Discretizing logistic loss f (x) = log(1 + e −w T x ) does not fit exactly into the setting of Theorem 1 due to nonexistence of x * .

we introduce a second-order ODE that generates an accelerated first-order method for smooth functions if we simply discretize it using any Runge-Kutta numerical integrator and choose a suitable step size.


Generalised simplex-like algorithms were developed for SDPs [11], but to the best of our knowledge are currently merely of theoretical interest.

the bisection then started with the lower (infeasible) value of 0 and the upper value of 999.


The best rank-k approximation A k is obtained by projecting A onto the subspace spanned by its top-k principal components V k , which is the n × k matrix containing the top-k right singular vectors of A.

we develop a general tool that can be used with any existing sparse PCA heuristic.


However, as each processor starts sampling, the global count matrix is changing in a way that is unknown to each processor.

for each run of each algorithm, a sample was taken after 500 iterations of the Gibbs sampler, well after the typical burn-in period of 200-300 iterations.


In other words, as the quality of social network increases, the minimum sample complexity decreases.

a feature-based side information was also considered on top of stochastic block model [47,59].


Existing algorithms are usually based on the spatial [5,6,21] or frequency [3,15,16] domain.

we first evaluate the proposed method on the dataset degraded by Gaussian kernels with 1% noise.


A Pareto-dominated convention is unpreferable because there is another convention that makes both agents better off.

this makes the expected steps to reach an absorbing state polynomial in k. A KSAP agent pays more attentions on the most recent k observations and will freeze its action once coordinated.


(See Section 1.1 for a more detailed discussion.)

this technique has been used in several related problems and is standard by now [14,9].


In the L 2 case, we use the convention that 0 0 = 1.

it overlaps with, but is neither a special case nor a generalization of the remaining functional forms in the table.


In this paper, we first place a gamma prior on it as r ∼ Gamma(r 1 , 1/c 1 ).

no analytical conditional posteriors are provided and Gibbs sampling is not considered as a viable option [12].


Then, if x is the closest sample point to x , we have for n sufficiently large, |x − x| ≤ τ 0 and f (x) ≥ f (x 0 ) + δ/2 and thus f , contradicting the fact that x is the maximizer of the KDE over samples in its τ -radius neighborhood.

then x 1 and x 2 are points which respectively attain the highest values of f on P 1 and P 2 .


Computing the optimal policy is intractable, so we develop an approximation based on Monte Carlo tree search [12] and progressive widening to reason about continuous time [13].

using richer features (RNN) the model is able to learn from the crowd and the amount of supervision needed reduces over time.


Poisson sampling is executed in the following way: proceed down the list of elements and carry out one randomized experiment for each element, which results either in the election or in the nonselection of the element [16].

theoretically, we provide the error bound analysis, which supplies a justification for the algorithm and give a tradeoff between the subsample size and approximation efficiency.


In this sense, Line 10 maximizes the upper confidence bound on the true expected reward.

they are not suitable for many retrieval settings since the set of available articles can change frequently (e.g., news recommendation).


In SG or CD algorithms, all it entails is to substitute ∇A m (p, x) with ∇S(p, x).


We propose a new method for clustering based on finding maximum margin hyperplanes through data.

one can obtain soft clusterings efficiently using widely available software.


From this equation, we may infer the following: If P t R t = k, then the FDR will be bounded by ↵ as long as the total alpha-wealth P t ↵ t that was used for testing is smaller than k↵.

instead of presenting the most general and improved algorithms immediately, we choose to present results in a bottom-up fashion, introducing one new concept at a time so as to lighten the symbolic load on the reader.


The n-step returns from a given state are independent.

tD(λ) is able to achieve O(F ) time and space for two reasons.


One natural next step should be to generate direct quantitative predictions of behavior in one task based on a model trained on another task -ideally on an individual subject level, and in a task that fits in our framework that has not been extensively explored (for example, an internal-context Flanker variant, or a context-dependent response congruence judgment task).

figure 2 shows mean RTs and accuracies produced by our model for the AX-CPT, under the same parameters that we used for the flanker model.


[3] introduced the kernel methods machinery for conjoint analysis on the individual scale.

they are sub-optimal because they do not take into account the previous answers of the consumer.


Moreover, each corrupted row/column item has perturbed feature x i = u i + ∆u i and y i = v i + ∆v i , where ∥∆u∥ ∞ ≤ ξ 1 and Theorem 3 suggests that, if features have good quality in the sense that items with corrupted features are not too many, for example g(n), h(n) = O(log n), then sample complexity of DirtyIMC can be O(n log n √ log n) = o(n 3/2 ) as well.

we propose a dirty statistical model which balances between feature and observation information simultaneously to complete a matrix.


Table 1 summarizes results and shows that while several standard architectures succeed at these tasks in the interpolation case, none of them succeed at extrapolation.

we see that even over a basic task using a simple architecture, all nonlinear functions fail to learn to represent numbers outside of the range seen during training.


Gaps between L 1 and L 2 regularization in the presence of irrelevant features.

such that the actual sample complexity for the learning rule on this specific distribution is governed, up to polylogarithmic factors, by this quantity.


We compare the base exponential family embeddings (EFE) model (Rudolph et al., 2016) with our context selection procedure.

we introduce a binary hidden vector to indicate which elements the target depends on.


To provide insight into the nature of our algorithms, we focused on a single non-trivial domain.

the motivation for this approach comes from the recursive nature of tree search: if the heuristic can be adjusted to match the value of a deep search of depth D, then a search of depth k with the new heuristic would be equivalent to a search of depth k + D with the old heuristic.


Consider the typical situation in forward selection where we have a current working set I and we are interested in choosing the next basis vector, x i .

this is probably because DMAX has a bigger set of basis functions to choose from, than SB.


However, the joint probability distribution P(x, y) is often not known in practice.

clearly, this is a least square problem with a closed form solution.


Moreover, we show that this algorithm needs to query only O(k log n) such e I .

let P : [n] → R be a distribution, and let Q be the empirical distribution after O( k+log 1/δ ε 2 ) samples from P . Then with probability at least 1 − δ, we have that P − Q A k ≤ ε.


Furthermore, we ran extensive grid-searches over the λ, β parameter space using default networks (not shown) and found that the model robustly learns both tasks with a wide range of parameters.

the sensitivity to cue location, SI cue , was defined |0.5((R P L + R AL ) − (R P R + R AR ))|.


In contrast, methods such as DR, AP and the primal-dual hybrid gradient descent (PDHG) proposed in [29] used for SSL on hypergraphs [17], require performing a complete gradient descent and computing a total of R projections at each iteration.

suppose that W = βD, where β is a hyper-parameter, and D is a diagonal degree matrix such that Dii Djj log 1 ) iterations to return an -optimal solution.


Probabilistic classification performance is measured by the conditional logloss (the negative conditional likelihood), logloss Ptrg(X of the estimator, P (Y |X), under an evaluation distribution (i.e., the target distribution, P trg (X)P (Y |X), for the sample selection bias setting).

expert-provided source distributions, feature functions, and constraint statistic values, respectfully denoted P � src (x), f � (x, y), and c � , can be specified to express a range of assumptions about the conditional label distribution and how it generalizes.


Empirically, the speedup factor can be as high as 30 for densely connected problems.

mPLP follows a block coordinate descent strategy in which optimization is performed over a subset of variables, keeping all the other variables fixed [5].


Figure 1b shows this tradeoff against A80.

if we want a strategy that is at most suboptimal, we can vary p to produce a strategy that is the best response among all such -safe strategies.


The method labeled 'True' simply learns the parameters given the true model.

assuming the algorithm is run until the convergence criterion is satisfied, there is no impact of the feature introduction heuristic on the final outcome, but only on the computational complexity.


For example, one may wish to ask whether the system exhibits second-order dynamics by examining the extracted trajectories.

it is unclear how to choose the shape of the smoothing kernel to achieve this in the two-stage methods.


For example, we may assume ε i ∼ N (0, σ 2 I D ); i.e., a multivariate normal distribution with mean zero and variance-covariance proportional to the identity matrix.

lemma 2.2 The matrix J(f ; x 0 ) is orthonormal for any x 0 , i.e., J T (f ; x 0 )J(f ; x 0 ) = I d . Given the previous condition, model (1) is still not uniquely defined.


In [3] the idea is to introduce a statistics, and large deviation bounds for it, conditioned on sampling from a SBM (with covariates) and on a given C. Experiment Setup Given G, we obtain a clustering C 0 by spectral clustering [15].

moreover, from Political Blogs data, we see that "smoothing" a graph, by e.g.


Direct democracy is just a representative democracy where each group has one voter.

we also consider cost of voting, which is not considered in [12,23].


To overcome this deficiency, we devise a key-value-free MAP-REDUCE scheme to avoid on-disk data shuffling operations.

we distribute the computations over multiple computational nodes (MAP step) and then collect the results to calculate the ELBO and its gradient (REDUCE step).


In contrast, the UCB algorithm [5] achieves non-trivial regret after T = O(k) rounds.

this models, for example, the problem of learning the association between loan applicants and repayment rates over time by repeatedly granting loans and observing repayment.


For example, (1) has the following CCD approximation However, CCD also introduces strong bias which makes it insufficient to capture the complexity of inferred posterior distributions on real data (see Figure 5).

consider a parent-child pair in an SBN, S i and S πi , where π i denotes the index set of the parent nodes of S i .


1) for constructing diffusion geometry based on a measure µ.

4, we explain how this operator allows us to ensure the data we generate follows diffusion geometry and the manifold structure it represents.


Remark 1 Although we can interpret problem (4) as a MAP estimate of β under appropriate priors when scaling parameters (θ, ρ) are fixed, it does not enjoy an elegant Bayesian interpretation if we perform joint estimation of β and the scaling parameters (ω, ν) because it ignores normalization factors of the appropriate priors.

although some methods have been developed for either adaptive or multi-task learning, to the best of our knowledge, adaptive multi-task Lasso is the first method that can consider prior information on SNPs and multi-task learning simultaneously in one single framework.


Their method produces comparable cuts to the ones in [5], while being computationally much more efficient.

note that F is in general nonconvex and nondifferentiable.


We perform this comparison for various classification and regression problems, as summarized in Table 1.


Assume X = Y + ∆ where Y is a nonnegative matrix whose rows have unit 1 norm, where Y = F W is a rank-r separable factorization in which the rows of W are α-robust simplicial, and where ∆ ∞,1 ≤ .

under this hypothesis, we may also assume that each row of F and of W also sums to one [4].


The entropy condition will be satisfied when log kn k=1 C k card(Ω BI k ) n ε 2 n for some C > 0, where ε n = n −1/2 K f0 log 2β (n/K f0 ).

when {Ω 0 k } K0 k=1 / ∈ Ω, the complexity number K(f 0 , Ω) can be much larger.


The former negative correlation confirms that it is indeed easier to solve the task with more information in a query.

archive 3 , which has more than 300k such pairs.


We first trained our models with a column norm constraint [23] with  Evaluated Models We evaluated the ARSGs with different attention mechanisms.

the model with the hybrid attention mechanism with convolutional features was able to align sequences up to 200 phones long.


A single mapping discovered by a network would fail to elaborate the space of all bad functions, thus enforcing conditionality only on the relatively small set of bad functions it covers.

mine a history of bug fixes across multiple projects and attempt to reuse common bug fix patterns on newly discovered bugs.


classical cases of anechoic mixing arise in electrical engineering, when signals from multiple antennas are received asynchronously, or in acoustics when sound signals are recorded with multiple microphones resulting in different running times.


As such, immediate goals for future work include faster algorithm implementations, as well as developing effective postprocessing schemes (e.g., rounding) when the obtained solution is not an exact cluster matrix.

parameters: Our algorithm has two parameters: c A and c A c . The theorem provides a way to choose their values, assuming we know the values of the bounds p, q.


In this case, a treatment which is less effective on average but consistently effective on different patients may be preferable to an effective but risky treatment.

in the multi-arm bandit domain, the most interesting results are by [5] and [14].


This result did not require an ensemble, and as a result, the parser is also very fast.

the LSTM in contrast uses its short term memory to model the complex underlying structure that connects the input-output pairs.


In practice, we find that this leads to significantly improved reconstructions over user-specified shape PDFs.

this model contains ambiguities, since, for some 3D shape and motion, there will still be ways to combine different weights and a different rigid motion to produce the same 3D shape.


Condensation, a form of likelihood-weighted particle filtering, has been successfully used to infer the shapes of highly constrained "active" contours in video sequences.

the resulting set of particles approximates the posterior distribution at time t and is then propagated to the next frame.


The first group of algorithms finds representatives from data that lie in one or multiple low-dimensional subspaces and typically operate on the measurement data vectors directly [5,6,7,8,9,10,11].

the parameter λ > 0 sets the trade-off between the two terms.


In our results, the growing batch strategy (Grow) always had better test error performance than using the full batch, while for large datasets it also performed substantially better in terms of the training objective.

in Appendix F, we also consider constructing mini-batches by sampling proportional to f i (x s ) or f i (x s ) .


One can note that our non-linear model relies on the max function, which is not differentiable everywhere.

the baseline SVM with a polynomial kernel of order 2 and FSE with φ = max, outperformed their linear counterparts.


A ranking of the items V can be represented as a permutation π : {1, ..., M } → {1, ..., M } where π(m) = l denotes the rank of the item v m and m = π −1 (l).

second, given a new user u no optimization is necessary to produce a ranking of the items for u.


Therefore applying Talagrand's inequality in the version of [3] to the class G r we obtain Let us define ε r := 30ϕn(r) r + 2τ v nr 2−ϑ 1/2 + 7τ nr .

now assume that P has Tsybakov noise exponent q ∈ [0, ∞] in the sense of [9].


[8,Theorem 3] proves the convergence of DCA for general d.c. programs.

extending these results to the constrained setup as in ( 2) is not obvious.


Density estimation with Gaussian mixture models is a popular generative technique, mostly because it is computationally tractable and often produces good results.

in this section we therefore restrict the discussion to the first sampling assumption only; the discussion of the second sampling assumption, where generalized EM must be used, is omitted.


firing rate, spike-latency, resting potential of a neuron).

biophysical neuron models are typically fit to data with genetic algorithms applied to the distance between simulated and measured data-features [2,8,9,46].


This allows us to analyze the functional connection structure in a neural population at the same time as its relationship with further continuous signals of interest.

also, the weight assigned to each of the two Gaussians can be changed.


The main goal of this paper is to develop a batch policy that optimizes the unknown function as efficiently as possible.

in general these weights will be difficult to compute exactly, particularly due to the conditioning on the set S i .


An interesting application of the TDB-Lasso is in structural estimation of time-varying undirected graphical models [1,17].

we first address the issue of estimating jump points by analyzing the transformed TD-regression problem Eq.


Moreover, the variational filtering EM algorithm is derived from the filtering variational objective, providing a solid theoretical framework for filtering inference.

[9] down-weight the KL-divergence by a factor of 1e-6 at all steps.


Moreover, it is more powerful than two earlier families of relaxations: the Sherali-Adams [22] and Lovász-Scrijver [23] hierarchies.

their sum give PSD moments which approximately satisfy all constraints.


The SpikeSlab0.5 was the worst performing model, but the performance was improved by SpikeSlabKL .

we apply Theorem 5 to formulate equivalent solutions of (1) that may be simpler to solve.


From the above derivation, we can see that the essential part of the CVI algorithm is to compute the expectations and variances of RMN features, both of which can be done by any inference procedures, including the mean field as we have used.

third, we'd also like to treat the introduced hidden variables as free variables and to make their cardinalities adaptive.


in fact, numerical simulation can be used to show that N = 30 suffices to recover the ground truth in 95 out of 100 runs [26].


if the decision maker is risk neutral, then the solutions based on nominal parameters are good.


We introduce a new multi-layer domain discriminator which can be used for domain alignment following the recent domain adversarial learning approaches [13,64].

separately, domain alignment methods which focus on first and second order statistics have shown improved performance through applying domain alignment independently at multiple layers of the network [36].


The unified view shows more connections between moment matching and GAN, which can potentially inspire new algorithms based on well-developed tools in statistics [15].

we observe varied poses, expressions, genders, skin colors and light exposure in Figure 2b and 2e.


Lines 14 -18 in Algorithm 1 are added only for the data analysis in Section 5.3, in which p is massive compared to n in that log(p) is comparable to n, and the algorithm may not scale down the size of p sufficiently for even obtaining a ridge regression estimator afterwards.

the support of β is S = {1, 2, 3, 4, 5}.


Acknowledgment This work was partially supported by MEXT kakenhi (25730013, 25120012, 26280009, 15H01678 and 15H05707), JST-PRESTO and JST-CREST.

it did not perform well and was omitted.


Naturally, if f is a neural network approximating f and g approximates g, then we can compose these approximations to get an approximation of the composition.

this paper focuses on the representational capabilities of generative networks.


To allow us to verify the clustering performance, we labeled each cluster using twenty informative words, as listed in Table 2.

by this, we mean that the distance between any two clusters is consistent with the path length along some fixed tree whose leaves are identified with the clusters.


Dropout variational inference is a practical approach for approximate inference in large and complex models [15].

we derive the loss function using a Laplacian prior, as opposed to the Gaussian prior used for the derivations in §3.


(2015) to e O(✏ 3.25 ) for general unconstrained functions, where ✏ is a pre-specifed optimization accuracy; Jain et al.

for U 2 R m⇥r , ⇧ Orth (U ) returns a matrix U 0 2 R m⇥r that has orthonormal columns.


Here we develop a novel measure, termed the information-theoretic intersection information I II (S; R; C), that quantifies how much of the sensory information carried by a neural response R is used for behavior during perceptual discrimination tasks.

the redundant information SI(C : {S; R}) is then defined as the solution of the following convex optimization problem on the space ∆ p [20]: where CoI q (S; R; C) ≡ I q (S : R) − I q (S : R|C) is the co-information corresponding to the probability distribution q(s, r, c).


We revisit the notion of policy regret and first show that there are online learning settings in which policy regret and external regret are incompatible: any sequence of play that achieves a favorable regret with respect to one definition must do poorly with respect to the other.

the distribution ⇡ we want is now the limit of the sequence (⇡) T . The final step is to show that ⇡ is a policy equilibrium.


For each of the input/output examples (Figure 2d) we have constraints that model the program execution (Figure 2c) and enforce the desired output (P 1 taking value 1).

when learning from examples, there is often uncertainty over the correct program.


Intuitively, the acquisition function α n (x) should be high in areas where the maxima is most likely to lie given the current data.

note that for early iterations when n < m, we can efficiently sample θ (i) with cost O(n 2 m) using the method described in Appendix B.2 of [23].


While more flexible than previous approaches, the NPI only learns to reproduce an existing program.

for nearly all computational problems, it is feasible to design generic algorithms for the worst-case.


The neural networks use ReLU and batch normalization for some hidden layers.

this work was supported in part by Peng Cheng Laboratory and NSFC under grant 61872009.


Moreover, the standard deviations in must remain positive.

wingate and Weber [11] study in general probabilistic programs, as supported by languages like Church [12], Venture [13], and Anglican [14].


When both f and g are modular, Problems 1 and 2 are called knapsack problems [16].

define: where the remaining elements are chosen arbitrarily.


First, GEM does not leverage structured task descriptors, which may be exploited to obtain positive forward transfer (zero-shot learning).

we can interpret GEM as a model that learns the subset of correlations common to a set of distributions (tasks).


Previous attempts to alleviate catastrophic forgetting often relied on episodic memory system that stores past data [31].

recent evidence suggests that the hippocampus is more than a simple experience replay buffer.


2 An advantage of our method is that it allows us to have a different neighborhood size for each data point, depending on the local dimension of its underlying manifold at that point.

by applying SMCE with λ = 10 on almost 33, 000-dimensional vectorized faces, we obtain a misclassification rate of 2.34%, which corresponds to wrongly clustering 3 out of the 128 data points.


Hence, any predictor w can be written as w = (w i,j ) (i,j)∈G where w i,j is w's weight on φ φ φ i,j (x, y i , y j ).

the margin Γ(w, x, y) achieved by predictor w at example (x, y) is defined as, We consider the case where the feature map φ φ φ is a potential function for a Markov network defined by a complete graph G with nodes and ( − 1)/2 undirected edges.


It is based on the idea that bandwidth and variable selection can be simultaneously performed by computing the infinitesimal change in a nonparametric estimator as a function of the smoothing parameters, and then thresholding these derivatives to effectively get a sparse estimate.

the best rate of convergence is n −4/(4+d) , which is impractically slow if d is large.


To show the convergence, we have plotted the optimal values of the dual problem (D 1 ) at each iteration in Figure 1.

this observation inspires us to solve a special type of SDPs using boosting techniques.


Unfortunately, in our setup, we do not know a good kernel in advance.

we consider the problem of predicting online the entries in an m ⇥ n binary matrix U .


In a fully distributed scenario, players only have access to their previous actions and rewards.

next we define the expected total regret, which we want our distributed algorithm to minimize.


1), it refers to restricting the responses or errors that flow in the module from going to infinity, and preventing the network from encountering the vanishing of gradients in the backpropagation process [37].

overall, both SPNs outperform the other techniques with a significant margin of over 6 intersection-over-union (IoU) points.


Transfer nonadjacencies and endpoint orientations from each G i ∈ G to K and propagate the 3 changes in K using the rules described in [10] PAT({X, Y}, Z) ← all possibly active trails between X and Y given Z for all {X, Y} ⊆ V and The algorithm begins with the complete graph over V with all • endpoints and transfers nonadjacencies and endpoint orientations from each G i ∈ G at line 3, e.g.

some sequence of edge removals will provably produce H i at line 16 and it will be added to the output set since it is consistent with every G i ∈ G. by theorems 3.1 and 3.2, ION is an asymptotically correct algorithm for learning the complete set of PAGs over V that are consistent with a set of datasets over subsets of V with overlapping variables, if the input PAGs are discovered using an asymtotically correct algorithm that detects the presence of latent common causes, i.e.


It is surprising that data augmentation does not lead to more robust models.

it is interesting to note that for Cross-Lipschitz regularization (both kernel method and neural network) the "adversarial" sample is really at the decision boundary between 1 and 8 (as predicted) and thus the new decision is actually correct.


The RBM choice model can represent an arbitrary strength of the similarity effect.

our choice model is thus called the RBM choice model.


Furthermore, the classification boundary occurs uniquely at the point where z = (ŷ, x 1 , ..., x d ), where, from the assumptions, ŷ is the unique solution to (12).

both z +ε = (y + ε, x 1 , ..., x d ) and z −ε = (y − ε, x 1 , ..., x d ) are, with probability α, on the correct side of the regression surface, defined by z = (ŷ, x 1 , ..., x d ).


In this work, we address this gap and explore the statistical foundations of adversarially robust generalization.

the Gaussian model has one parameter for controlling the difficulty of learning a good classifier.


In sum, we conduct the training algorithm iterating with two steps: (i) Fixing the network parameters, we estimate the latent variables and determine the optimal segmentation reference under the sampling method.

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


However, in fully connected networks, the weight matrix of each layer is a dense Gaussian matrix.

the first network is trained with GAN to generate handwritten digits, and the second for celebrity faces.


Since learned predictors and risk scores increasingly support or even replace human judgment, there is an opportunity to formalize what harmful discrimination means and to design algorithms that avoid it.

all three are examples of observational approaches.


In Q4, the ellipsis of the predicate ("yearEstablished") comes from Q3.

we incorporate a dialog memory to maintain information from interaction history.


Assigning large weights to input features close to the gradient direction, locally in neighborhoods of support vectors, corresponds to increase the spatial resolution along those orientations, and therefore to improve the separability of classes.

compute the gradient vector ndi = \l dJ; 3.


Later as it also becomes "older", it will be cited by other newer posts as well.

to achieve fully nonparametric modeling of the hazard function, we can let m grow as we see more cascades.


the joint density of y + , ζ and {h k } where all the {h k } are integrated out.

this property can be ensured by considering autocovariances proportional to the class of kernels given by where β is a positive scalar governing the decay rate of the variance [16].


This ground truth was obtained by projecting the point cloud from LIDAR on the reference image.

first, we obtain the raw scores U (x, d) from Algorithm 1 for the shifts up to D max = 228.


Bauschke and Borwein [3] give a general condition for the linear convergence of alternating projections in terms of the value  ⇤ (defined in Section 3.1).

our analysis also shows the effects of additional properties of F . For example, suppose that F is separable, that is, F (V ) = F (S) + F (V \S) for some nonempty S ( V . Then the subsets A rm ✓ V defining the relevant faces of B satisfy either A rm ✓ S or A rm ✓ S c [2].


Although conceptually simple, the problem of blinding poses difficult challenges in a practical clinical setup.

we set the differential effect of treatment to ∆x = 0.1 and the standard deviation of variability within each of the assignment-response subgroups to σ − = σ 0 = σ + = 0.1.


We use p( 9 t Q = q, x) to denote the distribution pi (9) obtained from this algorithm; this can be read as "the density of 9 after asking query q and obtaining the response x".

the run time complexity of the algorithm is: 0(1 QI .


Compared with classical factorization Z V , such tri-factorization supports the asymmetric transitivity property of directed links.

recently, there exists growing number of works proposing embedding models specifically for network property preservation.


It is worthy noting that in the current implementation, the active set size M is fixed for all experts.

section 3 describes the proposed algorithm.


By reversing the roles of Hand W, the update rule for W can similarly be shown to be nonincreasing .• We have shown that application of the update rules in Eqs.

a simple additive update for H that reduces the squared distance can be written as (6) If 'flatt are all set equal to some small positive number, this is equivalent to conventional gradient descent.


Moreover, here we considered a simple square neighborhood for encoding the contact predictions in the temporal feature vector; more complex relationships could be discovered by exploiting different topologies for such feature vector .

despite considerable efforts, the accuracy of the best predictors at CASP rarely exceeds 20% for long-range contacts, suggesting major room for improvements.


SVM [9] can be thought as a generalized perceptron with a kernel that computes the inner product on transformed input vectors φ(x).

because the cost is invariant for all kinds of mislabelings, the ordinal information is not taken into account.


Here we have two simple examples of Gaussian and Bernoulli mean estimation problems, in which the sensitivities are unbounded.


functions whose restriction to some neighborhood around any point is Lipschitz), the Lipschitz constant may be computed using its differential operator.


In this section, we discuss concrete families of priors and mechanisms for choosing among them in data-dependent ways.

one can construct Markov chain algorithms that are geometrically ergodic, in which case n 1/q is replaced by a term 2 W(n) , allowing one to spend computation to control the 1/d 0 term.


Similarly in image restoration, they determine the statistical weights given to the prior knowledge and the received data.

if we introduce a freezing threshold () so that all spins with (Ui)2 > (}2 are frozen, then the freezing fraction f is given by (11) The thermal average of a dynamic spin in the second stage is related to the cavity fields in both stages, say, for spin 1, where 11,1 is the cavity field in the second stage, r is the order parameter describing the spin correlations of the two thermodynamic stages: i Xtr is the trans-susceptibility which describes the response of a spin in the second stage to variations of the cavity field in the first stage, namely The cavity field 11,1 is a Gaussian variable.


Bourdev and Brandt coined the term, "soft-cascade", where the entire detector is trained as a single strong classifier without stages (with 100's or 1000's of weak classifiers sometimes called "features").

determining the optimal target detection rate for each stage of the cascade remains an unsolved issue.


Due to the use of sampled bucket sequences, the time per iteration is nearly independent of the size of the abstraction.

let σ t i be the strategy used by player i on round t. The average overall regret of player i at time T is: Moreover, define σt i to be the average strategy for player i from time 1 to T . for each information set I ∈ I i , for each a ∈ A(I), define: There is a well-known connection between regret and the Nash equilibrium solution concept.


The latter work introduced training of segmentation models for specific losses.

an example of the latter type of feature would be "number of times the instruction [mov] appears in this block".


To ensure robust comparison, for each configuration, after convergence during training, a different model is saved at every 3000 iterations.

each image is associated with a 50-word lexicon defined by wang et al.


Work on cluster tree estimation has a long history.

by Assumptions 2 and 5, we have that there exists σ > 0 and η > 0 such that the following holds uniformly: Vol(B(x, τ 0 ) ∩ L f (λ + σ)) ≥ η.


Second, we compare to a structure learning approach for weak supervision [2] and show how we outperform it over a variety of domains.

in the second and third settings with high-order dependencies, structure learning struggles to recover the relevant dependency, and performs worse than Coral even as more training data is provided.


( 5), we have Now let f satisfy (10) and let x, y ∈ B.

in particular, they prove that if B = R n , d(x, y) B = x − y 2 we have the gradient characterization They softly enforce this condition by adding a penalty term to the loss function of D that takes the form where the distribution of X is taken to be the uniform distributions on lines connecting points drawn from P G and P r . penalizing the 2 norm of the gradient corresponds specifically to choosing the 2 norm as underlying distance measure on image space.


Any walk between x and y with length , yi with length l, we will show that every node By the definition of G h x,y , v i must be included in G h x,y .

by extracting a local subgraph around each target link, we aim to learn a function mapping the subgraph patterns to link existence, thus automatically learning a "heuristic" that suits the current network.


Does this training procedure significantly reduce the dependence between paths?

in this section, we use three lesion studies to show that paths in residual networks do not strongly depend on each other and that they behave like an ensemble.


We imagine that a concept has an average location in the space, but that each "observation" of the concept is a noisy realization of this average location.

this formulation, which we have called Hierarchical LRE (HLRE), solves two problems encountered in RAAMs.


On the other hand, extending the stochastic approximation and martingale limit arguments that underlie the bandit analysis to the ε = 0 case is not straightforward.

this paper examines the equilibrium convergence properties of no-regret learning with exponential weights in potential games.


To see this we must compute the capacity of ReLU units.

proof: A binary-weight homogeneous linear threshold function in N variables has N coefficients and thus there is at most 2 N such functions.


For a given class of signals, our objective is to design wavelets that yield approximately sparse expansions in Eq.

we learn the update and predict operators that minimize some sparsity surrogate of the detail (wavelet) coefficients of given training functions {f n } nmax n=1 .


We can see that the classifier-based approaches "-" perform poorly: when training trajectories consist of only oracle actions, learning is severely biased.

second, the parser's total runtime and accuracy on a sentence are unknown until parsing is complete, making this an instance of delayed reward.


Other works in visual control have relied on model free methods that operate on a a low-dimensional state representation of images obtained using autoencoders (Lange et al., 2012;Finn et al., 2016;Kietzmann & Riedmiller, 2009).

when the number of training examples is increased to 100K both models are at par.


In fact, human behavior in 4 l moons U h R is similar to 4 l moons U .

for a given GP with kernel k, the evidence p(y 1:l | x 1:l , k) is the marginal likelihood on labeled data, integrating out the hidden discriminant function sampled from the GP.


As we have solved for Y * in closed form in Equation ( 8), we can plug this result into Equation ( 1) to obtain a formulation of the problem of optimizing Π * that does not require a simultaneous optimization over Y .

0 Given Π We now address the subproblem of solving for the optimal structure matrix, Y , subject only to positive semi-definiteness, for any Π.


By spending O(n • 2 n ) time in the beginning of the branch and bound for computing the scores of optimal BN extensions of every V ⊂ V , we can then look up these scores during branch and bound in O(1) time.


In this case, the optimization problem associated with computing pred * PD (u) above is a minimum weighted feedback arc set (MWFAS) problem, which is known to be NP-hard.

recently, Ramaswamy and Agarwal [16] showed the existence of such surrogates, but their result involved an unwieldy surrogate space, and moreover did not give an explicit, usable construction for the mapping needed to transform predictions in the surrogate space back to the original prediction space.


Note that the case (i) is possible only when the condition in the step (a) holds during the construction of y NEW .

to derive a contradiction, assume that n t e [1] ≤ n t e [0] and construct a tree-structured GM T e (t) of depth t + 1, also known as the computational tree, using the following scheme: 1.


it is possible to reach any state from any other state).

each time the pair (i, a) occurs N t (i, a) increases by 1, so the first count is no more than 2 log T J i,a (p i (a); P, 3 ) − δ .


We define the ψ-transform of a loss function as follows.

for the original sequence (θ i ), we see lim sup ψ(θ i ) > 0, so we cannot have ψ(θ i ) → 0.


For example in Equation ( 4) ) oc for the gamma distribution.

nN trained by stochastic gradient descent (SGD) or its variants is known to suffer from overfitting especially when training data is insufficient.


The original model, f ∼ N (0, Σ θ ) and ( 7) define a joint auxiliary distribution P (f , g | θ) given the hyperparameters.

for non-Gaussian observation models, inferring the parameters that specify the covariance structure can be difficult.


On the other hand, IHT for standard sparse regression [10] requires n = ⌦( 2 s log p).

in this paper, we propose to solve (5) using an Iterative Hard Thresholding (IHT) scheme.


Note that this computation is linear in the number of unlabeled random variables and linear in the number of states.

maximum likelihood learning aims at finding model parameters w which assign highest probability to the training set D. Assuming the data to be independent and identically distributed (i.i.d.


Since π is stationary, we have d π P π = d π , and so  The following derives a bound on the Q values as a function of the mixing time.

their algorithm is not directly applicable to our setting, due to the fact that in our setting, decisions must be made with respect to the current state of the agent (and the reward could be changing frequently), while in their setting the decisions are only made with respect to a single state.


Correspondences between instances in source (English) and target (Japanese) domains are observed.

when trying to find matching between instances in different domains, we cannot directly measure the distances since they consist of different types of features.


The qualitative results seem to be fairly stable as a function of these smoothness parameters.

by generating ground truth using assumptions similar to those embodied in the models we intend to test, we risk invalidating the results.


11 We expect nontrivial interactions between clusters, even when we do not explicitly model them as in [14].

note that the principle submatrices of a PSD matrix are also PSD; hence, if C ∈ PSD N then C SS , A ∈ PSD K . not only is the recovered A an unbiased estimator for A * M , but also it is now doubly non-negative as A * M ∈ DN N K after the rectification.


samples Refer to the supplementary material for L 2 error bounds and formulas for ν + ε = ν ε (R × Ω) for the gamma, symmetric gamma, and symmetric α-stable processes.

the learned kernel is then used for GP infilling with 900 training points, taken by down-sampling the training data, which is then applied to the original 44,100 Hz natural sound file for infilling.


PCN-E-5), PCN slightly under-performs ResNet-50 but outperforms ResNet-34, while using fewer layers and parameters than both of them.

interestingly, the spatial distribution of the prediction error (averaged across all layers) highlights the apparently most salient part of the input image, and/or the most discriminative visual information for object recognition (Fig.


Theoretically understanding the empirical performance of PSOS(4) as stated remains open.

we constrain the rank of the SDP matrix in PSOS to be at most r, and solve the resulting non-convex problem using a trust-region coordinate ascent method, cf.


The claim holds for n = 1 as s 1 s −1 The rectangle with side lengths as −1 n and bs n has circumference 2(as −1 n + bs n ) and area as −1 n bs n = ab.

x 2 +c − 1 for the derivative of φ c . φ c (x) > 0 for c < 0 and φ c is monotonously increasing.


Return-based methods (where return refers to the sum of discounted rewards � t γ t r t ) offer some advantages over value bootstrap methods: they are better behaved when combined with function approximation, and quickly propagate the fruits of exploration (Sutton, 1996).

3 Analysis of Retrace(λ) We will in turn analyze both off-policy policy evaluation and control settings.


In fact, straightforward applications of ERM lead to "catastrophic forgetting" [McCloskey and Cohen, 1989].

also seen in Table 2, the final ACC of GEM is an increasing function of the size of the episodic memory, eliminating the need to carefully tune this hyper-parameter.


We fix ν = 0.05 for the artificial dataset and Web-1, and fix ν = 0.02 for Web-2 and Web-3.

we classify each data point into one of the K = 5 classes and rank the data points according to the class labels (data points with the same labels are arbitrarily ranked).


Proof Technique As a fundamental step in the proof of Theorem 2 we prove tight asymptotic bounds for high-order norms of the approximation factor.

for a synthetic set of generated bit-vectors, we show that whenever ε 2 δ the constant hidden by the Θ-notation is at least 0.75 (except for very sparse vectors, i.e.


(b) Learning curves when using different number of conjugate gradient iterations to compute F −1 θ k g in ( 5).

we use the term states and observations interchangeably.


high-dimensional), ǫ ∼ N (0, σ 2 I n ), and the columns of X are normalized to have ℓ 2 norm √ n. Given such a linear model, two key tasks are to identify the relevant set of variables and to estimate β with bounded ℓ 2 loss.

a special case of design matrices that satisfy the Restricted Eigenvalue assumptions are the random design matrices.


Secondly, we find that Vapnik's key inequalities become equalities once "the misclassification error" is replaced by "the margin error" (defined as the rate of data instances incurring positive costs).

the main results are given in Section 2.


In the full version of the paper, for the specific problem of portfolio selection, where f t (x) = − log(r t • x), we give a faster implementation whose per iteration running time is independent of the number of iterations, using the more sophisticated "online Newton method" of [HKKA06].

another approach to connecting worst-case to average-case investing was taken by Jamshidian [Jam92] and Cross and Barron [CB03].


The reward received at transition s a − → s is given by the random variable R(s, a, s ); usually one is interested in the expected value of this variable, which we will denote by r(s, a, s ) or by r(s, a) = E S ∼p(•|s,a) [r(s, a, S )].

by appropriately defining the rewards one can induce different task decompositions.


Note that the average sum in the right-hand side, i.e., the objective function, can be equivalently written as: Remark 1.

in order to obtain an SSVM-like formulation, the hinge loss is used instead of the discontinuous 0/1 loss in the above formulation.


• B: We also use only fully supervised data in this variant, but we employ Laplacian regularization in addition to Tikhonov regularization (Equation ( 2)).

the analysis of resting state activity poses a challenge, as it is not stimulus-driven, and is therefore difficult to analyze or to reveal using hypothesis-driven analysis methods.


Our method can be directly plugged into any recognition system that relies on linear templates.

we can obtain multiple templates in this case by zero-padding the original template (to represent various translates of that template; Figure 3).


If the discount factor ϑ satisfies Assumption 4.1 and α 2 + ϑ 2 β 2 < 1 2 , then the operator T π is a contraction with respect to • ξ .

it is known that if ξ is the steady state distribution of the policy π under evaluation, then Π is non-expansive in • ξ [4,2].


We consider sequential prediction of outcomes y 1 , y 2 , .

the goal is to exploit similarities between tasks.


An agent using normal Q-learning in a finite MDP repeatedly observes a state s, chooses a legal action a, and then observes an immediate reward r and a transition to a new state s . The Q-learning equation is given by: ∆Q where γ is a discount parameter, and α(t) is an appropriate learning rate schedule.

nevertheless Hyper-Q does exhibit substantial reduction in Bellman error, and also significantly exploits PHC in terms of average reward, as shown in figure 3.


Furthermore, because our model is equivalent to a Boltzmann machine, one could propose a framework for data-based influence maximization based on well-known Boltzmann machine learning techniques.

in the previous section we found that MF-IIM is efficiently solvable if there exists a stable nonnegative steady-state.


This section shows that the choice of a good parameterisation is not obvious, and that the use of the Riemannian geometry of the simplex [Ama95, GC11] is important in designing Langevin MCMC algorithms.

note that the β−1 term in Equation 9 has been replaced with β in Equation 10 as the −1 cancels with the curvature terms as detailed in Table 1.


The first step is to find a good objective function on which to do gradient descent.

projection is a common technique for stabilizing the transient behavior of stochastic approximation algorithms (see, e.g., Kushner & Yin, 2003).


Large deviation principle [16] states that, the probability that an opponent with strategy q behaves like p * is roughly exp (− .

partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players.


In particular, apart from LEML, no other embedding approach could scale to the large data sets and, even LEML could not scale to Ads1M with a million labels.

we now show that the optimal solution A to (3) indeed minimizes the loss (7) upto an additive approximation error.


Existing VMMs address these problems by allowing models to differentiate between contexts at nonconsecutive past timesteps, ignoring intermediate observations [13,22,10,24,4].

conversely, the frequency of each particular context in the data decreases as its length increases, so it may be difficult to accurately model long-term dependencies without requiring prohibitive amounts of data.


More precisely, the nature of sampling manifests through parameter c, which is limited by r β .


Learning with recurrent neural networks (RNNs) on long sequences is a notoriously difficult task.

we added one more layer to the dilated CNN, which enlarges its receptive field size to 1,024.


A linear algorithm will have difficulty because the mapped data is not linearly separable.

in [6,5] preprocessing the data with a square root was demonstrated to yield good results.


In the next section we will derive the general (algebraic) nonlinear family which is based on "lifting" the input matrices A, B onto higher dimensional spaces and feeding the result onto the < •, • > machinery developed in this section, i.e., sim(A, B) =< ψ(A), ψ(B) >.

this dichotomy is probably most emphasized in the area of computer vision, where image understanding from observations involve data instances of images or image sequences containing huge amounts of data.


Splitting data does not generate anomalies.

the number of iterations for the Gibbs sampling was 500, and the anomaly score was calculated by averaging over the multiple samples.


For the probability simplex with d vertices, the pyramidal width is actually the same as its width, which is 2/ √ d when d is even, and 2/ d−1/d when d is odd [2] (see Appendix B.1).

the Frank-Wolfe (FW) optimization algorithm [9], also known as conditional gradient [23], is particularly suited for the setup (1) where M is only accessed through the linear minimization oracle.


Since the non-zero elements of the optimal solution correspond to the k ⇤ smallest values of , then Equation ( 3) is equivalent to the following quadratic equation in : Solving for and neglecting the solution that does not agree with The above implies that given k ⇤ , the optimal solution (satisfying KKT) can be directly derived by a calculation of according to Equation ( 5) and computing the ↵ i 's according to Equation (1).

for any nonzero weight ↵ ⇤ i > 0 the following holds: Squaring and summing Equation ( 2) over all the nonzero entries of ↵, we arrive at the following equation for : Algorithm 1 k ⇤ -NN Input: vector of ordered distances 2 R n , noisy labels y 1 , .


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

entries of B) are different at each "pixel" (i, j).


For IMC, we use the feature vectors directly.

note that the transpose H T is used here instead of H, which is used in the fully observed case.


The procedure Almost-Convex-AGD is the same as in [4].

finding the global optimal solution to a generally non-convex problem is intractable [13] and is even a NP-hard problem [10].


Our motivation for studying SIMs under such a constraint can ultimately be traced to the vast sufficient dimension reduction (SDR) literature.


Whatever n, there are therefore many eigenvalues for which Ail» n/u 2 , corresponding to degrees of freedom which are still mainly determined by the prior rather than the data (compare (11)).

i now apply the result for the learning curve (11 ,12) to some exemplary learning scenarios.


In four different settings of n, p, and the decay parameter η, we compared the nominal 90% confidence intervals (CIs) of four methods: "oracle", "ridge", "normal", and "OLS", to be described below.

we now state some population-level assumptions.


For efficiency, the A2C objective and meta-objective were accumulated over all time-steps within an n-step trajectory of experience.

the true value function is unknown and therefore, for both prediction and control, a sampled return is instead used as a proxy.


Using the notation above, assume F and κ are well-conditioned, and C(n) and m/n are Ω(log c n) for some suitably large c. The algorithm for the simplified model shown in Figure 1 and that for the bipartite model (appears in [19]) give us an (1/ log 2 n, , O(1/ log n))approximation algorithm w.h.p.

our goal is to estimate {x i } i∈[n] based on B for suitably large n. Simplified Model.


We perform robust optimization to train our classifiers on perturbations generated by projected gradient descent.

we study the MNIST [34], CIFAR-10 [33], and SVHN [40] datasets.


This approach can be extended to a class of nonstationary covariance functions, thereby allowing the use of a Gaussian process (GP) framework, as shown in [9].

we provide sufficient conditions on the number and spatial location of samples required to guarantee state recovery, and provide a lower bound on the minimum number of samples required to robustly infer the hidden states.


Numerical experiments showed that the proposed gNAC algorithm can estimate gNG efficiently and outperformed the NAC algorithm.

we provide a general view of the estimation of the gNG(ι) using the theory of the estimating function, which provides well-established results for parameter estimation [14].


Next, we exploited this criterion to examine the quality of model solutions θ v , θ m , θ o discovered by the vanilla, DML and ONE training algorithms respectively.

the existing online distillation methods lack a strong "teacher" model which limits the efficacy of knowledge discovery.


in forward and backward blocking, but stronger (Rf2) in the sharing paradigm.

ifjQfjl as a function of v . The upper curve shows the average maximum diagonal element of the same matrix.


. . , ŵ CT , obtained e.g., by ordinary grid-search, our first problem is to provide a theoretical approximation level ε in the sense of (3) 2 .

given a lower and an upper bound of the score of each validation instance, a lower bound of the validation error can be computed by simply using the following facts: ) Furthermore, since the bounds in Lemma 1 linearly change with the regularization parameter C, we can identify the interval of C within which the validation instance is guaranteed to be mis-classified.


Multi-task learning (MTL), transfer learning (TL), and domain adaptation (DA) techniques have recently been utilized to leverage the relevant data and knowledge of different domains to improve the predictive power in all domains or one target domain [Pan andYang, 2010, Patel et al., 2015].

the key question is whether we may integrate available data from all different sources or domains to achieve reproducible disease prognosis based on NGS count data.


For K-means it has been proved that the global minimizer of the WSS objective function on the sample converges to a global minimizer on the underlying space (e.g., Pollard, 1981).

clustering is often formulated as a discrete optimization problem.


When ∇ 2 f LI n (i.e., LI n − ∇ 2 f is positive semidefinite), if ∆t/t small and ∆t < 2/ √ L, we see that all the roots of (3.2) lie in the unit circle.

although it has been empirically observed that this method significantly boosts convergence, there is no general theory characterizing the convergence rate.


Can we recover the column-space of the low-rank matrix L 0 , and the identities of the non-zero columns of C 0 , exactly and efficiently?

finally, for any matrix X let P I ′ (X) denote the matrix with all columns in I ′c set to 0, and the columns in I ′ left as-is.


The work of [6] also offers a weak guarantee wherein they are only able to tolerate a 1/ √ d fraction of corruptions.

we assume that b * is a k * -sparse vector albeit one with potentially unbounded entries.


This tends to favor frequent n-grams [11,23], leading to issues such as incorrect semantic coverage, and lack of diversity.

in our study, we found that the number of distinct noun-phrases in a dataset is significantly smaller than the number of images.


A finite convex combination of copulas is a copula, so r (a) is a copula density.

2 shows an average log-likelihood of models trained on training sets with N = 50, 100, 200, 500, 1000, 2000, 5000, 10000 and evaluated on 2000-example test sets (averaged over 10 training and test sets).


Rather, all input data points lie on a low-dimensional surface which is embedded in an Euclidean space whose dimensionality is given by the total number of camera pixels.

the experimental setup consists of an open-field square arena of about 80 x 80 cm in a standard laboratory background (Fig.


We have presented regularized learning with networks of features, a simple and flexible framework for incorporating expectations about feature weight similarities in learning.

x i ≈ j∼i P ij X j , where j ∼ i denotes the samples, j, which lie close to i on the manifold.


Starting at initial values x 0 , the optimizer will converge to a local solution that maintains the same order as the initial x 0 's.

fortunately, in our experience, simply applying any standard manifold learning algorithm to estimate x 0 in a manner that preserves distances in Y yields good performance.


The repair policy receives notifications and decides which actions can fix the observed problems.

the worst performance is of the reactive Q function (Q 1 ) over the latest observation.


Using these equalities and Jensen's inequality, we obtain the following: where the last expectation is taken over the joint measure of Z T 1 and Z 0 T 1 .

the error is defined by but for notational simplicity we set l = 1.


. . , V n−f } is a vector proposed by a correct process.

we report here on the evaluation of the convergence and resilience properties of Krum, as well as an optimized variant of it.


Our method either outperforms competing methods, or is close to the best performing alternative.

for larger datasets, the bootstrap is to be preferred, since it costs O(m 2 ), compared with a cost of O(m 3 ) for Pearson (due to the cost of computing ( 8)).


We carried out two measurements that demonstrate the desired amplification by ABC, and the compressive growth of BM responses due to saturation.

im- plemented in the log-domain, with Class AB operation, our silicon cochlea shows enhanced frequency responses, with compressive behavior around the CF, when ABC is turned on.


A ratings r is called equivalent to r, denoted as r ∼ r, if P(r) = P(r).

with RDPS as the new assumption, we study the statistical consistency of pairwise ranking methods.


Based on the peaked prior assumption, p(µ) ≈ δ(µ− μ), we have p(x(t), φ) = p(x(t)|µ, φ)p(µ)p(φ) ≈ p(x(t)|φ, μ).

the intermediate layers demonstrate a multiplicative gain modulation by attention, as observed in primate V4 neurons [8]; and the temporal behavior of the final layer, representing the marginal posterior, qualitative replicates the experimental observation that LIP neurons show noise-dependent firing rate increase when aligned to stimulus onset, and noise-independent rise when aligned to the decision [13].


We provide efficient inference and parameter estimation methods for the latent subspace model.

the distribution q 1 is reconstructed once the optimal q 0 is achieved, see [25] for details.


The only lower bound of which we are aware is due to [20], which shows a bound of Ω(kd/ε 2 ) for learning mixtures of spherical Gaussians (and hence for general Gaussians as well).

density estimation has a long history in the statistics literature, where the focus is on the sample complexity question; see [6,7,19] for general background.


In modal regression, we are interested in estimating the modes of the conditional f (y|X = x) given samples from the joint distribution.

taking δ → 0 and r s → 0 gives us guarantees for all points which have a unique mode in which it can be assigned to.


Several recent papers have considered ways to alleviate this burden by incorporating prior knowledge into the metric, either in the setting of K-means clustering [1,2] or spectral clustering [3,4].

we have observed that for small q, the function to optimize is smoother and thus easier to optimize-in particular, the long plateaus of constant values are less pronounced.


The subjects were matched for sex and educational level, but not for age.

only yoked rats fail to acquire the escape response.


Hence, by grouping kernels generated from the same feature descriptor together and employing the new MKL formulation, classifiers which are potentially well-suited for object categorization tasks can be built.

the mirror-descent based algorithm presented in the paper not only solves the proposed formulation efficiently but also outperforms simpleMKL in solving the traditional l 1 regularization based MKL.


(ii) Generative modeling techniques in which a specific class of statistical models is chosen to describe the data.

to perform such optimization, the Minimum Description Length (MDL) principle [14] is used.


In this work, we show that one does not need a special training strategy such as stochastic depth to drop out layers.

it changes the distribution of paths seen during training.


, 0: = L Xi ,11"i O:Xi ,11"i ' The average parameter value OXi l11" i ' which typically serves as the regularized parameter estimate given a network structure m , is given by where N Xi ,11"i are the cell-counts from data D; E[•] is the expectation.

given a uniform prior over the network structures, p(m) =const, the posterior distribution p(mID) over the graphs thus becomes increasingly spread out as 0: grows, permitting more variable network structures.


Apart from network architectural designs, another direction is to exploit the interaction of appearance and motion information of action.

we cannot naïvely adopt the way of learning offsets in [2].


We employ 64 dimensional word embedding vectors and 128 dimensional hidden state for every LSTM.

moreover, the proposed model with history embeddings further increases the accuracy by 1.7%.


Note that the AHP effect of the output spike train can be modeled seamlessly (as a virtual synapse) in this framework.

a slight variation of the GRBF which takes the sum of Gaussian functions, rather than their product, was also explored.


In both the linear and nonlinear case, the architecture and training procedure remains the same as NCAR and C-NCAR, respectively.

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


We make use of graph convolution G conv from [11] to further propagate information on the graph.

a residual connection allows us to insert GCU into a network without changing its behavior (by using a zero initialization of the batch normalization after G conv ).


The simplest example of a covariant neural network is a classical S + 1 layer CNN for image recognition.

the final layer can be similar to the earlier ones, except that it only needs to output this single (single row) matrix.


In the presence of missing entries, the 1 -minimization in (2) becomes non-convex, since coefficients and a subset of data entries are both unknown.

getting trapped in local optima does not allow MFA to take full advantage of such a model, as opposed to SSC-Lifting.


We note that some other recently developed dropout-related methods, such as maxout, also involve an additional computational factor.

when evaluated on the MNIST and NORB datasets, we found that our method achieves lower classification error rates than other feature learning methods, including standard dropout, denoising auto-encoders, and restricted Boltzmann machines.


Figure 2 illustrates the convergence process of the SSEM algorithm compared to that of the EM algorithm for regression.

starting the RVM learning with as many basis functions as examples, i.e.


A positive time means the presynaptic spike was followed by a postsynaptic spike.

recall that the sliding threshold, θ is a function of the expected firing rate of the neuron.


Suppose player i is to play at s: under perfect recall, player i remembers the sequence of their own states reached, which is the same for all h ∈ s, since they differ only in private information seen by opponent(s); as a result For some history h and action a, we call h a prefix history h ha, where ha is the history h followed by action a; they may also be smaller, so h ha hab ⇒ h hab.

(i) both required Poker-specific domain knowledge, and (ii) neither were model-free, and hence are unable to learn directly from experience, without look-ahead search using a perfect model of the environment.


Essentially, after spending a certain cost we report a point (BO) or a classification (LSE), but there is no preference on the values of f (x t ) for the points x t chosen before coming to such a decision (in contrast with other notions such as cumulative regret).

in this paper, we provide a unified treatment of the two via a new algorithm, Truncated Variance Reduction (TRUVAR), which enjoys theoretical guarantees, good computational complexity, and the versatility to handle important settings such as pointwise costs, non-constant noise, and multi-task scenarios.


Note that since we only consider α < 2, the efficiency of d(α),fp does not achieve 100% when α → 2−.

samples of the stable distribution S(α, d (α) ), i.e., the task is to estimate the scale parameter from k i.i.d.


4 left) during test time to validate our network's robustness to non-uniform and sparse data.

to validate that our approach is suitable for large scale point cloud analysis, we also evaluate on semantic scene labeling task.


2) and they obtain similar final accuracy.

we have the following theorem that establishes the connection between ( 2) and ( 4): Theorem 1 The optimal objective p * to problem ( 2) is equal to the optimal objective p * δ to problem (4).


For example, the authors of [8] associate a measure of texturedness with each point in an image in order to suppress contour processing in textured regions and vice versa.

previous work on learning boundary models includes [11,7].


To better understand the operation of the novel kernel, we rewrite the kernel function K as follows: Figure 2: Non-zero entries of the matrix κ(t) that defines the mutagenetic tree Fisher kernel.

we now derive a Fisher kernel for the mutagenetic trees mixture models introduced in the previous section.


Lasso and elnet both show similar performances and give a stronger sparsity than ARD, which indicates that ARD fails to impose strong sparsity in this synthetic case due to its complete independencies among dimensions when data is less sufficient and noisy.

aRD returns a quite noisy estimation due to the complete independencies and weak likelihood.


our algorithms only require the ability to sample from a specific distribution over the decision set.


We consider learning a weight matrix consisting of the weight vectors for m linear predictive models: In this paper, we propose a non-convex multi-task feature learning formulation to learn these m models simultaneously, based on the capped-ℓ 1 ,ℓ 1 regularization.

moreover, the parameter estimation error decreases quickly and converges in a few stages.


For example, we can generate X as follows: where σ denotes a threshold.


Observe that when the matching graph M is such that deg M (u) > T n for some user u ∈ B ∪ G, no algorithm will be able to uncover all M matches in expectation, since Steps (1 B ) and (1 G ) of our learning protocol entail that the expected number of times each user u logs into the system is equal to T n . In fact, this holds even for the Omniscient Matchmaker A * , despite the prior knowledge of σ.

the following theorem guarantees that EM T (OOMM) = Θ T n 2 M , which is as if we were able to directly sample in most of the T rounds pairs of reciprocal edges.


The robot then keeps turning left and right.

in our work, we allocate grid points from a uniformly-spaced grid dynamically by simulating trajectories of the agent through the belief space.


For both datasets, Online RepOMP shows a better performance than Online SDS MA , Online RG, and the online dictionary learning algorithm.

a down-side of Replacement Greedy is its heavy computation: in each greedy step, we need to evaluate T t=1 f t (Z t ) for each (Z 1 , .


As in [5], we assume it employs independent Gaussian processes to capture the state change in each dimension for a given action.

our experiments demonstrated that the BA solution can be effectively approximated, and that the resulting generalization can lead to substantial gains in efficiency in discrete tasks with large trees.


The search is performed over the space of ordered decomposable DAGs.

the upper bounds obtained via BNSL can be at times can be quite weak when the network structures contain many immoralities.


Appendix VIII gives more details for both properties.

dN-p-LM can beat p-LMS by very significant differences (exceeding 40%), in particular when p < 2, i.e.


More precisely, assuming the system is initialized to a safe state (i.e., y 2 Y 0 = [y max /2, y max ]), then it should avoid an unsafe region (i.e., y = 0 ^(x  x p L _ x x p + L), where L is half the paddle length).

according to the 0-1 loss g(⇡), the worse policy ⇡ left (J(⇡ left ) = 0) is better, whereas according to our loss `(⇡), the better policy ⇡ right (J(⇡ right ) = (T ↵)) is better.


Could we recover the two-dimensional relations between pixels automatically?

how specific to natural images and how strong is that prior?


To evaluate the CA and CR rates, it is necessary to pick a threshold above which the classifier's probability estimate is interpreted as an "accept," and below which is interpreted as a "reject"-call this the criterion.

business practices complicate the scenario and place some unique constraints on predictive models.


We next present some examples that illustrate Theorem 1.

our setting is much more general than binary classification, and includes regression, multi-class classification and certain kinds of conditional random fields that are not covered by previous work.


By arguments similar to those in Theorem 4, it can be shown that any stable non-positive steady-state is unique, attains the minimum total opinion among steady-states, and is smooth and convex for decreasing h. The above result paints a significantly simplified picture of the MF-IIM problem when J is stronglyconnected and there exists a stable non-negative steady-state m(b).

theorem 3 shows that the objective M M F (b + h) is well-defined.


Signal model expressing the relationship between voxel activations and observed fMRI time courses.

neither of these assumptions is appropriate for studying functional specificity.


Multi-armed bandit (MAB) is a game that lasts for an unknown time horizon T [4,17].

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


Currently, it is only known how to solve conjunctive queries in ACs.

for all data sets, we divided the data into a single train, tune, and test partition.


The width η of the negative Gaussian is set to be twice as large as the width σ of the positive Gaussian.

after spikesorting, spike trains from 32 neurons were binned at 2 0ms resolution, and the response of a neuron to a stimulus at time t was defined to consist of the the spike-counts in the 1 0 bins between 40ms and 240ms after t. each population response Y t is a 3 20 dimensional vector.


[22] have raised issues with its convergence proof.

it cannot alleviate the large number of inference oracle calls unless the data is very sparse such that every instance appears only in very few blocks.


Note that for every w ∈ S u we have that ∆ G(s) (v, w) ≥ 2d/3.


The most difficult densities are those for which there are multiple widely separated modes, each of which is associated with disjoint subsets of the input mixture labels.

if the error is larger than Zδ, we need to refine at least one of the label sets; we use a heuristic to make this choice.


The first, "discriminative", criterion we consider is the single-linkage criterion.

t ′′ has fewer clusters that do not respect S hand T has, and hence we have a contradiction.


. . , ŵTn } of unit L 2 norm weight vectors where each ŵTi operates on a unit L 2 norm feature vector φ φ φ Ti (x, y).

but the support vector machine (SVM) substitutes the hinge for the discrete loss and, modulo a margin assumption, can nonetheless efficiently find a hyperplane with a guarantee of good generalization.


Note that neither of these steps depends explicitly on the observed values of the neural signal u t or the decoded output xt .

( 1)) and the electrode observations (CA, CB, and R C of eqs.


We use the ratio between the margin and the radius of the minimum enclosing ball to measure the goodness of a kernel, and present a new minimization formulation for kernel learning.

it has been shown in recent literature [7,9] that different types of norm constraints fit different data sets.


The update of θ is based on the samples generated from q φ (H|V), and is identical to (10).

in the work presented here, we introduce the Temporal Sigmoid Belief Network (TSBN), which can be viewed as a temporal stack of SBNs, where each SBN has a contextual hidden state that is inherited from the previous SBNs and is used to adjust its hidden-units bias.


A segmented image can provide a "target" transition matrix to which a learning algorithm matches in KL divergence the "learned" transition probabilities.

a low conductivity set A is a subset of I such that h(A) = max( P AA , P AA ) is small.


1 2 mln-w w 2 (1) For linearly non-separable problems, a generalization of the optimal hyperplane method has appeared in [2], where a slack variable f.i is introduced for each data point (xi, yi) for i = 1, ... ,n. We compute a hyperplane Wn that solves min~wTw+CLf.i s.t.

it is suitable for non-separable problems.


Other work proposes variants of semi-stochastic algorithms to approximate the exact gradient direction and reduce the gradient variance [47,34].

2 The dataset has high testing accuracy, so most of the examples are too easy for the model after a few epochs.


Our objective is to learn both the underlying tree structure T and the parameters θ using a max-margin setting.

it is possible that at the conclusion of this phase, the local structures do not fully agree (the relaxation is not tight).


The cost function is named size regularized cut (SRcut), and is defined as where is the size regularization term, which can be interpreted as below.

[16] modified k-means method to deal with a priori knowledge about must-link and cannot link constraints.


Note that we have also introduced Euclidean regularization over the parameters (i.e.

some recent work has been able to capture restricted forms of latent structure in a conditional model-namely, a single latent cluster variable [18][19][20]-but this remains a rather limited approach.


First, the group additive structure may not be unique, which will lead to the nonidentifiability problem for the group additive model.

thanks to the additive structure, the nonparametric estimation of f or equivalently the individual f i 's for 1 ≤ i ≤ p becomes efficient and does not suffer from the curse of dimensionality.


In GP ODE solvers they arise, perhaps more naturally but also with less structure, by the choice of the c i and the kernel.

there are no methods of order p > s. High order is a strong desideratum for ODE solvers, not currently offered by Gaussian process extrapolators.


The asymptotics mn−1(h) as n → ∞ imply that the mixture distribution Ln,K+ in (10) converges to the true Gaussian mixture distribution p T of (9).

we developed a fast online clustering and parameter estimation algorithm for Dirichlet process mixtures of Gaussians, capable of learning in a single data pass.


As a result, if max θ∈A λ | θ, xj | < mλ, we can also conclude that [β * λ ] j = 0 by (R1).

for j ∈ {1, . . . , p} and Px j = 0, let x = −ξx j . Denote , the dual problem of (UBP ) is equivalent to: We can now solve problem (UBP ) in the following theorem.


This endows DNN models with an ability of directly learning from attacks and further resisting them, in a principled way.

[1] present an information theoretic method which helps on improving the resistance to adversarial attacks too.


This trajectory is observed during model learning and is the inference target.

first, this task can be viewed as a stem towards the development of a Brain Machine Interface (BMI) which gradually and rapidly become a possible future solution for the motor disabled patients.


We focus on binary classification in the unit interval: X = [0, 1], Y = {0, 1}.

consider the moment when the teacher has already presented a teaching sequence (x 1 , y 1 ), .


We place each patient in a separate cluster, and then proceed in each iteration to merge the two clusters that are most similar to each other.

cardiovascular disease is the leading cause of death globally and causes roughly 17 million deaths each year [3].


Empirical evaluations have compared the appropriateness of different surrogate losses, but these still leave the possibility of undiscovered surrogates that align better with the ordinal regression loss.

the naïve implementation of SAG requires storing the gradient of each sample, which may be expensive in terms of the memory requirements.


(2) The second category [18,23,27,51,58,65] involves using the predicted labels of the unseen class data in an iterative model update/adaptation process as in self-training [62,63].

one approach to overcoming the above challenge is zero-shot learning (ZSL) [48,25,46,50,8,69,10,1,61].


This can be done via randomized rounding [Park and Boyd, 2015, Goemans andWilliamson, 1995]: Instead of letting x 2 [0, 1] n , the integrality constraint x 2 {0, 1} n in (3) can be replaced by the inequalities x i (x i 1) 0 for all i 2 [n].

we replace the quadratic programming relaxation of Kolter and Jaakkola, 2012 with a relaxation to an semi-definite program (SDP), which, based on the literature of relaxations is expected to be tighter and thus better.


We note that we and other authors found the most reliable criterion for comparing unsupervised POS taggers to be MTO.

we use the Wall Street Journal part of the Penn Treebank [8] (1,173,766 tokens).


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.

very recently, [33] made some progress towards this conjecture by proving that O * (d 1 4 ) gradient evaluations are required in the special case where U is separable into orthogonal O(1)-dimensional strongly convex components satisfying Lipschitz gradient, Lipschitz Hessian and fourth-order regularity conditions.


We demonstrate the proposed methodology for flow cytometry data auto-gating, described above.

when we say that the training and test distributions are "similar," we mean that there is some pattern making it possible to learn a mapping from marginal distributions to labels.


Remark 2 (ALTERNATIVE LOSS FUNCTIONS) For simplicity, all our results are stated for the case of the 0-1 loss I{g(X i , X j ) = e i,j }, but they straightforwardly extend to more practical alternatives such as the convex surrogate and cost-sensitive variants used in our numerical experiments.

we also showed how sampling schemes applied to the population of edges (not nodes) can be used to scale-up such ERM-based predictive methods to very large graphs by means of a detailed rate bound analysis, further supported by empirical results.


Evidently, for this problem the likelihood-based functions are poor surrogate measures for per-label accuracy: Figures 2c and 2d show declines in training and testing set accuracy, despite increases in the objective function.

to obtain a smooth approximation to this objective function, we can express the condition that the algorithm predicts the correct label for y (t) j in terms of the posterior probabilities of correct and incorrect labels as Substituting equation ( 8) back into equation ( 7) and replacing the indicator function with a generic function Q(•), we obtain When Q(•) is chosen to be the indicator function, Q(x) = 1{x > 0}, we recover the original objective.


Furthermore, the SVM performance (3.4% error) is currently the best result reported in the open literature.

the basic training principle behind SVMs is finding the optimal linear hyperplane such that the expected classification error for unseen test samples is minimized -i.e., good generalization performance.


Let Z be a countable space endowed with a probability mass function P(z).

similar to learnability, uniform convergence is, by definition, sufficient for generalization [1], but it is not necessary because the learning algorithm can always restrict its search space to a smaller subset of H (artificially so to speak).


We can compute wR t naively in O(N ) time by calculating w R t and keeping the K largest values.

though we can only guess at what class of memory models will become staple in machine learning systems of the future, we argue in Supplementary A that they will be no more efficient than SAM in space and time complexity if they address memories based on content.


Then for all other vertices i v ∈ Ω\{i p }, we compute the distance d ip,iv and check whether d ip,iv < ∆ 2 for some precision parameter ∆ > 0.

our final experiment is to evaluate the proposed SBA algorithm in estimating continuous graphons.


In this case, our experiments in Section 6 indicate that the MLE performs much better by managing overlapping decision regions more gracefully.

if Λ defines decision regions where multiple classes have approximately the same probability, however, then it is possible that ∆ MV (Λ) will be small.


The RBM also plays a critical role in deep belief networks [4], [5], but we do not use this connection in this paper.

the algorithm maintains a term ∂O/∂r t which is computed from ∂O/∂r t+1 and ∂ log Q(v t+1 |r t )/∂r t using the chain rule, by the equation where a.b denotes component-wise multiplication, the term r t .(1 − r t ) arises from the derivative of the logistic function s ′ (x) = s(x).


Using local kernel interpolation, the latent function f is expressed as a deterministic local interpolation of the inducing variables u (section 3).

we used a minibatch size of 5,000 for stochastic gradient training of SV-DKL.


As evidence, we reference figure 1, where we show Tensorflow with RMSProp efficiently finding and optimizing a least-cost path in a two-dimensional nonlinear Navigation domain.

hence, while larger optimization rates may cause overshooting the optima, rates that are too small may simply converge too slowly for practical use.


Similarly, for left turns, $ is biased to the left.

when T Q is very large, at some point, the left ring becomes inactive.


The areas where these relations are particularly strong are Shannon's coding theory [2] and classical spin systems with quenched disorder, which is the replica theory of disordered statistical systems [3].

the paramagnetic solution, which is also valid for general β, K, and C, is in the form of π(x) = δ(x) and π = δ(x); it has the lowest possible free energy per bit f PARA = −1, although its entropy s PARA = (R−1) ln 2 is positive only for R ≥ 1.


as a case-study, we consider whether GraphSAGE can learn to predict the clustering coefficient of a node, i.e., the proportion of triangles that are closed within the node's 1-hop neighborhood [38].


Let q ∈ {1, . . . , t} and P q be the matrix comprised by the top q eigenvectors of P . Then max argmax Proof See [15] for a proof of a slightly more general result (Theorem 3.4).

to find such a Λ and therefore recover the correct M , we need to enforce that we are at the optimal c (c * ), i.e.


In this paper we apply microphone array techniques to a manikin head.

then, rather than proceeding with peak-finding we employ discriminative learning methods by casting the azimuth estimation as a multiclass prediction problem.


We have provided a simple and efficient extension to the dominant-set clustering framework to deal with the grouping of out-of-sample data.

x S , which is the vector of ∆ n defined as is a strict local solution of program (4).


Input: Initial candidate architectures set X to train NAO model.

( 2), based on encoder E and performance predictor f . Denote the set of enhanced representations as E = {e x }.


From the training set, we randomly chose N = 100, 1000, or all labels for the supervised cost.

the proposed model is simple and easy to implement with many existing feedforward architectures, as the training is based on backpropagation from a simple cost function.


Let argmin i 1 d i and For q ∈ {2, ∞}, when λ ≥ λ max,q , the solution of the optimization program (4) is equal to Z = e 1 , where e denotes the vector whose elements are all zero except its -th element, which is equal to 1.

to do so, we propose a row-sparsity regularized trace minimization program on Z that consists of two terms.


A by-product of our analysis is the extension of the theoretical results of Mansour et al.

we used the full training sets per domain to learn the source model and densities.


The state space in the maze consists of the |S | = 36 rooms.

eB-CRP-PIG computed the best policy only once, yet, was able to outperform the exploit [15] strategy.


We note that Theorem 4 of [3] can be used to show that this bound does not, in fact, depend on and ¨.

this amounts to the mapping which sends a document 4 to its maximum likelihood model § 4 .


The corresponding NEO output of the raw sequence in (a).

1/f α −neuron noise is induced from distant neurons [12][13][14].


The same equality holds true for group B.

our work directly minimizes the amount by which each group's marginal reconstruction error increases.


At each iteration, SG-HT only evaluates gradient of one (or a mini-batch) randomly selected sample for variable update and hard thresholding.

as a direct consequence, the statistical error bound O( ∇ I f (x * ) ) of AHSG-HT can be improved in the sense that the cardinality | I| = 3k + k * has better dependency on the restricted condition number κ s . To better illustrate the boosted efficiency, we establish the computational complexity of AHSG-HT in IFO and hard thresholding in Corollary 2, whose proof is given in Appendix C.2.


6, we can write the value function as: where j indexes the possible sensing locations, and l j indexes the possible stopping actions for the sensing location j.

humans seem capable of planning and decision-making in very high-dimensional settings, while readily adapting to different behavioral context.


Small values of k correspond to more passive-like behavior, while larger values of k take fuller advantage of the sequential nature of active learning.

based on this quantity, we let Z = {(X t , Y t )} ∞ t=1 denote an infinite sequence of independent D XY -distributed random variables.


In this work, we therefore investigate discriminative learning of latent PCFGs, hoping to gain the best from both lines of work.

we extend this line of work by investigating discriminative estimation techniques for automatically refined grammars.


In principle, one could alternatively use a feature vector representation using these frequencies directly, as in (a).

to illustrate these definitions, we show that two specific cases of the naive Bayes and TFIDF classification methods belong to the class of algorithms described above.


The complexity is O(T N) per iteration, because updating any of the first T term approximations requires N operations.

computational complexity does not get worse than O(T N) and the resulting algorithm turns out to be faster.


. . , α d ), j ∈ [n], Following Scheme 2.1, we first describe the relevant parametrized subset of RLM problems.

due to difficulties which arise when studying the complexity of general optimization problems under discrete computational models, it is common to analyze the computational hardness of optimization algorithms by modeling the way a given algorithm interacts with the problem instances (without limiting its computational resources).


After x k visits the terminal state, it enters a recurring sink state x S at the next time step, incurring zero cost, i.e., C(x S , a) = 0, ∀a ∈ A.

we may rewrite (13) as From ( 14), it is easy to see that λ − λ1{s T ≤ 0}/(1 − α) is an unbiased estimate of the sub-gradient of L(θ, ν, λ) w.r.t.


When Hybrid-MST is in MST mode, the runtime is approximately n times more efficient than Crowd-BT and GM method.

recently, with the access of big data, preference aggregation from pairwise labeling has been widely applied in recommendation systems such as on movie, music, news, books, research articles, restaurant, products according to user's preference selection; or in social networks for aggregating social opinions; or in sports race, chess and online games to infer the global ranking of the players, etc.


A point in ds,dt is called an event, denoted by y = (y 1 , .

it is possible to construct a sub-manifold of K n so that the embedder can learn whether a dimension is space-like or time-like.


In this paper we consider the online version of MDPs when the reward function is allowed to change arbitrarily.

the requirement that the full reward function must be given to the agent at every time step significantly limits their applicability.


As the covariance matrix K n is fully occupied, the input points x are fully correlated within a piecewise trajectory, as well as across different trajectories; this enables the exploitation of high capacity correlations.

( [23], Theorem 5) the maximum information gain satisfies γ n = O log(n) d+1 , i.e.


The forward and reverse AIS estimators are shown in Figs.

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


The algorithm starts with a random parameter w and an empty constraint set.

[12] provides better detection results than ours on diving detection.


This is because w i = (1 + ν)y i for i = l + 1, . . . , n and ν ≥ 0.

it is only evaluated on the smaller data sets, i.e., "IBM-s" and "Course-s".


This is due to the prototype nature of the ASIC and its input/output; the core can already be operated about 20 times faster.

according to a special measure the performance peaks when the liquid is inbetween order and chaos.


The concept of nullspaces for linear operators is well-established [11], and does in many ways relate to real-number linear algebra.

it might be of interest to examine possible alternatives to this algorithm that does not use a parametric approach.


For example, in the case of news article recommendation, there may be thousands of articles, and some of those are bound to be similar to each other.

we are inspired by the kernel transfer learning framework of Blanchard et al.


SDP-cert provides non-vacuous certificates for all networks considered.

robust training on CNNs leads to better error rates: for example, adversarial training against the PGD adversary on a four-layer feedforward network has error 9% against the PGD attack, while a four-layer CNN trained using a similar procedure has error less than 3% [21].


Figure 7 depicts the system transforming an image patch from scale 2 to 3 of a 256x256 pixel image.

our results show that in many cases, a reduced representation of such two-way mappings can be found, even for small patches.


As such, even though we specify a prior on partitions with 2 L−1 − 1 changepoints, the resulting functions can appear to adaptively use fewer by averaging over the uncertainty in the discontinuity location.

the acceptance rate tends to decrease as higher posterior probability partitions A are discovered, especially for trees with many levels and large input spaces X for which the search space is larger.


A similar approach (VoxNet) was proposed in [19].

as 3D data is becoming more accessible, we believe that our method will stimulate more work on feature learning from 3D data.


M. Define q(x, z) = p(x)q(z | x), where q(z | x) is a fixed inference model.

it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator.


As has been pointed out in [4], the shape of unimodal tuning functions can strongly influence the coding accuracy of population codes of angular variables.

second, we will investigate how different noise correlations structures impact population coding on different timescales.


The model simply cannot assume highly unlikely stances-these are either not representable at all, or have reduced probability-and thus avoids compensatory, unrealistic body proportion estimates.

factor analysis is too limited to be of practical use, and GTM-while flexible-has two important practical problems: (1) the latent space must be discretised to allow tractable learning and inference, which limits it to very low (2-3) latent dimensions; (2) the parameter estimation is prone to bad local optima that result in highly distorted mappings.


the pdf in (3) can be treated as a probability mass function (pmf) over s ∈ κ(σ (i) (1 : t − 1)) and sampling from it becomes equivalent to sampling Hence, we can interpret a particle x (i) σ(1:t−1) as a sequence of indices of selected graph vertices σ(1:t−1) is a vector of ones assigned to RVs with indices in σ (i) (1 : t − 1).


YASS has demonstrated state-of-the-art performance in accuracy, stability, and computational efficiency; we believe the tools presented here will have a major practical and scientific impact in large-scale neuroscience.

each group can be processed in parallel, allowing for high data throughput.


Our approach begins with the augmented bases used in CBP, but adds basis vectors greedily, drawing on the well known Orthogonal Matching Pursuit algorithm [11].

cBP (with a Taylor basis) recovers coefficients using: Here we denote by F the matrix with columns {f n,j (t)} and F the matrix with columns {f n,j (t)}.


The VOR is a short-latency reflex eye movement that stabilizes images on the retina during head movement.


As we show in this paper, alpha-divergences have the disadvantage of inducing high-variance gradients, since the ratio between posterior and variational distribution enters the bound polynomially instead of logarithmically.

this expenses some tightness of the bound but makes the method more flexible by allowing us to optimize over V 0 as well, as we describe next.


In this section, we present the result of simulations comparing the monotone algorithm and our algorithm PFS r . The experiments were carried out as follows: given a buyer's valuation v, a discrete set of false valuations v were selected out of the set {.03, .06, . . . , v}.

for this setting, the buyer would no longer have an incentive to lie, thus, an algorithm such as binary search would achieve logarithmic regret, while the regret achieved by the monotone algorithm is only guaranteed to be in O( One may argue that the monotone algorithm is too specific since it admits a single parameter β and that perhaps a more complex algorithm with the same monotonic idea could achieve a more favorable regret.


The value of is the maximum sum of features that occurs in the training data.

mixture models [11] have been widely applied to problems in classification.


Influence spread maximization addresses the problem of selecting the most influential source nodes of a given size in a diffusion network [51].

we consider selecting a subset of Ω to maximize the facility-locationtype objective [30] f (S) = nuser i=1 max j∈S M ij .


As concrete examples, we show two screening methods SIS and HOLP are both strong screening consistent (subject to additional constraints) with large probability if n > O((ρs+σ/τ ) 2 log p) under random designs.

letting C = X T X/n and β be a given coefficient vector, the IC is expressed as for some θ > 0, where C A,B represents the sub-matrix of C with row indices in A and column indices in B.


SMartiRank will replace (2) with a comparison of sample estimates of the two quantities.

there is a node v i,t for each round 1 ≤ t ≤ T + 1 and each index 0 ≤ i < t (that is, for each bin constructed during training).


suppose we are given the predictions from some pre-trained model for N individuals, but are concerned that these predictions may not be fair.


It seems clear that distributed architectures will always be required for extremely large networks; however, as efficiency decreases with greater distribution, it also makes sense to study techniques for learning larger networks on a single machine.

preprocessing in each column comes from a convolution with a fixed set of filters, defined by the dictionary.


The robot fails to execute the specified move action and stays in place with probability 0.2.

it results in deeper networks that are computationally expensive to evaluate and more difficult to train.


Due to the fact that the cost function of MMP is piecewise defined, one cannot find a closed-form relation between ∆w and ∆v π .

a strong assumption considered in IRL-based al- gorithms is that the reward is a linear function of state-action features, and the frequencies of these features can be estimated from a few demonstrations even if these demonstrations cover only a small part of the state space.


This of course would not be realistic if D = 2 64 .

this may raise significant issues in user-facing applications where the testing efficiency is crucial.