivial ROC curves for recognition that are in at least broad qualitative agreement with experiments.


For all three cases, the policy gradient method fails to discover a placement that is better than Post or Single GPU within a pre-specified amount of learning time.

post outperforms the policy gradient method by a training time reduction of 39.5%, 34.6% and 51.7% for 2 GPUs, 4 GPUs and 8 GPUs, respectively.


Examples from the topical field of systems biology are the reconstruction of transcriptional regulatory networks from gene expression data [1], the inference of signal transduction pathways from protein concentrations [2], and the identification of neural information flow operating in the brains of songbirds [3].

dynamic Bayesian networks (DBNs) have been applied, as they allow feedback loops and recurrent regulatory structures to be modelled while avoiding the ambiguity about edge directions common to static Bayesian networks.


While using different step sizes at different levels is a natural idea, it introduces some complications.

if a branching program is constructed naively based on this approach, it is possible for the number of nodes to increase exponentially with the depth.


If the random variable Z i+1 has value z, then we may express F i+1 as a function of z.

we have The discrepancy r(z) between the value of F i+1 (z) and the value of f (z, ✓) can then be used as a measure of the error in the linear method, and penalised.


As a result of the communication procedure, the master receives a convex combination of the stochastic gradients evaluated at each worker i.

the master receives gradients of the form g λ (t) = n i=1 λ i g i (t − τ (i)) for some λ in the simplex, where τ (i) is the delay of worker i, which puts us in the setting of Theorem 2.


It is also possible to efficiently draw a joint sample if the distribution over k takes the form p(k) = 1 { r k r = D} • r p(k r ).

there is an arbitrary but independent prior over each k r value, along with a single constraint that the chosen k r values sum to exactly D. Given a sample of k, it is straightforward to sample y using R calls to dynamic programming.


We will prove that asymptotically, SRB exhibits a "grouping effect".

for kernel K = µI − G, G defined in (4), we will look at the minimizer β * = Qα * of the loss function (2), and in the spirit of [18], establish a bound on the difference |β * i1 −β * i2 | of the coefficients on two similar components.


This type of reasoning also applies to the activities of complex cells with receptive fields in the spatiotemporal domain.

there is comparatively less ambiguity in the activities of complex cells with larger receptive fields than in the activities of cells with smaller receptive fields.


proposition 1 The two-target algorithm with targets 1 = 3 n 2 and 2 = m n 2 satisfies: Proof.


Although it may appear somewhat abstract at first sight, we illustrate that this result has a number of concrete consequences for specific models.

we recover the best known results about estimation in s-sparse models with general designs [1,7], as well as a number of new results, including convergence rates for estimation under q -sparsity constraints, estimation in sparse generalized linear models, estimation of block-structured sparse matrices and estimation of low-rank matrices.


Clusters are then derived from the analysis of the ESSs of the clustering game.

given a k-graph H = (V, E, s) modeling a hypergraph clustering problem, where V = {1, . . . , n} is the set of objects to cluster and s is the similarity function over the set of objects in E, we can build a game involving k players, each of them having the same set of (pure) strategies, namely the set of objects to cluster V . Under this setting, a population x ∈ ∆ of agents playing a clustering game represents in fact a cluster, where x i is the probability for object i to be part of it.


A regular log-normal distribution lnN (µ, σ 2 ) has a positive skewness, which means a sampled value from such distribution has more than 0.5 probability to be less than its expected value, resulting in a higher likelihood of underestimation.

if X ∼ lnN (µ, σ 2 ), then E[X] = exp(µ + σ 2 /2) and median[X] = exp(µ), thus the Pearson 2 coefficient of X is greater than 0.


In this work, we introduce a new form of exchangeability, distinct from both vertex exchangeability and Kallenberg exchangeability.

we say that a graph sequence is edge exchangeable if the distribution of any graph in the sequence is invariant to the order in which edges arrive-rather than the order of the vertices.


Note that the player doesn't observe the functions f t , only the losses that result from his past actions.

in the bandit feedback model, the player observes f t (X 1:t ) on round t, whereas in the full-information model, the player observes f t (X 1:t−1 , x) for all x ∈ A.


We have seen that SVI is designed to find the posterior for a particular, prechosen number of data points D. In practice, when we run SVI on the full data set but change the input value of D in the algorithm, we can see degradations in performance.

we try values of D equal to {0.01, 0.1, 1, 10, 100} times the true D in Fig.


This scaling is more favorable than might be expected from the initial condition because the order of the error "heals" from 1/2 to 1 in the long time limit.

the error from the initial, non-optimal parameter selection decays during the optimization dynamics, becoming much more favorable at late times.


Our algorithm seeks to minimize this loss function over the finite-dimensional vector space H and returns a function To define an equivalent optimization over the matrix version of H, we introduce the following notation.

for each string x ∈ PS, fix a pair of coordinate vectors (u x , v x ) ∈ R P × R S such that u x Hv x = H(x) for any H ∈ H. u x and v x are coordinate vectors corresponding respectively to a prefix u ∈ P and a suffix v ∈ S, and such that uv = x.


Full experimental details are reported in [32].

we compared I II (S; timing; C) with the intersection information carried by rate I II (S; rate; C), i.e.


Let subscript t − 1 denote corresponding values under the posterior measure P t−1 (•) = P(•| Ht−1 ).

e t−1 [•] and I t−1 (•; •) are random variables that are functions of Ht−1 .


Inspired by the notion, several studies have focused on designing algorithms that exploit this similarity to learn a cross-lingual alignment between the embedding spaces of two languages, where the two embedding spaces are trained from independent text corpora [6,7,8,9,10,11,12].

recent research has shown that such cross-lingual alignments can be learned without relying on any form of bilingual supervision [13,14,15], and has been applied to training neural machine translation (NMT) systems in a completely unsupervised fashion [16,17].


Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly.

results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.


In Cartesian coordinates, this yields the density An immediate consequence of any L p -spherically symmetric distribution being specified by its radial density is the possibility to change between any two of those distributions by transforming the radial component with (F −1 2 • F 1 )(||y|| p ), where F 1 and F 2 are cumulative distribution functions (cdf) of the source and the target density, respectively.

for a fixed p, any L p -spherically symmetric distribution can be transformed into a factorial one by the transform This transform closely resembles contrast gain control models for primary visual cortex [13; 20], which use a different gain function having the form g(y) = 1 c+r with r = ||y|| 2 2 [17].


Here, we use this local description to construct a global field of Gaussian scale mixtures (FoGSM).

we model subbands of wavelet coefficients as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF.


It has received a significant amount of contributions and has been applied in many problem areas such as database record segmentation [2], energy minimization for computer vision [10], critical load factor determination in two-processor systems [16], end-of-session baseball elimination [6], and most recently by [19,18,20] in product portfolio selection.

it is a key technique for many estimation and assignment problems.


Given the interesting capabilities of variational GP-SSMs, we believe that future work is warranted.

we want to focus on structured variational distributions q(x) that could eliminate the need to solve the smoothing problem in the auxiliary dynamical system at the cost of having more variational parameters to optimize.


Given the same k, the model with a larger s performs better.

model ( 3) is better than model (2) even though they only differ in the direction of the skip connections.


Accelerated methods: Accelerated SG methods, which despite their name are not related to the aforementioned AFG method, take advantage of the fast convergence rate of SG methods with a constant step size.

accelerated SG methods use a constant step size by default, and only decrease the step size on iterations where the inner-product between successive gradient estimates is negative [23,24].


It can be applied to (almost) any optimization problem and many existing algorithms can be interpreted in terms of CCCP.

we prove relationships to some applications of Legendre transform techniques.


Compared to BHq, DeepPINK obtains equivalent or better power in 10 out of 13 cases with with much better controlled false discovery proportion.

deepPINK shows remarkable performance for APV where it recovers 18 mutations without any mutation falling outside the TSM list.


Advertisers can be particular about whom they spend money on, and are willing to pay a premium when the right impression comes along, a process known as targeting.

advertisers can use context to specify which auctions they would like to participate in, as well as how much they would like to bid.


Still, in spite of its success, the additive model of adaptation in adaptive Spike Response Model effectively changes neural gain with at most a fixed step-size, and thus cannot respond quickly to changes in signal variance that are large compared to this step-size.

brette [22] argues that adaptation modulation has to be multiplicative for neurons to respond with the same level of neural activity to drastic changes in dynamic range, as is observed experimentally (e.g.


The problem of estimating SPAMs has received considerable attention in the regression setting (cf., [9,10,11] and references within) where (x i , f (x i )) n i=1 are typically i.i.d samples from some unknown probability measure P. This setting, however, does not consider the possibility of sampling f at specifically chosen points, tailored to the additive structure of f . In this paper, we propose a strategy for querying f , together with an efficient recovery algorithm, with much stronger guarantees than known in the regression setting.

we provide the first results guaranteeing uniformly accurate recovery of each individual component φ l of the SPAM.


Zhang [2005] explicitly goes via the exponential moment method to derive sharper concentration results.

for the regression problem with squared loss, Zhang [2005] gives a result similar to ours (see Theorem 8 therein).


However, our cost guarantees will, and must, refer to analysts (or perhaps groups of analysts) behaving in specific ways.

we define a non-adaptive user as a subsequence {u j } j2[M ] consisting of queries which do not depend on any of the history, i.e.


Since we mainly focus on sparse estimation, we fix α > 0 as a small constant in numerical studies.

as each W r is of unit rank, it can be decomposed as W r = σ r w (1) the sparsity of a unit-rank tensor directly leads to the sparsity of its components.


In subsection 4.2, we show that for drifting distributions, our upper bounds in Theorem 3.1 and Theorem 3.2 are almost tight.

we show that now even for full-information algorithms, a large 3  T dependency in the regret turns out to be unavoidable, even for small V and Λ.


In this paper, we use a local GSM as a basis for a globally consistent and spatially homogeneous field of Gaussian scale mixtures (FoGSM).

the FoGSM is formulated as the product of two mutually independent MRFs: a positive multiplier field obtained by exponentiating a homogeneous Gaussian MRF (hGMRF), and a second hGMRF.


We apply SGAN for style transfer [7,30].

as y is modeled as digit/object category on all three dataset, we suppose z shall encode any other information that are orthogonal to y (probably style information).


Humans still obtain a vivid percept of a cylinder even when each dot has a short "dot life".

each dot appears at a random starting frame, continues to appear for a small number of frames, and then disappears [12].


It is well-known that noregret condition in two-person k-sum games implies convergence to equilibrium (see, e.g., [13]).

the pair of mixed strategies which are the empirical distributions of play over time approaches the set of Nash equilibrium of the stage game.


These limitations of VAEs are becoming increasingly understood.

the traditional VAE seeks to maximize a lower bound on the log-likelihood of the generative model, and therefore VAEs inherit the limitations of maximum-likelihood (ML) learning [22].


Moreover, there are theoretical reasons to prefer a model in which subregions are always laterallysymmetrical.

in instances where the subregions are symmetric (the topic in panel B3 for the unconstrained subregions model and all topics for the constrained subregions model), the subregion weights provide a measure of the relative lateralization of function.


First, while it is effective as a black-box explanation system, MAPLE itself is a highly accurate predictive model that provides faithful self explanations, and thus sidesteps the typical accuracy-interpretability trade-off.

we demonstrate, on several UCI datasets, that MAPLE is at least as accurate as random forests and that it produces more faithful local explanations than LIME, a popular interpretability system.


Now consider four different definitions of the DN transform expressed in terms of the individual element of the output vector as Here x \i denotes the vector formed from x without its ith component.


Note that if U is a orthobasis for a subspace, U ⌦ is a |⌦| ⇥ d matrix with columns u i⌦ where u i 2 U , rather than a set of orthonormal basis vectors.

the matrix U ⌦ need not have orthonormal columns.


In this paper, we propose a new interpretation of Random Features that justifies its usage with ℓ 1 -regularization -yielding the Sparse Random Features algorithm.

we show that the Sparse Random Feature algorithm can be seen as Randomized Coordinate Descent (RCD) in the Hilbert Space induced from the kernel, and by taking D steps of coordinate descent, one can achieve a solution comparable to exact kernel methods within O(1/D) precision in terms of the objective function.


Given a matrix A 2 R n⇥d , and p 2 [1, 2), output a rank-k matrix M such that with probability at least 1 Our first contribution is Algorithm 1, ROBUST-LRA, which given an input matrix A 2 R n⇥d returns a differentially private rank-k approximation to A with a multiplicative approximation factor of ↵ = O((k log k) 2(2 p)/p log d log n) and an additive approximation error of ⌧ = e O " 1 k 2 (n + kd) .

for p = 1, we have ↵ = O(k 2 log 2 k log d log n) and ⌧ = e O " 1 k 2 (n + kd) .


we are able to obtain a fair linear model without any other constraint and by using a representation that has one feature fewer than the original one 3 .


Furthermore, this initialization prevents interferences that may result from the "pseudo-labels" given to unlabeled examples at the first E-step.


In this paper, we impose additional structure on the fibers.

we assume the fiber consists of a number of geometrical quantities, such as scalars, vectors, and tensors, stacked into a single K n -dimensional vector.


Such a strategy however is grossly inefficient if we are only interested in the posterior for x = x o . Conversely, if p(θ) closely matches p(θ | x = x o ), then most simulations will produce samples that are highly informative in learning q φ (θ | x) for x = x o .

if we already knew the true posterior, we could use it to construct an efficient proposal prior for learning it.


For example, it can be used to analyze the performance of approximate minimizers obtained through approximate optimization techniques.

consider f (w; θ) as in (2), where (z; θ) is convex and L-Lipschitz in z, the norm of φ(θ) is bounded by B, and r is λ-strongly convex.


We assume nothing about the classifiers except that each produces an output in {0, 1}.

we do not assume the classifiers are independent or related in any way.


Algorithm 1 Approximate saddle-free Newton Require: | Ĥ|← ∂ 2 s ∂α 2 by using an eigen decomposition of Ĥ for j =1→m do g ←− ∂s ∂α λ←argmin λ s((| Ĥ|+λI) −1 g) θ ←θ+V(| Ĥ|+λI) −1 g end for end for We now search for a solution to the saddle-point problem within the family of generalized trust region methods.

the analysis of optimization algorithms near saddle points discussed in Sec.


The practical meaning of the state-value function V is that it quantifies how desirable and promising it is to reach a state i, also accounting for future rewards to be expected.

if one knows the current state i it is a simple and efficient rule of behavior to choose that action a that will lead to the neighbor state j with maximal V (j) (the greedy policy).


Figure 7b also demonstrates that the fitted model accounts for the change in STA observed at different contrast levels.

we simulate responses of the model (equation (3) with Poisson spike generation) on each of the two contrast stimulus sets, and then compute the STA based on these simulated spike trains.


We show that the combination of the proposed algorithm and system effectively reduces both the communication cost and programming effort.

300 lines of codes suffice to implement 1 -regularized logistic regression with nearly no communication overhead for industrial-scale problems.


In this paper, we present an extension to Pinsker's theorem where estimation is carried out under storage or communication constraints.

we place limits on the number of bits used to encode an estimator, and analyze the excess risk in terms of this constraint, the signal size, and the noise level.


We evaluate the performance of Prox-QN method on two problems, sequence labeling and hierarchical classification.

we plot the relative objective difference (f (w t )−f (w * ))/f (w * ) and the number of non-zero parameters (on a log scale) against time in seconds.


In this work, we support checking diverse safety properties of networks including five different classes of properties based on the input constraints.

we specify the safety properties of neural network based on defining constraints on its input-output.


This implies that the neuronal gain functions -the firing rate of the post-synaptic neurons as a function of the average • http) / culture.neurobio.ucla.edu/ "'pel firing rate of the pre-synaptic neurons -must be sigmoidal: small at low firing rate to provide stability, high at intermediate firing rate to provide a threshold (at an unstable equilibrium), and low again at high firing rate to provide saturation and a stable attractor.

a requirement for the co-existence of a stable background state and multiple attractors is that the gain function of the excitatory neurons be super linear at the observed background rates of a few Hz [2,3].


2: return n 2 k 2 min v∈R n p k,A| S ,d| S ,b| S (v).

we sample a constant number of indices from the set {1, 2, . . . , n}, and then solve the problem (1) restricted to these indices.


In this section we extend the notion of optimal scoring to unsupervised learning problems, leading to a new framework for dimensionality reduction and clustering analysis simultaneously.

we relax EΘ in (1) as a sample scoring matrix Y and define the following penalized model: under the constraints The following theorem provides a solution for this problem.


A crucial observation is that, for any sampling model that is invariant under a relabelling of the nodes, this probability only depends on the pattern H(w).


We find that for network SIMPLE the negative log-likelihood loss, while performing best for the simple example of the arm, performs poorly on faces.

this model fails to disambiguate the left and right eye, as shown in Figure 9 (right).


Rather than simply choosing the matrix W based on random hyperplanes, we will specifically construct this matrix to achieve good reconstructions.

we will look at the squared error between the original distances (using d) and the reconstructed distances (using d).


We propose and motivate the study of patient risk processes to model the evolution of risk over the course of a hospital admission.

we consider the problem of using time-series data to estimate the risk of an inpatient becoming colonized with Clostridium difficile (C. diff ) during a hospital stay.


This is a problem of practical importance, and we expect that a large margin model should have better generalization abilities.

we randomly remove some fraction of the training set, going down from 100% of training samples to only 0.125%, which is 68 samples.


A better feature rebuilding provides the agent a preferable representation in the shared layers.

the agent can possess a global view of the symptom information.


1 illustrates the spectral properties of the Bethe Hessian that justify this algorithm: the spectrum is composed of a few informative negative eigenvalues, well separated from the bulk (which remains positive).

as observed in [8,5], it avoids the spurious eigenvalues with localized eigenvectors that make trimming necessary in the case of [3].


The proof is based on the observation that if the algorithm has not queried some clusters long enough, it is unaware of the nodes that have been reassigned between them.

if a node v moves from C i to C j at time t and the algorithm does not query one of the two clusters after time t it has small chances of guessing the cluster of v. Some nontrivial analysis is needed to show that a sufficiently large number of such nodes exist, regardless of the choices of the algorithm.


Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems.

the availability of large-scale data from social networks and sensor networks offers an unprecedented opportunity to predict state-changing events at the individual level.


This formalism allows us to combine information from a number of cells to improve the resulting characterization.

we combine equivalence constraints gathered from pairs of cells which have similar responses, and train a single distance function for both cells.


We utilize the encoder-decoder architecture recently introduced in [1], which is illustrated in Figure 2.

we represent a triplet (q, H, I) with e t by applying three different encoders, based on recurrent (RNN with long-short term memory units), hierarchical recurrent (HRNN) 2 and convolutional (CNN) neural networks, followed by attention and fusion units (Figure 2 (a)-(f)).


In this way, we can study the stimulus dependence of binary neural population activity in a regularized framework in a rigorous way.

we can use it to extract non-linear features in the stimulus that a population of neurons is sensitive to, while taking the binary nature of spike trains into account.


As a consequence, we come to the conclusion that the loss functions used in these methods can bound (1−NDCG) and (1−MAP) from above.

the minimization of these loss functions can effectively maximize NDCG and MAP.


In the context of a statistical treatment of persistent homology, the ability to embed probability measures on the space of persistence diagrams into a RKHS is appealing.

the problem of testing whether two different samples exhibit significantly different homological features -as captured in the persistence diagram -boils down to a two-sample test with null hypothesis H 0 : µ P = µ Q vs. a general alternative H A : µ P µ Q , where P and Q are probability measures on the set of persistence diagrams.


While some of these models behave better than others in terms of computational tractability, one basic limitation affecting all of them is a sort of parametric assumption concerning the probability laws underlying the observed network properties.

currently available models of network structure assume that the shape of the probability distribution generating the network is known a priori.


As a result, we have Similarly, we maximize the variational lower bound over s: Consequently we have for each j, To estimate β, we develop an active-set method to iteratively maximize the model marginal likelihood over elements of β.

we use a strategy similar to Tipping and Faul (2003)'s approach: given the approximation factors N (t|X T w, diag(h) −1 ), the distribution over eigenvectors N (v j |s j w, (λ v η j ) −1 I), and the prior distribution N (w|0, diag(β) −1 ), we can compute and decompose the log marginal likelihood L(β) = log p(y|X, s, λ v ) into two parts: L(β j ) and L(β \j ) where j and \j index the elements of β in the active set and the rest elements, respectively.


We employ an idea of Burer and Monteiro [2] that has far reaching consequences.

the positive definite constraint in the SDP formulation above is trivially satisfied if we define L and R via Burer and Monteiro showed that as long as L and R have sufficiently many columns, then the global optimum of ( 4) is equal to that of we may assume that the number of columns is less than m + n. This formulation of the max-norm is nonconvex because it involves a constraint on the product LR , but Burer and Monteiro proved that each local minimum of the reformulated problem is also a global optimum [9].


The motivation to this problem lies at the heart of modern machine learning applications where the goal is to facilitate more accurate learning from less data by interactively asking for labeled data, e.g., active learning and crowdsourcing.

automated clustering algorithms that rely just on a similarity matrix often return inaccurate results.


The work here presented deals with this more general case, where there are different dimensionalities/complexities present in the point cloud data.

we have samples not of a manifold but of a stratification.


Third, we propose a maximum causal Tsallis entropy imitation learning (MCTEIL) algorithm with a sparse mixture density network (sparse MDN) by modeling mixture weights using a sparsemax distribution.

we show that the causal Tsallis entropy of an MDN encourages exploration and efficient mixture utilization while Shannon entropy is less effective.


The catch is that, in order to get guarantees in L 1 -distance using this approach, would require us to learn to very small L 2 distance (because of the Cauchy-Schwarz inequality).

if the unknown distribution P has support size N , we would have to learn to L 2 distance / √ N in (i), and then in (ii) test that we are within L 2 -distance / √ N of the learned hypothesis.


Within each Θ I , the prior is uniform across all binary partitions.

let {Ω i } I i=1 be a binary partition of Ω of size I, and F({Ω i } I i=1 ) is the collection of piecewise constant density functions on this partition (i.e.


Like the versions studied by Bertsekas and Tsitsiklis, we assume that policy evaluation is not performed exactly.

we assume that Sarsa updating is used to learn the weights of a linear approximation to the action-value function.


Then we are guaranteed that In particular, we have the bounds: :::; p(M-1 K) :::; Amax (K) (4) It should be noted that the conditions of this theorem are sufficient, but by no means necessary, to guarantee convergence of the ET algorithm.

we find that indefinite cutting matrices often lead to faster convergence.


They define how in future, as t > t i increases, the elements of c(t) will continue to deterministically decay (at different rates) from c i+1 toward targets ci+1 .

c(t) is given by ( 7), which continues to control h(t) and thus λ k (t) (via (4), except that i has now increased by 1).


The hyper-parameters are randomly selected from a pre-defined range.

an annealing schedule is applied to the range of the learning rate over generations.


Ignoring computational considerations, we cannot hope for a scheme such as the one above to achieve acceptable regret or Bayes risk.

denoting the Gittins policy by ⇡ G, , we have Lemma 3.1.


In this setting our results depend on a quite different complexity measures: the upper and lower Minkowski dimensions of the space, thus exhibiting a phase transition between the finite case (that corresponds to Minkowski dimension zero) and the infinite case.

we give an upper bound on the regret of O(T d+1 d+2 ) where d ≥ 1 is the upper Minkowski dimension.


(I) is needed to ensure that any strategy σ 1 that P 1 computes in S cannot be exploited by P 2 changing their strategy earlier in the game.

we add a constraint that v σ1,BR(σ * 1 ) 2 for all P 2 root infosets I.


For example, in logistic regression, the link function g is logit and g −1 is the sigmoid function; and in linear regression, the link functions is the identity function.

learning in GLMs means learning the actual linear combination w. the likelihood of y given x can be written as p(y|w, x) = h(y)exp yw x − A(w x) , where x ∈ X , y ∈ Y, A is the log-partition function, and h(y) the scaling constant.


We present stark information-theoretic lower bounds for both relative and absolute -erroneous oracles, for any constant and even sub-constant > 0.

we show that: • For minimizing a convex function (or maximizing a concave function) f : [0, 1] n → [0, 1] over [0, 1] n : we show that for any fixed δ > 0, no algorithm can achieve an additive approximation within 1/2 − δ of the optimum, using a subexponential number of calls to an absolute n −1/2+δ -erroneous oracle.


More recently, the question of whether condition (2) is also necessary for the existence of linear representer theorems has been investigated [15].

[15] shows that, if Ω is differentiable (and certain technical existence conditions hold), then (2) is a necessary and sufficient condition for certain classes of regularization functionals to admit a representer theorem.


The proof of Theorem 4.2 relies critically on the fact that each element is seen exactly once.

once the algorithm decides to discard an element from its memory, this element is gone forever, which is a standard assumption for streaming algorithms.


In this work, we propose a new learning method, Contrastive Learning (CL), for image captioning.

via two constraints formulated on top of a reference model, the proposed method can encourage distinctiveness, while maintaining the overall quality of the generated captions.


(a)−(c), our method and [18] present similar ROC performance.

both methods are quite good at ranking for classification.


In particular, it conditions on the embedding z and previous state x t 1 to generate the vector x t autoregressively.

the autoregression is over the components of the vector x t . Wavenet lessens the load of the encoder which no longer has to carry information that can be captured by modeling auto-correlations between components of the state vector .


We proposed uncertainty-aware attention (UA) mechanism that can enhance reliability of both interpretations and predictions of general deep neural networks.

uA generates attention weights following Gaussian distribution with learned mean and variance, that are decoupled and trained in input-adaptive manner.


In this subsection, we present how geodesics in the Poincaré ball model are usually described with Möbius operations, and push one step further the existing connection between gyrovector spaces and the Poincaré ball by finding new identities involving the exponential map, and parallel transport.

these findings provide us with a simpler formulation of Möbius scalar multiplication, yielding a natural definition of matrix-vector multiplication in the Poincaré ball.


For a joint CDF, the problems of inference and likelihood evaluation, or computing conditional CDFs and marginal PDFs, both correspond to mixed differentiation of the joint CDF [6].

the conditional CDF (x |x ) is related to the mixed derivative ∂ In the case of evaluating the likelihood corresponding to the model, we note that for CDF (x| ), the PDF is defined as In order to perform maximumlikelihood estimation, we require the gradient vector ∇ log (x| ) =  As described above, inference and learning in a CDN corresponds to computing derivatives of the CDF with respect to subsets of variables and/or model parameters.


We solve the above problem by a simple subgradient descent approach.

at iteration t, given the current solution α t and b t , we compute the gradients as where ∂ (z) stands for the subgradient of (z).


16 The modeling studies are also more ambiguous than they might seem, since their most convincing focus is on the tribulations of catastrophic interference.

17 slow learning is necessary in systems with rich distributed or population coding because changes in synaptic efficacies occasioned by incorporating new information can easily overwrite the neural substrate for the storage of old information (the hoary stability-plasticity dilemma 18 ).


They are useful theoretical tools as well.

because of the equivalence H ≡ S m and the data processing inequality, the algorithmic stability of a lazy learner provides a lower bound to the stability of any possible learning algorithm.


We consider the problem of reinforcement learning in high-dimensional spaces when the number of features is bigger than the number of samples.

we study the least-squares temporal difference (LSTD) learning algorithm when a space of low dimension is generated with a random projection from a highdimensional space.


This algorithm learns both domain invariant and task discriminative features under multiple domains.

we propose a novel MDAN model by using neural networks as rich function approximators to instantiate the generalization bound we derive (Fig.


We consider the problem of learning control policies via trajectory preference queries to an expert.

the agent presents an expert with short runs of a pair of policies originating from the same state and the expert indicates which trajectory is preferred.


In this paper we extend this model's predictions about reading time to other cases where the best interpretation turns out to be incompatible with incoming words.

we suggest that any evidence which causes the probability of the best interpretation to drop below its next competitor will also cause increases in reading time.


For greater modeling flexibility, we take a nonparametric approach in defining the mode space of our switching dynamical processes.

we develop extensions of the sticky HDP-HMM for both the SLDS and switching VAR models.


⇤ In this section, we propose three algorithms that can be applied to solve the KCMAB problem and present their analyses.

we consider the Upper Confidence Bound (UCB) Policy [2], and Choose arm a(t) = t. 3: end for 4: For all arm i, compute r i (t) = q 2 log t Ni(t) and u i (t) = μi (t) + r i (t) Choose arm a(t) = argmax i u i (t) (with compensation max j μj (t) μa(t) (t)) 7: end for Algorithm 1: The UCB algorithm for KCMAB.


Blocking refers to the issue discussed in the Introduction concerning the sequence of category labels: Should training exemplars be blocked or interleaved?

should the category label on one trial tend to be the same as or different than the label on the previous trial?


Points in the training sample that are not covered by the K-point minimal graphs are identified as tail events.

let X K,T denote one of the Denote the corresponding set of edges between X i and its k-NN by {e i(1) , .


Specifically, the reward is determined by values of: (1) the UCs governing the MUCT; (2) a set of unobserved variables (other than the UCs) where each affects an endogenous variable in the MUCT; and (3) the IB.

there is no UC interplaying across MUCT and its outside so that µ x = E[Y |x] where x is a value assigned to the IB X.


This situation poses difficulties for some existing separation and localization algorithms, which often assume large numbers of microphones [Dorfan et al., 2015], an array of closely spaced microphones [Mandel et al., 2009, Lewis, 2012, or known sound characteristics [Oldfield et al., 2015, Wang andChen, 2017].

we examine the situation of sound sources in a large, known, anechoic two-dimensional space, with pairs of two omni-directional microphones placed at arbitrary points and orientations.


Moreover, the performance of the network is highly dependent on the hyper-parameters used for training.

recent studies have shown that Neural Networks can easily be fooled by imperceptible perturbation to input data [15].


Algorithm  with equality if X ⊤ S X S ≻ 0 for all subsets S of size k. Lemma 4.2 extends a result from [2, Lemma 3.9] on column-subset selection via volume sampling to all ESPs.

it follows that removing one element (by volume sampling a set of size n − 1) will in expectation decrease f by a multiplicative factor which is clearly also attained by a greedy minimization.


We model the locations for all ROIs in the atlas space using a Gaussian model (mean: 𝑀 𝑋 𝑗 ,and standard deviation:  Under the above definition, if any ij X is within the range of 3 j X s from the distribution model center j X M , the anatomical constraint energy will always be one; if not, there will be an exponential increase of the energy which punishes the possible involvement of outliers.

this energy factor will ensure the optimized ROIs will not significantly deviate away from the original ROIs.


The model we consider, as well as the aforementioned class of strategies, builds off of the work of Chakraborty and Kearns [4].

we assume the MM is given an exogenously-specified price time series that is revealed online.


In our setting, input bits are deterministic, hence independent.

mathematically, a protocol P is protocol compatible if each column P (τ ) is a rank-one tensor, when reshaped into a k-th order tensor P (τ ) ∈ [0, 1] 2×2×...×2 , where there exist vectors u (1) .


It is evident that random initialisation does not allow the RNN to improve its performance in a reasonable amount of epochs.

for random initialisation with p = 50 (Rnd 50), we have reported the average and range of variation over the 6 different trails: different initial points do not change substantially the performance of RNN.


These trajectories corroborate what is currently known about skin disease in scleroderma.

we see individuals who have minimal activity (e.g.


We note that a product distribution is one where all marginals are independent, so this is equivalent to testing if a collection of random variables are all independent.

in the case where n `'s are large, then the first term dominates, and the sample complexity is O(( when d is a constant and all n `'s are equal to n, we achieve the optimal sample complexity of ⇥(n d/2 /" 2 ).


In [19], an order between the concentrability coefficients was introduced: a coefficient A is said to be strictly better than B -a relation we denote with A ≺ B -if and only if i) B < ∞ implies A < ∞ and ii) there exists an MDP for which A < ∞ and B = ∞.

it was argued that In this sense, 1) (µ, ν), while its definition might suggest improvement as κ increases.


In contrast, traditional B2B distance needs to compute the distances between bags belonging to different classes involving inter-class distance metrics, which inevitably complicates the problem.


The canonical aspect ratios can be determined by clustering aspect ratios of all ground-truth bounding boxes [22], or based on the viewpoints, provided we have labels for each viewpoint.

suppose that there is a candidate example x i to be borrowed by the target class c and there are L canonical aspect ratios of c. We transform x i into x l i by resizing one dimension so that {x l i } 0≤l≤L contains all L canonical aspect ratios of c (and x 0 i = x i ).


Yet another approach (if applicable) is to use a "comple-mentary mixtures of Z MLP-experts" model (or a neuro-fuzzy modular network) that combines Z smaller-size MLPs complementarily; the associated residual vector to be minimized becomes: r(") = y(") − t = Z i=1 wioi − t, where scalar w i , the ith output of the integrating unit, is the ith (normalized) mixing proportion assigned to the outputs (F -vector o i ) of expert-MLP i.

note that each expert learns "residuals" rather than "desired outputs" (unlike in the committee method below) in the sense that only the final combined outputs y must come close to the desired ones t. there are strong coupling effects (see page 80 in [5]) among all experts; hence, it is crucial to consider the global Hessian across all experts to optimize them simultaneously [7].


In principle, by using this joint training strategy, the learned paragraph embedding vector will preserve both reconstruction and classification ability.

we consider the following objective: where α > 0 is an annealing parameter balancing the relative importance of supervised and unsupervised loss; D l and D u denote the set of labeled and unlabeled data, respectively.


Our test problems confirm the convergence properties of ECOLS and also illustrate some of its properties.

the empirical results illustrate the regularization effect of the op(∞)-norm constraint that tends to "shrink" predicted values toward zero.


. . , z n ] ∈ R L×n , we wish to learn a multi-regression model to predict the embeddings Z using the input features.

we require that Z ≈ V X where V ∈ R L×d .


We note also that our analysis applies to more adversarial settings than stochastic optimization (e.g., to online convex optimization [5]).

an adversary may choose an arbitrary sequence of functions subject to the random data sparsity constraint (2), and our results provide an expected regret bound, which is strictly stronger than the stochastic convergence guarantees provided (and guarantees high-probability convergence in stochastic settings [3]).


We note that while the 2 statistic for testing hypothesis is prevalent in statistics providing optimal error exponents in the large-sample regime, to the best of our knowledge, in the small-sample regime, modified-versions of the 2 statistic have only been recently used for closeness-testing in [19,20,21] and for testing uniformity of monotone distributions in [22].

[19] design an unbiased statistic for estimating the 2 distance between two unknown distributions.


In addition, we found out experimentally that when the data contains object images with rich backgrounds, performance of subclass recognition and localization is improved when using models with increased relative location weight.

a part hypothesis in the model includes appearance, location and scale components with relative weights λ i /(λ 1 + λ 2 + λ 3 ), i = 1, 2, 3, learnt automatically by the algorithm.


Because given a set S i , we can only observe the jumping time of the events in each counting process without knowing the identity of the covered items (which is a key difference from [8]), the best thing we can do is to sample from these historical data.

let the number of counting processes that a single item s ∈ V is involved to induce be N s , and the collection of all the jumping timestamps before time T be J s . Then, for the s-th entry of τ , with probability |J s |/nN s , we uniformly draw a sample from J s ; and with probability 1 − |J s |/nN s , we assign a time much greater than T to indicate that the item will never be covered until infinity.


In what follows, we let W t denote the actual value taken on by the function in a process defined by (2).


guarantee like where R is increasing in each kg t k. For example, when the convex space W has diameter D, As foreshadowed in Section 3, we will need to consider the case of biased gradients.

e[g t ] = rF (w t ) + b t for some unknown bias vector b t . Given these biased gradients, a natural question is: to what extent does controlling the regret R T (w ? )


We would evidently prefer to have a more efficient online algorithm, which can guarantee equivalent or better error bounds.

we believe that the best way to achieve this is to have a search algorithm which uses estimates of error reduction as a criteria to guide the search over the reachable beliefs.


The linear predictor Z = ΛX learned from a position-normalized training dataset gives exactly the position-unbiased CTR estimation.

we are hypothesizing that all candidate ads are to be presented in a same imaginary position.


We now compare our algorithm against other dimensionality reduction techniques.

in this paragraph we present head-to-head comparisons for the following five methods: (i) SVD: the Singular Value Decomposition (or Principal Components Analysis) dimensionality reduction approach -we use MatLab's svds function; (ii) LLE: the famous Local Linear Embedding algorithm of [18] -we use the MatLab code from [23] with the parameter K determining the number of neighbors setting equal to 40; (iii) LS: the Laplacian score feature selection method of [10] -we use the MatLab code from [22] with the default parameters 2 ; (v) HD: we run the k-means algorithm on the High Dimensional data; and (vi) RP: the random projection method we proposed in this work -we use our own MatLab implementation.


R3) At the points {z} where a * i z = 0 for certain i ∈ M, the corresponding weight will be w i = 0.

the losses (z; ψ i ) in (2) that are nonsmooth at points z will be eliminated, to prevent their contribution to the reweighted gradient update in (10).


Although these update equations do require that we differentiate with respect to a function of another gradient term, such "double backprop" terms (see e.g., Drucker and Le Cun [1992]) are easily computed by modern automatic differentiation tools.

we propose the regularized update (4) The intuition of this regularizer is perhaps most easily understood by considering how it changes the Jacobian at equilibrium (though there are other means of motivating the update as well, discussed further in Appendix F.2).


However, by reparametrizing our O N 2 variational parameters according to the framework described in [12] we can obtain a set of O(N ) less correlated variational parameters.

we first take the derivatives of the variational bound ( 14) w.r.t.


It follows that with a formulation like (3), the only way to utilize unlabeled data is to replace K by a kernel K in (3), or k by k in (2), where K (or k) depends on the unlabeled data.

the only benefit of unlabeled data in this setting is to construct a good kernel based on unlabeled data.


Therefore, rather than just maximizing the margin, a trade-off regularizer should also be used to minimize the spread of the projected data.

we will couple large margin estimation with regularization which seeks to bound the spread |w ⊤ x + b| of the data.


Supposing D XY satisfies Tsybakov noise, we define a quantity based on a standard generalization bound for passive learning [12].

[12] have shown that, for any V ⊆ C, with probability at least 1 − δ/(4km 2 ), sup h,g∈V Consider the following modification of k-batch CAL, designed to be robust to Tsybakov noise.


The coupling between the systems will be linear as described by the connectivity matrix W. Using this factorization, approximate state estimation can then be efficiently performed via approximations of loopy belief propagation (BP) [14].

we show that the loopy BP updates at each of the factor nodes associated with the integrate-and-fire and calcium imaging can be performed via a scalar standard forward-backward filter.


We incorporate a target density ρ n (or simply ρ, when n is clear from the context) by normalizing W so that W = 1 and taking G to be a sample from G n (ρW ).

we set Q = H n (ρW ) = ρH n (W ) and then connect i to j with probability Q ij , independently for all i < j. Stochastic block models are specific examples of W -random graph in which W is constant on sets of the form I i × I j , where (I 1 , .


Since entries of the confusion matrix are positive, we find it helpful to incorporate this prior knowledge into the initialization stage of the Opt-D&S algorithm.

when estimating the confusion matrix entries by Eq.


In this regime, both N and T are fixed and given to the algorithm.

the algorithm cannot control the experimentation deadline N . We are mainly interested in the asymptotic behavior of the algorithm when both N and T go to infinity.


Let p(y) be a two-component mixture of a (univariate) Bernoulli distribution.

let φ(x) and ψ(z) be the identity maps, Λ provide the mean of the Bernoulli, and p(X = 0.4) = 1/2, p(X = 0.6) = 1/2.


Q-learning with locally consistent data: An alternative approach is to simply maintain a single regressor, but ensure that any batch of Q-labels is self-consistent before updating the regressor.

given a batch of training data and the current regressor, we first create a single set of consistent labels for each example (see below), then update the regressor using these labels.


To make this more concrete, we test the hypothesis that the majority of the eigenvalues are consistent with those of randomly selected stimulus vectors, but that the last 4 eigenvalues fall significantly below this range.

we perform a Monte Carlo simulation, drawing (with replacement) random subsets of 623 stimuli from the full set of raw stimuli.


Let us observe that if we have a minibatch and normalize a particular node x using either the minibatch statistics or their moving averages, then the results of these two normalizations are related by an affine transform.

let µ be an estimate of the mean of x, and σ be an estimate of its  standard deviation, computed perhaps as a moving average over the last several minibatches.


In order to achieve scalability, we will summarize the k-gram frequency vector distributions.

we will use Count-Sketch [Charikar et al., 2004]  and b < d controls the approximation quality.


Consider the pairwise binary graphical model for the independent set problem on G = (V, E) given by the edge potentials ψ ij (x i , x j ) = 1 − x i x j for all (i, j) ∈ E. We can easily check that the 6-cycle has 18 distinct independent sets while the disconnected cover has only 16 independent sets.

the disconnected 2-cover does not provide an upper bound on the number of independent sets in all 2-covers.


Recent studies have found that AD is closely related to the alternation in the functional brain network, i.e., the functional connectivity among different brain regions [ 2]- [3].

it has been shown that functional connectivity substantially decreases between the hippocampus and other regions of AD brains [3]- [4].


As a consequence, some of the machinery that has been developed for analyzing the generalization performance of kernel machines can be applied in our setting.


This paper showed that the SAG iterations achieve a much faster convergence rate, but the SAG iterations may also be advantageous in terms of tuning step sizes and designing termination criteria.

the SAG iterations suggest a natural termination criterion; since the average of the y k i variables converges to g (x k ) as x k −x k−1 converges to zero, we can use (1/n) i y k i as an approximation of the optimality of x k . Further, while SG methods require specifying a sequence of step sizes and mispecifying this sequence can have a disastrous effect on the convergence rate [7, §2.1], our theory shows that the SAG iterations iterations achieve a linear convergence rate for any sufficiently small constant step size and our experiments indicate that a simple line-search gives strong performance.


The main argument in favor of convex formulations is that we can effectively decouple modeling from optimization, what has substantial theoretical and practical benefits.

it is of great value in terms of reproducibility, modularity and ease of use.


Instead, we demonstrate in this paper an efficient solution based on linear algebra by exploiting the inherent structure of the problem and the HMM filter.

the contributions of this paper are three-fold: 1.


Define Q ::@, p-1 + C T R- 1 C, and M ::@, Q + K. Suppose the cutting matrix K is symmetric and positive semidefinite.

then we are guaranteed that we have the bounds: :::; p(M-1 K) :::; Amax (K) (4) It should be noted that the conditions of this theorem are sufficient, but by no means necessary, to guarantee convergence of the ET algorithm.


(FollowTheLeader) Perhaps the most natural algorithm one might think of is to simply select x t as the best point in hindsight.

the learner can choose (BeTheLeader) When the learner is prescient, then we can do slightly better than FollowTheLeader by incorporating the current loss function: x t = arg min x∈K t s=1 s (x).


This stands in stark contrast to, even the conventional single layer, neural network where the bottom-layer parameters are optimized with respect to the data distribution and the loss function.

we designed our experiments to distinguish four cases: • Random Basis (RB): we use the (approximated) kernel machine in its traditional formulation [30,8].


Tractable flows-based model Parameterizing the variational distributions with flows is proposed to mitigate the limitation of expressive ability of the variational distribution.

assuming a series of invertible transformations as {T t : R r → R r } T t=1 and z 0 ∼ q 0 (z|x), we have −1 by the change of variable formula.


First, before drawing the sample, we erase the contribution of c t to these sufficient statistics.

if an ancestor gets no occupancy in either the stock and the HMM urns afterwards, we remove it from our repository.


As described in [30], the mIBP defines a distribution over an unbounded set of binary Markov chains, where each chain can be associated to a binary latent feature that evolves over time according to Markov dynamics.

if we denote by M the total number of feature chains and by T the number of observable components (event mentions), the mIBP defines a probability distribution over a binary matrix F with T rows, which correspond to observations, and an unbounded number of columns (M → ∞), which correspond to features.


The variance of the overall estimator then becomes equal to the variance of the column vector ¢ .

if each row produces the same estimate, the estimator will have zero variance.


Let A be a learning algorithm which, based on the sample S, constructs a hypothesis (estimator) h from some set of hypotheses H. Denoting by (y, h(x)) the instantaneous loss of the hypothesis h, we wish to assess the true loss L(h) = E µ (y, h(x)) where the expectation is taken with respect to µ.

the objective is to provide data-dependent bounds of the following form.


There are 17, 770 and 624, 961 items in netflix and yahoo-music, respectively.

we obtain the user embeddings {w i } 2 R k   and item embeddings h j 2 R k by the standard low-rank matrix factorization [4] with k 2 {50, 200}.


For non-parametric regression with the square loss, one pass SGM has been studied in, e.g., [29,22,26,9].

[29] proved capacity independent rate of order O(m − 2ζ 2ζ+1 log m) with a fixed step-size η m − 2ζ 2ζ+1 , and [9] derived capacity dependent error bounds of order O(m − 2 min(ζ,1) 2 min(ζ,1)+γ ) (when 2ζ + γ > 1) for the average.


This procedure can be repeated for a fixed number of iterations, or until a convergence criteria is met.

in the experiments below our algorithm iterated between the step exactly 10 times.


However, as pointed out in [2], it makes little sense to solve an easier problem by 'reducing' it to a much more difficult one.

the prior knowledge carried by the (unlabeled) test points can be incorporated into an algorithm, potentially leading to superior performance.


Oracle Problem: We develop our candidate solution ( L, Ĉ) by considering the alternate optimization problem where we add constraints to (2) based on what we hope its optimum should be.

recall the SVD of the true L 0 = U 0 Σ 0 V ⊤ 0 and define for any matrix X the projection onto the space of all matrices with column space contained in U 0 as P U0 (X) := U 0 U ⊤ 0 X.


Learning time invariance by injecting random noise: we have found it helpful to add "dummy" memories to regularize T A .

at training time we can randomly add 10% of empty memories to the stories.


2b: Bounding p t ∞,u from a warm start Unfortunately, we cannot apply our results of step 2a directly since we are only assuming that X 0 has a warm start, not a stationary start.

we only assume that X 0 − Ỹ0 2 < ω for some ω > 0, where Ỹ0 ∼ π is at the stationary distribution.


Best of the three initialization methods, by starting at the hybrid algorithm results, the search algorithm in very few steps can find  the local optimum, which often happened to be the global optimum as well.

it only takes 1 or 2 steps of search in the 10-node chain case and 1 to 3 steps in the 50-node tree case.


2 for the remaining equations in this paper, the priors are assumed to be equal, and hence are dropped from subsequent equations.


We hope these techniques lead to the discovery of fast and efficient distributed algorithms for other clustering problems.

what can be shown for the k-median or k-means with outliers problems are exciting open questions.


The AP loss of an output R is defined as 1 − AP(R * , R), where AP(•, •) corresponds to the AP of the ranking R with respect to the true ranking R * .

the parameters are obtained by solving the following convex optimization problem: The computational complexity of solving the above problem depends on the complexity of the corresponding loss-augmented inference, that is, For a given set of parameters w, the above problem requires us to find the most violated ranking, that is, the ranking that maximizes the sum of the score and the AP loss.


Lemma 1 links the random variables W n and W n to the Hausdorff distance and the coverage for R and R n . Thus, we call them coverage random variables.

now we define the L 1 and L 2 coverage risk for estimating R by R n as Risk 1,n (and Risk 2,n ) is the expected (square) projected distance between R and R n . Note that the expectation in (4) applies to both R n and U R . One can view Risk 2,n as a generalized mean integrated square errors (MISE) for sets.


However, there is a unique, so-called adapted system of modules, for which this issue does not arise.

if, as is usually done, we let the indexing set T m be the set of Standard Young Tableaux (SYT) of size m (see Appendix A in the supplementary materials for the exact definition), such as then the adapted modules at different levels of the coset tree are connected via where is the tableau that we get by removing the boxes containing n − k + 1, . . . , n from t . We also extend these relationships to sets in the obvious way: We will give an explicit description of the adapted modules in Section 4.


Then, with probability 0.99, q T − u 2 ≤ ǫ, where q T is the T -th iterate of Algorithm 1.

algorithm 1 obtains an ǫ-accurate solution with number of samples (n) given by: ǫ 2 log((σ 2 + .75)/(σ 2 + .5)) .


We can also express the input constraint l j ≤ x j ≤ u j as a quadratic constraint, which will be useful later.

l j ≤ x j ≤ u j if and only if (x j −l j )(x j −u j ) ≤ 0, thereby yielding the quadratic constraint x 2 j ≤ (l j +u j )x j −l j u j .


We refer to the set of edges that share the ith parameter p i by E i = {e ∈ E|π(e) = i}.

for any e 1 , e 2 ∈ E i , π(e 1 ) = π(e 2 ) and hence w e1 = w e2 = p π(e1) .


In this experiment, we consider the problem of graph classification, where vertices are unlabeled and edges are undirected.

a graph G is given by G = (V, E), where V denotes the set of vertices and E denotes the set of edges.


It is important to note that the absolute values of the tags do not matter, only the distances between tags.

a network is free to assign arbitrary values to the tags as long as the values are the same for detections belonging to the same group.


When it comes to networks, triangular motifs (Figure 1) are already of significant interest in biology [13], social science [19,9,10,16], and data mining [21,18,8].

2-and 3-edge triangular motifs are central to the notion of transitivity in the social sciences -if we observe edges A-B and B-C, does A have an edge to C as well?


Recently, kernel methods have been adapted to this purpose.

kernel dimensional reduction (KDR) develops a kernel-based contrast function that measures the degree of conditional independence [7].


Note that the conditions of Theorem 2 are very mild.

the condition for plurality votes is satisfied under the Mallows model with all five distances we consider, and the condition for veto votes is satisfied under the Mallows model with the Kendall tau, the footrule, and the maximum displacement distances.


Comparing this to the foregoing results, here we do not require that d = O(log log n).

allowing larger values of d allows us to construct networks with constant multitasking capacities, albeit only with respect to matchings whose size is at most n/d 1+4α .


Though training DNNs with softmax or SVM as output activation is effective in many tasks, it is possible that alternative activations that consider manifold structure of data by interpolating the output based on both training and testing data can boost performance of the network.

resNets can be reformulated as solving control problems of a class of transport equations in the continuum limit [21,5].


The multiple gates allow the network to adapt the flow of information depending on the task at hand.

they enable writing to the memory cell (controlled by input gate, i t ), adjusting the timescale of the memory (controlled by forget gate, f t ) and exposing the memory to the network (controlled by output gate, o t ).


Our factored logistic regression model is best described as a variant of a multinomial logistic regression.

the weight matrix is replaced by the product of two weight matrices with a common latent dimension.


It performs far better than using an assumption of fixed widths, but it still imposes unrealistic constraints on the relative positions of characters.

the portion of the ink generated by the current character is assumed to be independent of the preceding character.


Second, lower order sub-structures tend to be more numerous while a vast majority of the sub-structures occurs rarely.

a few sub-structures dominate the distribution.


Assuming Gaussian sensing vectors however, such nonconvex paradigms can provably locate the global optimum, several of which also achieve optimal (statistical) guarantees.

starting with a judiciously designed initial guess, successive improvement is effected by means of a sequence of (truncated) (generalized) gradient-type iterations given by where z t denotes the estimate returned by the algorithm at the t-th iteration, µ t > 0 is learning rate that can be pre-selected or found via e.g., the backtracking line search strategy, and ∇ (z t , ψ i /y i ) represents the (generalized) gradient of the modulus-or squared modulus-based LS loss evaluated at z t . Here, T t+1 denotes some time-varying index set signifying the per-iteration gradient truncation.


Define S := B(x, r) ∩ M for a point x ∈ M . Then where r 1 = τ − τ 1 − 2r/τ .

if r ≤ ǫτ /72d for 0 ≤ ǫ < 1, then Lemma 8 (Separation) Assume that we pick k, r and R to satisfy the conditions: Then with probability 1 − δ, we have: (1) All points in A σ−r and A ′ σ−r are kept, and all points in S σ−r are removed.


In this construction, rather that drawing the ✓ ⇤ i ⇠ G 0 once as in (5), one may draw ✓ ⇤ i ⇠ G 0 for the first block of time, and then a simple Gaussian auto-regressive model is employed to allow the {✓ ⇤ i } drift a small amount between consecutive blocks.

if {✓ ⇤ ji } represents the atoms for block j, then ✓ ⇤ j+1,i ⇠ N (✓ ⇤ ji , 1 0 ), where it is imposed that 0 is large.


The estimation of discrete distributions given finite data -"histogram smoothing" -is a canonical problem in statistics and is of fundamental importance in applications to language modeling, informatics, and safari organization (1)(2)(3).

estimation of discrete distributions under Kullback-Leibler (KL) loss is of basic interest in the coding community, in the context of two-step universal codes (4,5).


First, we study the behavior of the proposed algorithm on synthetic data.

we constructed a data set comprised of 10000 samples in 9 Gaussian clusters of unit variance.


In this paper we assess the performance of the first player using the notion of regret.

given a number of rounds T and a fixed vector u ∈ S, we define the regret of the first player as the excess loss for not consistently playing the vector u, Our main result is an algorithmic framework for the first player which guarantees low regret with respect to any vector u ∈ S. we derive regret bounds that take the following form where f : S → R and L ∈ R + .


[14] for online submodular function maximization: we run n copies of some low regret online learning algorithm, E 1 , E 2 , .

. . E n , each with action space A = V . We use the ith copy E i to select the ith item in each predicted sequence S t . the predictions of E i will be v 1 i , v 2 i , .


This problem is often referred to as multiclass learning.

in other multiclass problem settings it is common to encode the set Y as a prefix of the integers {1, . . . , r}, however in our setting it will prove useful to assume that the labels are encoded as the set of r standard unit vectors in r . the i'th label in Y is encoded by the vector whose i'th component is set to 1, and all of its other components are set to 0.


• We obtain a characterization of the optimal sample complexity for estimating the entropy rate of a stationary reversible Markov chain in terms of the sample size, state space size, and mixing time, and partially resolve one of the open questions raised in [2].

we show that when the mixing is neither too fast nor too slow, the sample complexity (up to a constant) does not depend on mixing time.


Finally, a learning algorithm is a sample compression learning algorithm (that is identified solely by a compression set z i and a message string σ) iff there exists a Reconstruction Function R : (X × Y) |i| × K −→ H, associated with A.

here, H is the (data-dependent) classifier space and R outputs a classifier R(σ, z i ) when given an arbitrary compression set z i ⊆ S and message string σ chosen from the set M(z i ) of all distinct messages that can be supplied to R with the compression set z i .


Methods in (5) have many attractive properties.

we are able to derive class-size independent generalization bounds for this method.


Indeed, as observed in [1], the addition of the entropy h makes the problem significantly more amenable to computations.


That is, for each destination point C , the total of the incoming G -weight has to sum to e . In fact, it is quite easy to prove that this yields unbiased estimates [12]  Crucially, this argument does not depend on how the block decomposition is chosen or how the G -weights are set, so long as they satisfy (1).

one could fix any block decomposition and weighting scheme, even one that depends on the target distribution £ and random variable ¢ , without affecting the unbiasedness of the procedure.


We do not apply any other special preprocessing to the data.

we do not binarize the parse trees or handle unaries in any specific way.


Generality has implications on inference and learning.

inference, i.e., solving the program involves back-propagation through the non-linear output transformation T . Note that backpropagation through T encodes top-down information into the inferred configuration, while forward propagation through H provides a classical bottom-up signal.


Our analysis of the SALP in this section is predicated on the knowledge of an idealized constraint violation distribution, which is this same idealized sampling distribution.

we will require access to samples drawn according to the distribution π µ * ,ν given by Here ν is an arbitrary initial distribution over states.


The Pearce model instead spreads graded activation over x, based on a measure of similarity between the observed stimulus compound (or element) and the compounds represented by the model's configural units.

if we denote the number of stimulus elements present in an observed stimulus pattern a as size(a), and in the pattern represented by the ith configural unit as size(i), then the activation of unit i by pattern a is given by x i = size(overlap(a, i)) 2 /(size(a) • size(i)).


In terms of the coefficients θ α,β defined in (11), as k → ∞, we have Figure 4 (L,M) graphs the above two expressions.

the plots highlight the reduction in bias compared to ρ lin and the fact that the variance is decreasing in ρ as for b = ∞.


Therefore, we can compute the conditional expectation of p(jlx), denoted by Pr(jlxi = z), given that Xi assumes value z, where Xi represents the ith component of x.

pr(jlxi = z) = E[Pr(jlx)lxi = z] = J Pr(jlx)p(xlxi = z)dx.


First, like the input provided to V1 by LGN, the input to our computation is isotropic.

the input is composed of spots not edges.


This proposition implies that we can express our problem of minimizing (3) as minimization of D(P Q ) where P and Q are distributions of the random variable (J, X).

we define: where q j and r ij = P (j|x = x i ) are probability distributions over the set {j} n j=1 .


Extensive experiments on MNIST, CIFAR-10 and ImageNet have shown the effectiveness of our method.

when combined with the FGS-based adversarial learning, our method achieves even better results on various benchmarks.


The algorithm is simple, involves very minimal communication, scales efficiently in both sample and feature size, and has theoretical guarantees.

we show model selection consistency and coefficient estimation efficiency.


We prove that for each i ∈ [d], X h i (t) converges weakly to a deterministic function X i (t) as η → 0.

we rewrite (3.8) as, (3.9) Taking the limit of η → 0 at a fix time t, we have Since ∇f ( X h (t)) 2 is bounded at the time t, we have 1 η Var X h (t + h) − X h (t) X h (t) = O(h).


Note that β > 1 restricts the set of ∆ which satisfy the inequality, yielding the restricted error set.

∆ cannot go in the direction of θ * , i.e., ∆ = αθ * for any α > 0.


Given lack of space, we cannot detail the kernelization of all these methods, but they follow in the same manner as in the above two examples.

each of these methods may be run in kernel space, and our analysis yields new insights into these methods; for example, kernelization of LMNN [11] using Theorem 1 avoids the convex perturbation analysis in [16] that leads to suboptimal solutions in some cases.


We define a neural network with L layers and n i nodes in the ith layer as a composition of functions of the form Here A i : R ni−1 → R ni is an affine function.

a i is the sum of a linear function and a constant vector.


This paper focuses on the former, i.e., the question of integrity.

how can a client perform inference using a deep neural network on an untrusted cloud, while obtaining strong assurance that the cloud has performed inference correctly?


Bounded accumulation models postulate that decisions are made based on a decision variable.

this decision variable is driven towards the correct alternative and is perturbed by noise.


We define the subspace H m and dictionary I as γ-preserving w.r.t.

space H n if Notice that the inverse since φ i ∈ Φ n , we have that in the worst case the error is bounded as we know that in the best case the error can be reduced up to Note that the directions associated with the larger eigenvalues are the ones that occur most frequently in the data.


Inspired by recent results in imitation learning [37] and inference machines for classification [17,38], we take an alternate route and use an RNN to model the exchange of information between nonparametric nodes.

we introduce an RNN node b µ i!j for each message and connect them in time according to Eq.


If we believe that P "closely approximates" P f , and know the probability p xi i ≡ P(M xi a→i = 1 for all a ∈ C(i)) that x i is in the consistent domain for variable i of f , for every variable i, clause a and possible assignment x i , we can use them to dynamically order both the variables and the values they can take during search.

we first compute p 1 i = P(M u a→i = 1 for all a ∈ C − (i)) and p 0 i = P(M u a→i = 1 for all a ∈ C + (i)) for each variable i, where C + (i) and C − (i) are the sets of clauses where variable i appears as a positive and a negative literal, respectively.


Let (f, ε) be a solution to optimization problem (5), then with probability at least 1 − 2ζ, Theorem 3 suggests that if we want to control the non-coverage rate on average at the nominal α −1 or α 1 rates with high probability, we should choose the α −1 or α 1 values to be slightly smaller than the desired ones in optimization (3) in practice.

we need to make The next theorem ensures that the empirical ambiguity probability from solving (5) based on a finite sample will converge to the ambiguity given by the solution on an infinite sample (under the constraints E(H −ε (Y f (X))|Y = j) ≤ α j , j = ±1).


While RIAL can share parameters among agents, it still does not take full advantage of centralised learning.

the agents do not give each other feedback about their communication actions.


The causal support model can be most easily described in the context of causal graphical models [12] (see Figure 1(b)).

we consider two graphical models, Graph 0 (G 0 ) and Graph 1 (G 1 ), and we want to determine the log posterior odds of the models given some data D (i.e.


As for r 2 , the proof is straightforward by similarly casting its definition into the sum of conditional expectations.

theorem 3.1 indicates clear relationships between the sparsity and robustness of linear models.


Once this is done, we can evaluate for each test point x whether it satisfies δ ≤ w, Φ(x) − ρ ≤ δ * .

we have an implicit description of the region in input space that corresponds to the region in between the two hyperplanes in the RKHS.


Multi-stage ORDA further improves this rate to be uniformly-optimal.

sAGE [8] achieves a nearly optimal rate since the parameter D in the convergence rate is chosen such that E x t − x * 2 2 ≤ D for all t ≥ 0 and it could be much larger than V ≡ V (x * , x 0 ).


This metric can be addressed by all models which operate by first stochastically generating a sequence of hidden states and then defining a distribution over the data-space given the state sequence.

for our model we approximate the marginal by a Monte Carlo estimate of (2) Note that sampling from p(h) boils down to sampling ξ 1...T from independent standard normals and then applying F g . the non-autoregressive property of our model allows us to estimate all words in some set S using K samples each by using only K independent trajectories h overall.


As we run Hamiltonian Monte Carlo as described in §2.2, h changes at every step, as we let h = V (q n ) + K(p n ).

we actually vary the metric structure as we run the chain, or, alternatively, move between different Riemannian manifolds.


We can use a special case of a more general algorithm given in the appendix (Appendix B.2, Algorithm 3).

we replace line 10 with the step w ⌧ +1 = (r ) 1 (r (w ⌧ ) r ⌧ ) where (w) = 1 2 kwk 2 r . We set r = log(p 0 )/(log(p 0 ) 1).


Recently, DeepMind demonstrated that it is possible to improve DC power usage efficiency (PUE) using a machine learning approach [13].

they developed a predictive model of PUE in a large-scale Google DC, and demonstrated that it can be improved by manipulating the temperature of the water leaving the cooling tower and chilled water injection setpoints.


The AM criterion is used to label T-F units that do not belong to any segments generated in initial segregation; such segments, as discussed earlier, tend to miss unresolved harmonics.

unit u ij is labeled as target speech if the final square error is less than half of the total energy of the corresponding signal and the AM repetition rate is close to the estimated target pitch: Psychoacoustic evidence suggests that to separate sounds with overlapping spectra requires 6-12% difference in F0 [6].


Assume that F can be parameterized as F = {f θ : θ ∈ R d }, that we are given a sufficient statistics summary function φ : X × Y → R d , and that function evaluation is given by f θ (x, y) = θ, φ(x, y) .

we let we have chosen our mechanism to encode a particular exponential family model, with C x (•) chosen as the conditional log partition function over the distribution on y given x.


The star in the denominator of the above equation is used to denote unconstrained emissions.

the denominator is the normalization of the weighted transducer [10].


This demonstrates the effectiveness of making FastGRNN's parameters low-rank, sparse and quantized and allows FastGRNN to fit on the Arduino  Uno having just 2 KB RAM and 32 KB flash memory.

fastGRNN was able to recognize the "Hey Cortana" wakeword just as accurately as leading RNNs but with a 1 KB model.


This can guide the choice of < 1, which our method leverages to offer some improvement while ensuring safety.

one way that the value of can be calibrated is by judging its value against the discrepancies in estimated propensities that are induced by omitting observed variables [10].


Condition (8) is required for identifiability if we only operate on statistics over different triplets (along with their separator sets).

if we resort to operations over only low order statistics, we require additional conditions such as (8) for identifiability.


Such a strategy indeed forms the basis of many adaptation techniques in PADMM, and ADMM.

if γ k increases, then τ k also increases and β k decreases.


From Figure 1(a), we observe that when the fixed number K of components equals the actual number, they yield comparable performance; while when they are not equal, the errors of D-FMM substantially increase.

k less than the actual number results in significant underfitting (e.g.


Besides Euclidean distance, the family of Bregman divergences can be used to measure the difference between Bµ(t) and v here.

given a function f (•) : R m → R convex in its argument, we can use Activity Homogenization.


By combining the result in Corollary 5 with Theorem 4, we can infer that in the heavily loaded regime, the time taken by Q-ThS to achieve O poly(log t)/✏ 2 t scaling is, in some sense, order-wise close to the optimal in the ↵-consistent class.

for any 2 (0, 1), there exists a scaling of K with ✏ such that the queue-regret under Q-ThS scales as O poly(log t)/✏ 2 t for all t > (K/✏) while the regret under any ↵-consistent policy scales as ⌦ (K log t/ log log t) for t < K/✏.


These results provide empirical evidence that feature engineering is an important source of inductive bias for unsupervised structured prediction problems.

we found that using Brown cluster reconstructions and specifying features which span multiple words significantly improve the performance.


on the last data we were unable to wait until LADM stopped.


Correspondingly, the bipartite graph along which messages are passed has ⌘p(p + 1)/2 minimizer-nodes that connect to the (⌘ + 1)p equality-nodes.

the equalitynode associated with the break-point variable x i (s), ⌘ > s > 0, is connected to 2(p 1) different g coll minimizer-nodes and two different g cost C minimizer-nodes.


This is the well-known missing data problem in causal inference.

if unit k received treatment, Y k (1) is the observed outcome, and Y k (0) is missing data, i.e., counterfactual.


In these cases, if we want to analyze the full procedure (from a learning theoretical sense), it is desirable to have a more precise information on the selected subspace than just its reconstruction error.

from a learning complexity point of view, it is important to ensure that functions used for learning stay in a set of limited complexity, which is ensured if the selected subspace is stable (which is a consequence of its convergence).


Part of this work was completed while the second author was at the Simons Institute at Berkeley.

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


Ridge leverage scores are closely connected to the residual Π ⊥ m φ i 2 after the projection Π m discussed in Definition 2.

using Lemma 2 we have that the residual can be bounded as It is easy to see that, up to a factor γ 1−ε , high-RLS points are also high-residual points.


Starting with the next node selected in our greedy algorithm, we begin to see hubs being chosen.

the first ten airports selected in order are: BNA, Chicago, Atlanta, Oakland, Newark, Dallas, San Francisco, Seattle, Washington DC, Salt Lake City.


The estimation of α is straightforward and we here focus on the best estimation of θ one can expect, assuming α is known.

we derive a lower bound on the minimax error of any estimator θ of θ.


Instead, we impose a weaker condition known as restricted strong convexity (RSC).

such conditions have been discussed in previous literature [9,1], and involve a lower bound on the remainder in the first-order Taylor expansion of L n . our main statistical result is based on the following RSC condition: where the α j 's are strictly positive constants and the τ j 's are nonnegative constants.


In this work, we use max-pooling units [14,13].

given a vector of simple cell responses s (i) , we will train complex cell features whose responses are given by: c where G j is a set that specifies which simple cells the j'th complex cell should pool over.


We are also able to accelerate SAG and SAGA in general, even though the improvement is less significant than for MISO.

sAGA without acceleration proves to be the best method on ocr.


Finally, what if our primary assumption is not met?

what if subjects are not quite behaving optimally with respect to p(θ)?


However, our unified framework opens the door for its use in verification.

kolter & Wong [13] identified an efficient way of computing bounds for the type of problems we encounter, by generating a feasible solution to the dual of the LP generated by the Planet relaxation.


The proposed approach succeeds in exploiting the two properties of ERM problems to improve complexity bounds of first-order methods.

we show that to reach the statistical accuracy of the full training set the adaptive sample size scheme reduces the overall computational complexity of a broad range of first-order methods by a factor of log(N ↵ ).


We will later discuss an application of PSDD multiplication to probabilistic inference, in which we cascade these multiplication operations.

we end up multiplying two factors f 1 and f 2 , represented by PSDDs n 1 and n 2 and the corresponding constants  1 and  2 .


Our performance bound is based on showing that W can be sandwiched between two simplicies with a small scaling factor.

consider the following simplex,  Using Hoeffding's inequality [18] (see Appendix B) with ⌧ = b q log m n , we have and a union bound over j = 1, . . . , m gives us where the last inequality follows from Bernoulli's inequality.


Some preprocessing was performed on the label relations to ensure consistency with our assumptions.

all implications were added to each instance to ensure consistency with the hierarchy, while mutual exclusions were defined between siblings whenever this did not create a contradiction.


We now introduce an intermediate (and simpler) algorithm, called treeCutter, which improves on the optimality factor when the diameter D G is not small.

we demonstrate that treeCutter achieves a good upper bound on the number of mistakes on any graph such that |E| ≥ 3|V | + |V |.