We refer to this as our nonlinear relationship because it expresses bias b(x) as a nonlinear function of the squared discriminability D(x) 2 .

we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution.


Let y = (Y1, Y2 , ... ,Yn)T be the map from the graph to the real line.

it fo llows from the Stokes theorem that -div and V are form ally adjoint operators, i. e. if f is a function and X is a vector field fM (X, V f) = fM div(X)f. Thus We see that .c is positive semidefinite and the f that minimizes fM IIV fl12 has to be an eigenfunction of .c.


This analytical finding suggests the following generic, iterative procedure to obtain characterizers that minimize model variance: 1.

given an OOM A = (R m , (τ a ) a∈O , w 0 ) with an induced probability distribution P A , its reverse OOM A r = (R m , (τ r a ) a∈O , w r 0 ) is characterized by a probability distribution P A r satisfying A reverse OOM can be easily computed from the "forward" OOM as follows.


A dictionary of various matching pursuit methods and their corresponding parameters is provided in Table 1.

our formulation gives rise to a new class of influence measures that we call GrangerRanks, that may be seen as causality-based alternatives to hyperlink-based ranking techniques like the PageRank [17], popularized by Google in the early days of the internet.


The "Infomax" formulation of leA considers the problem of maximizing the mutual information between N-dimensional data observations {x} which are input to a network resulting in N-dimensional output signals {s} [6].

instead, it directly maximizes the mutual information between the outputs and inputs of a nonlinear network.


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

this crossover may reflect the presence of a much more sophisticated theory of force transfer than is captured by the spatiotemporal decay model.


1, we first notice that the same terms: appear on the RHS of the update rules of both algorithms.

finally, we conclude the paper and discuss some future directions in Section 5.


We could try to approximate this density function by placing Gaussian kernels on each observation u i and v i .

these two drawbacks can be addressed by recent methods in copula modelling called vines [1].


LSI uses singular value decomposition to discover the important associative relationships of word features [10], and create a reduced-dimension feature space.

cross language text classification is an important learning task in natural language processing.


On the other hand, for x ≥ λb , we have Thus, Algorithm 2 gives an option to trade-off consistency and robustness.

the processing requirement x j of a job j is unknown to the algorithm and only becomes known once the job has finished processing.


To illustrate structure learning in a simple task, suppose you are alone in a casino with many rooms.

because the subjects are not told the coupling state of the environment and the arms appear as separate options we conclude that people are capable of learning and exploiting task structure.


Then we have which is a standard result from the singular value decomposition (SVD) [12].

as some concrete examples, we can construct a large family of clipped µ 1 L q + µ 2 l 2 2 where 0 < q ≤ 1 by restricting f ′ i = w i I(|w i | < ǫ) + c for some constant ǫ and c. Also, SCAD [9] satisfies all three conditions so it belongs to f * .


Given a pair of input images {I 1 , I 2 }, we train a deep network to generate the dense optical flow field f = [u, v].

our approach differs from these methods in that we use both labeled and unlabeled data to learn optical flow in a semi-supervised framework.


The quality of a clustering using the measures presented in this paper can be computed in polynomial time in terms of n (the number of points in the data set).

while this intuition can be readily formulated in terms of clustering quality (namely, "changes as these should not decrease the quality of a clustering"), the formulation through clustering functions says more.


To alleviate the problem, different authors suggested to determine the dependence K * = K * (K) by various (rather ad hoc) empirical [15] or pseudo-Bayesian techniques [16].

the situation is even worse for the Laplace's rule, β = 1.


We will address the nondifferentiable training issue in Section 3.

but different from the synthetic experiments, LDA does not work well on these real data sets.


Both of these formulations can be explained as the same linear propagation framework of Eq.

the three-way connection, also with a sparse w t , can form a relatively dense A with the multiplication of several different tridiagonal matrices.


The storage capacity diverges as  Using a simple neural network model, we have discussed the mechanism that TAH enables the network to store and retrieve a pattern sequence.

in terms of the storage capacity, the covariance learning is better than TAH.


In classic popout experiments, a vertical line among horizontal lines presents a highly salient target.

given an analogous representation corresponding to higher visual areas that encode form, depth, convexity etc.


Question Answering The stanford question answering dataset [31](SQuAD) was recently proposed to advance machine reading comprehension.

we multiply G with task-specific features such as input embeddings and hidden states (see Figure 1).


But, you may tell when you just look at an image of actions, under the hints of the backgrounds, objects and postures.

the lower accuracy of variant (b) may indicate the uselessness of the extra attention mechanism on the inputs, since the learnt spatiotemporal features of 3DCNN have already paid attention to the noticeable spatial regions.


We next design a generic differentially private training and validation procedure that provides endto-end privacy provided this stability condition holds.


The commercially available 4-16 core CPUs on servers and desktop computers fall into this category.

in this paper we prove that online learning with delayed updates converges well, thereby facilitating parallel online learning.


We then describe how this approach can be generalized to compute low dimensional projections of the inputs via a novel direct optimization.

unfortunately, optimization of ǫ(M) subject to rank-constraints on M leads to a minimization problem that is no longer convex [8] and that is awkward to solve.


(3) The proposed method has no conflict with the weight regularization.

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


Thus the objective ∆ Eff can be interpreted as a (non-standard) information gain in terms of the (exponentiated) Rényi entropy.

this fundamental problem has been studied in a number of areas, including statistics [17], decision theory [13], machine learning [19,7] and others.


Note that the context range is determined from the boundary of one segment to the boundary of the other, and hence it is somewhat independent of the size of the object.

so we relax the constraint ∀i : This increases precision greatly at the cost of some drop in recall.


None of the methods could handle these effects when applied globally.

since the color change model represents a compact description of lighting changes, including nonlinearities, we are optimistic about these applications.


In addition, the practical termination criteria proposed for the previous PD method can be suitably applied to this method as well.

in Subsection 1.1, we introduce the notation that is used throughout the paper.


To correctly interpret the spatial uncertainty, e.g.

they do not represent observations of the exact same trajectory, but rather of distinct, nearby trajectories.


This line of research is orthogonal to our work since their analyses are regarding to the convergence of the distribution of the iterates to the stationary distribution of Langevin diffusion in total variation distance or 2-Wasserstein distance instead of expected function value gap.

bounding I 2 : Convergence to Stationary Distribution of Langevin Diffusion Now we are going to bound the distance between two invariant measures µ and ⇡ in terms of their expectations over the objective function F n . Our proof is inspired by [51,12].


In deep learning, two-part codes are widely inefficient and much worse than the uniform encoding (Graves, 2011).

deep learning models do not usually satisfy any of these hypotheses.


Interestingly, [6,9] have showed that SVRG can enjoy a linear convergence under the QEB condition.

then we compare SVRG QEB-RS and SVRG HEB-RS to other baselines for solving different problems on different data sets.


The following theorem shows that with appropriate parameters, NC-SMD (Algorithms 1) achieves an O( √ T log T )-regret bound.


This is consistent with the notion that using a "defensive" q distribution is advisable when it is not well matched to p (e.g., before optimization has completed).

consider again the "ELBO decomposition" in Eq.


As mentioned earlier, it is possible to obtain a result with variable learning rate where η = η i decays as i increases.

but in practice, as is also verified by the theory, one should adopt a small g; hence, the new learning rule ( 6) is expected to differ from (4).


Our goal is to cluster these multi-dimensional time-series automatically into a small number of motion templates without pre-labeling of the trajectories or assuming an a priori number of templates.

we will first introduce a generative approach for clustering and modeling multi-dimensional time-series with Bayesian Mixtures of LGSSMs and describe how this approach can be made tractable using a variational approximation.


For a given in-degree K, λ can then be plotted as a function of the STD of weights σ (centered at the critical value σ 0 of the STD for that K).

c) Same as panel B, but for an in-degree of K = 24.


Therefore, Finally, for any b ∈ ∆(∼ Γn ) and s ∈ S with b(s) = 1, and any other state ŝ with b(ŝ) = 1, it must be the case that s ∼ Γn ŝ and T n (0)(s, ŝ) = 0.

we can use this result in the definition of local refinement Γ j−1 ζj Γ j to conclude that s ∼ Γj−1,ζj s . Moreover, as ŝ This completes the definition of consistency on η, and it becomes clear that s ∼ Γn−1,ζn s ⇒ s ∼ Γ0,η s , or ∆(∼ Γ0,η ) ⊆ span(∆(∼ Γn−1,ζn )).


We also define B O = max s,o supp(p(•|s, o)) (resp.

characterized by a transition matrix This suggests that, given an estimate of P o , we could directly derive the corresponding estimates of R(s, o) and τ (s, o).


As suggested by Theorem 3 in almost all cases the normalisation improved the performance of the support vector machine solution at a statistically significant level.

in the case of linear classifiers, often a thresholded real-valued func-tion is used for classification.


By analogy, after observing matrix data with sufficient statistic S t = t q=1 X t , matrix Laplace predicts with the correspondingly smoothed matrix W t := St+I t+n .


In the legend, the estimated slopes of ∆R π (T ) (in logarithmic scale) are indicated after the policy names.

assuming, for example that µ 1 = µ 2 + ∆, then an ETC strategy π chooses the suboptimal arm We denote the set of all ETC strategies by Π ETC .


[31] to provide a general Optimistic Values Theorem in Appendix B.

a common assumption-when using linear regression for contextual bandits [20] and for reinforcement learning [31]-is that the variance of the target is a constant value 2 for all contexts x.


This makes computing even the expected value of max α β A,α an intractable task, let alone obtaining concentration of measure results that could give us upper bounds on the probability of condition 14 holding under the assumed distribution on A.

mLKNN's two parameters k (number of neighbors) and s (strength of the uniform prior) were kept fixed to 10 and 1.0, respectively, as was done in [20].


We also hope to explore applications to other domains such as gene expression data to refine the current logarithmic transforms necessary to compensate for well-known saturation effects in expression level measurements.

this method can get stuck in local minima.


The sociability and receptivity factors, referred to as control parameters, support a clear picture of the asynchronous, synchronous aperiodic and periodic synchronous patterns.

an asynchronous aperiodic regime (region B) is prone to evolve into an asynchronous (region A) or periodic synchronous (region C) regimes (Figure 6).


The asymptotic expansions in [43,37,23,40] likewise do not provide a computable finite-sample bound.

that algorithm suffers from the cost of cross-validating over both the dimension d and number of neighbors k. Also, the technique is only applicable in Hilbert spaces (as opposed to more general metric spaces) and provides only asymptotic consistency, without finite-sample bounds such as those provided by KSU.


This observation, combined with Theorem 2, leads to the following interesting consequence.

in all experiments, we set the algorithm parameters so that the empirical probability of successfully finding the exact nearest neighbor is at least 0.9.


The PMOS source follower M 3 − M 4 is used as a level shifter.

figure 5 illustrates this behavior in response to an input spike train of fixed duration.


observed data can be described by a set W := {W xy } x∈X ,y∈Yx where W xy is a real-valued score given to item y in context x.


Sequential effects have been demonstrated in domains as varied as legal reasoning and jury evidence interpretation (Furnham, 1986;Hogarth & Einhorn, 1992) and clinical assessments (Mumma & Wilson, 2006).

because responses are influenced by recent context, they are not as pure a measure of an individual's stimulus appraisal as one might wish for.


We have evaluated seven nowcasting algorithms, including the simplest model which always predicts the last frame, two optical flow based methods (ROVER and its nonlinear variant), and four deep learning methods (TrajGRU, ConvGRU, 2D CNN, and 3D CNN).

in this paper, we have provided the first large-scale benchmark for precipitation nowcasting and have proposed a new TrajGRU model with the ability of learning the recurrent connection structure.


If the set of under-explored arms contains at least B arms, i.e.

note that by this procedure, even in exploration phases, the algorithm exploits whenever the number of under-explored arms is smaller than the budget.


More importantly, the generative models considered in these studies were tailor-made to the specific pscychophysical task presented in the experiment.

these studies demonstrated that human observers parse sensory scenes by performing optimal estimation of the parameters of the objects involved [3,4,5].


. . , L N ) decompositions of X and rank-(1, K 2 , .

the nth-mode matricization of a tensor X is denoted by X (n) .


Furthermore, complex Ising models have found widespread use in machine learning, and our model is formally equivalent to a pair-wise Markov random field or a Boltzmann machine [18][19][20].

in the next section we show that if there exists a stable and entry-wise non-negative steady-state, and if J is strongly-connected, then M M F (b + h) is both smooth and concave in h, regardless of the interaction strength.


Our construction works by designing a sequence of functions f i where for a fixed n ∈ N all f nτ +j are identical (for j ∈ {1, . . . , n}).

this leads to bounds which, while still bearing a linear penalty in τ , make do with considerably improved constants.


Instead, we connect BP to the one-step gradient update solution of (3) and (4) and argue that the conditions of the subproblems (3) and (4) affect the efficiency of BP given the explanation of back matching loss.

there is no clear understanding on what is essential to the efficiency of BP.


Proof of of Corollary 2.2: We first observe that we have Obviously, the inclusion "⊂" directly follows from the above monotonicity.

given a function f : X → R, Lemma 2.3 shows that for P X -almost all x ∈ X there exists a unique t * (x) is the element in M * (x) that has the smallest distance to f (x).


All experiments were performed on the Shoes dataset [53], with the same training and testing data split for all retrieval methods and for training the user simulator.

the user provides iterative feedback about retrieved objects, so that the system can refine the results, allowing the user and system to engage in a "conversation" to resolve what the user wants to retrieve.


The target speech recognition system in this work consists of CTC-trained AM, RNN LM, and beam search decoder.

we used uni-directional models because this implementation is intended for online speech recognition.


The authors in [18] show that a neural network with ReLU activation functions can learn to perform holographic image reconstruction.

based on these attributes, we will introduce a gradient descent scheme to converge to the global minimum.


In order to handle many data sizes n simultaneously, we borrow from the idea above.

note that traditional lower-bounds for the offline setting derive a different worst-case distribution for each sample size n. our lower-bound is more appropriate to the streaming setting where the data arrives over time from the same distribution.


Many problems in statistical pattern recognition and analysis require the classification and analysis of high dimensional data vectors.

more specifically, the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform (SMT).


Since γ * 2 can be expressed as the optimum of semidefinite program, we can find in polynomial time a probability distribution P and a weight function Q on S such that γ * 2 (P − Q) is minimizd.

the analysis of random samples does not help us here, because these proofs do not reveal the structure that makes generalization possible.


The facial structure of the cut polytope, equivalently, the binary marginal polytope, has been wellstudied over the last twenty years.

[1] analyze the GMEC polyhedron, which is equivalent to the marginal polytope.


The cop arrested by the detective was guilty of taking bribes.

the cop / arrested by / the detective / was guilty / of taking / bribes.


In the following, we consider to upper bound A and B.

given a class of models parameterized by w and a loss function ℓ(•, •), the goal is to minimize E XY [ℓ(w; X, Y )] w.r.t.


it is unknown if their algorithm can find such minimizer since there could be many other local minimizers.


A sample of the results is shown in Figure 4; as can be seen, the proposed algorithms UCB-TC, UCB-UC, and UCB-BA generally outperform existing baselines in terms of minimizing regret relative to the top cycle, the uncovered set, and the Banks set, respectively.

for the three tournament solutions discussed above, we will define the following natural notions of individual regret: ∈ TC(P) In the special case when P admits a Condorcet winner i * , the three individual regrets above all reduce to the Condorcet individual regret, r CW P (i) = ∆ P i * ,i .


In addition, we show that in the stochastic setting SODA achieves an O a:∆a>0 Kε 2 ∆a pseudo-regret bound that holds simultaneously with the adversarial regret guarantee.

first we provide an upper bound for the expected regret of SODA against oblivious adversaries that produce loss sequences with effective loss range bounded by ε.


Therefore, for simplicity we will consider trajectories that are confined to the nonnegative orthant x 2: 0.

it has long been known that lateral inhibition in neural networks can lead to a winner-take-all competition, so that only a single neuron is active at a steady state.


To the best of our knowledge, there is no analytical solution to the influence estimation given Weibull transmission function.

(see Appendix F for additional results on the random and hierarchal networks) Scalability.


We measure this in the manner of [15]: remove a fraction (=50%) of graph edges, learn embeddings from the remaining edges, and measure how well the embeddings can recover those edges which have been removed.

if according to the objective, a graph is more accurately encoded by making longer walks, then they can learn to use a large C (e.g.


Since the αs are non-negative, and since there are ties neither the αs nor in the βs, the rearrangement inequality implies that the minimum value of R (p σ , σ ) is obtained for the single permutation σ for which the β σ -1 (k) are in reverse order relatively to the α σ -1 (k) (i.e.

[11] showed that many convex losses based on pairwise comparisons, such as those of RankBoost [12] or Ranking SVMs [14,4], are not calibrated with respect to the PD.


In this section we empirically compare SCIR to SGRLD on two challenging models: latent Dirichlet allocation (LDA) and a Bayesian nonparametric mixture.

the CIR process has a lot of nice properties.


However, across all problems, no person consistently outperformed the model.

in an ideal model, the aggregate answer should be as good as or better than all of the individuals in the group.


The mechanism which accepts examples from the oracle with some probability is called the filter.

vanilla FilterBoost and MadaBoost perform similarly in classification (Figure 4).


Fast multipole methods tend to work only in low dimensions and are specific to the choice of similarity metric.

in the following section, we introduce methods to speed up the matrix-vector product v = Aq.


Provided the generative model is stationary (i.e., x 0 = 0 and Q 0 = Π), SSID algorithms yield consistent estimates of the parameters A, C, Q, R, d without iteration.

an alternative is the spectral approach known as subspace identification (SSID) in the engineering literature [3,4,5].


as shown in Figure 4, the CRP prior was more effective than Bayes factors in this setting.


In the design of this algorithm and its performance analysis, we face two challenges: (i) we only have access to a sampled version A (B) of M (B) ; and (ii) U Σ(V (B) ) is not the SVD of M (B) since the column vectors of V (B) 1:k are not orthonormal in general (we keep the components of these vectors corresponding to the set of indexes B).

to translate our bound (1) in an additive error is easy: Sparsifying M to speed-up the computation of a low-rank approximation has been proposed in the literature and the best additive error bounds have been obtained in [AM07].


Thus, computing the proximal operator has polynomial complexity since SFM has polynomial complexity.

if the weight function d is symmetric, then the submodular function is also symmetric.


Using the multiplicativity and the low of total expectation, the proof is completed as As Eq.

as a result, the DEPM significantly outperformed the CEPM in both generalization ability and link prediction accuracy (Figs.


[17], who show that that locally private algorithms coincide with concepts that can be learned with polynomial sample complexity in Kearns's statistical query (SQ) model.

indeed, if we can find P * and Q * satisfying the saddle point (4), then the trivial direction of the max-min inequality yields To fully formalize this idea and our notions of privacy, we define two collections of probability measures and associated losses.


the training and test vocabularies are different.


Our problem (3) is a special instance of MWIS problem, since graph G exhibits an additional structure, which we will unitize in the proposed algorithm.

given an image, they first segment it with different bottom-up segmentation schemes to get an ensemble of distinct superpixels.


. . , X k } such that all variables in the subset take distinct values.

( 2) holds with at least probability 1 − δ: Proof.


We also do experiments on the Multitask Learning [6] problem to demonstrate that our algorithm can be used on very large datasets.

katyusha cannot solve the problem with linear constraints.


In CS-MRI, it commonly needs to run the ADMM algorithm in dozens of iterations to get a satisfactory reconstruction result.

2 Deep ADMM-Net for Fast MRI General CS-MRI Model: Assume x ∈ C N is an MRI image to be reconstructed, y ∈ C N ′ (N ′ < N ) is the under-sampled k-space data, according to the CS theory, the reconstructed image can be estimated by solving the following optimization problem: where is a under-sampling matrix, and F is a Fourier transform.


3, we empirically confirm that the recall value of geometrically related predicates are significantly increased, such as using, carrying, riding.

compared to previous models [33,18] that have been proposed to focus on message passing between nodes and edges, our model explicitly reasons about the relations within nodes and edges and predicts graph elements in multiple steps [35], such that features of a previous stage provides rich context to the next stage.


In computer graphics, BRDFs are most often specified using various analytical models observing the physical laws of reciprocity and energy conservation while also exhibiting shadowing, masking and Fresnel reflectance phenomenon.

random utility models such as (1) have a long and influential history in psychology and the study of individual choice behaviour in economic markets.


This statement may seem counter-intuitive given the known result that polynomial kernels K(x, y) are positive definite kernels.

figures 3(b) and 3(c) show the effect of the CRAFT method on MSE and classification accuracy.


First, activity of non-monitored presynaptic neurons may significantly distort reconstruction results.

naturally, in the presence of noise, reconstructions cannot be exact.


In this paper we have introduced Sobolev Training for neural networks -a simple and effective way of incorporating knowledge about derivatives of a target function into the training of a neural network function approximator.

[30] and antecedents propose a technique for Bayesian optimisation with Gaussian Processess (GP), where it was demonstrated that the use of information about gradients and Hessians can improve the predictive power of GPs.


In this paper , we present a new algorithm and an accompanying framework of analysis for geometrically motivated dimensionality reduction.

th e Laplacian of the graph obtained from the data points may be viewed as an approximation to the Laplace-Beltrami operator defined on the manifold.


Early research in human concept attainment suggested that learners do benefit from the opportunity to actively select examples during learning [11].

at iteration i of the learning task, a single shape at X i was displayed on a CRT monitor at a normal viewing distance.


Note that c/2 is the expected degree of the G ER (p, c/p) ensemble.

similarly, for both the Erdős-Rényi graph ensemble G ER (p, c/p) and small-world ensemble G Watts (p, d, c/p), we can establish that the threshold J * = Θ(1/c), and thus, the observations made for the Gaussian setting hold for the Ising model as well.


If we had connected the output of the horizontal stack into the vertical stack, it would be able to use information about pixels that are below or to the right of the current pixel which would break the conditional distribution.

as noted in [27], we observed great improvements in the visual quality of the generated samples.


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

the EA updates and fitness evaluations have a fairly small computational cost compared to the SGD updates.


Throughout the paper, the measures P o and P 1 assign probability measures to the paths X τ (t)|Θ = 0 and X τ (t)|Θ = 1 respectively, and we assume that P o << P 1 3 .

we conclude our analysis for the process µ t by noting that lack of information samples creates bias towards the belief that Θ = 0 (e.g.


The worst mean configuration (γ = 0.9 and h = 3) still outperforms EI by 0.5%.

the nested maximizations are replaced by the use of the base policy π.


Speed optimization of our software implementation is under way.

because such moves have a negative score and a card move from the pile to the talon or from the talon to the pile has zero score and is almost always available, our strategy would always choose the pile-talon move over the moves from a suit stack to a build stack.


According to the Bayesian model, these vi-sual and auditory inputs are represented by random variables V and A, respectively.

thus the ML model can also deal with the important tasks of stimulus discrimination and identification in the presence of incongruent visual and auditory cues.


If the method is not consistent, then the local error does not converge when the step size goes to zero.

stability may also be tackled by recent advances in lower bound theory provided by Taylor [2017] but these yield numerical rather than analytical convergence bounds.


However, these special conditions may fail to hold for generic complex objectives involved in practical applications.

in this paper, we explore the asymptotic convergence rates of the CR algorithm under the KŁ property of the nonconvex objective function, and establish the convergence rates of function value gap, iterate distance and second-order stationary gap for CR.


This posterior has the same structure as the full model, and in particular it maintains the correlations between layers.

we first sample l i ∼ N (0, I D l ) and then recursively draw the sampled variables where the terms in ( 15) are D l -dimensional and the square root is element-wise.


To perform sparse coding, we alternative between the two phases: 1) computing the sparse codes given LDS dictionary, which is similar to the conventional sparse coding task [13]; 2) optimizing each dictionary atom with the codes fixed.

we also report the running time for one epoch of each algorithm in Fig.


The resulting large weight of this feature is plausible as a surface-to-surface mapping is a necessary condition for a morph.

note that although the results are not identical to [1], our algorithm's accuracy is consistent with the human labeling on the scale of the latter's presumed accuracy (1-2mm).


This in turn helps us select a small number of columns of M β in a fast and greedy way to be the kernel matrix K. We defer the exact details on kernel selection to a later section ( §4.3).

the Markov matrix M is diffused using a small number of iterations to get M β .


Our approach satisfies the error bound tighter and reduces computational cost because: • Each cluster's maximum truncation number no longer depends only on its farthest point, so if most points are clustered close to the center the maximum truncation will be lower; • The weight of each source point is considered in the error contributions, so if a source point is far away but has a weight of q i = 0 its error contribution will be ignored; and finally • Each target can use a truncation number that depends on its distance from the cluster.

for each dataset we ran five experiments: the first four fixed one of the four methods (direct, direct+tree, ifgt, ifgt+tree) and used it for all conjugate gradient iterations; the fifth automatically selected the best method at each iteration (denoted by auto in figure 6).


Other attributes indicate whether the subject line or the sender address have been observed before within a window of time.

let x −i , t −i denote the sequence x, t without instance x i .


Our baselines demonstrate that deep reinforcement learning agents can learn to navigate in multiple cities and to traverse to target destinations that may be kilometres away.

we note that there are obvious limitations of our environment: it does not contain dynamic elements, the action space is necessarily discrete as it must jump between panoramas, and the street topology cannot be arbitrarily altered.


Note that h(⌧ ) is continuous and strictly decreasing, with h(0) = ⇡ 1 and h(1) = ⇡ 1 .

interestingly, OFO seems to properly adjust the values 1/b t+1 in an adaptive manner (b t is a sum of two terms, the first of which is t⇡ 1 in expectation), which is a very nice property of the algorithm.


Fourth, each component identification optimization typically takes ∼ 10 −5 seconds, and thus matching accounts for less than a millisecond of total computation and does not affect the overall computation time significantly (Figure 3d).

the use of ( 1) with mean-field variational approximations thus requires first solving a component identification problem.


In the next section we formally describe the framework that uses output coding for multiclass problems.

an example i "participates" in the solution for M (Eq.


Using (5), we obtain the predictive distributions p(y * |g * i , G, y) for all the g * i .

minutiae that are spatially close tend to have similar directions with each other [18].


Our base kernel set {k u } d u=1 contained only d univariate kernels with fixed bandwidth (one for each dimension): in other words, this was a feature selection problem.

the testing problem becomes more difficult when the number of Gaussian centers in the grid increases, and when ε → 1.


Attention learning has benefited from advances in deep learning.

to create the 'foreground' object s f ∈ T , we apply s a to F S→T (s) via an element-wise product on each RGB channel: s f = s a F S→T (s) (Figure 2 shows an example).


Here, we simply fix them to the set of vectors {−1, 1} R and use the differentiable approximation from [9] to backpropagate gradients through this non-differentiable embedding.

visual quality can be improved by incorporating generative adversarial networks (GANs) [14] into the learning process [4,15].


The primary contribution of this paper is a new framework for parallelizable feature selection, which is inspired by the theory of group testing.

for multi-class classification, mutual information (MI) is a popular choice.


We refine the initial estimate of Stage 1 by maximizing the objective function, which is implemented by the Expectation Maximization (EM) algorithm.

there will be three copies of W estimating the same matrix W -we average them for the best accuracy.


3, all of the performance metrics were higher when both sequence and structure information were used together.

direct identification of mature miRNAs is infeasible due to their short lengths, and researchers instead aim at identifying precursor miRNAs (pre-miRNAs).


The same holds for finite dimensional kernel clustering.

d.3 executes the general plan outlined above to prove our theorem.


Counting the number of parameters and constraints suggests identifiability when k < d − , but this is by no means a precise guarantee.

any rotation of p is an isotropic Gaussian, and so z ⊥ and z are independent, and p(y) = p (y )p ⊥ (y ⊥ ).


In this paper, we consider linear hypotheses only.

the commonality between the domains is represented by g c whereas g s and g t capture the idiosyncrasies of the source and target domain, respectively.


Here, different subspaces may correspond to motion of different objects in video sequence [11,17,20], different rotations, translations and thickness in handwritten digit or the latent communities for the social graph [15,5].

the support recovery analysis of Lasso does not extend to this case, as X −i typically does not satisfy the RIP condition [18].


The ventral striatum involved in reward prediction error δ(t) on shortest time scale (γ = 0), while the dorsolateral striatum correlated with reward prediction V(t) on longer time scales (0.9 ≤ γ ≤ 0.99).

in order to maximize the reward acquired in a long run, the subject has to select an action by taking into account both the immediate reward and the future reward expected from the subsequent state.


A compendium of gene expression experiments used in [Marion et al., 2004].

the proof for the GaBP case, however, does not carry over to the CBN setting and shedding theoretical light on this issue remains a future challenge.


when we can process a large number of examples on each machine at each round).

comparing (18) to the lower bound ( 16) we see a gap by a factor of K 2 in the optimization term, indicating the possibility for significant gains when K is large (i.e.


To reduce this complexity, Suttorp et al.

when replacing s t by ŝt = A −1 t (m t+1 − m t ), we obtain −1/2 t by A −1 t introduces a new random rotation matrix E T t , which changes in every iteration.


However, weighting the two visual cues using the α parameter described in equation (3) in the independent estimation of p(s, c|class) improves the results significantly.

these approaches combine multiple cues and multiple kernels and apply per-class cue weighting.


Moreover, we present a noise calibrated tensor power method with efficient privacy guarantees.

we consider sub-Gaussian noise as formulated in Definition 3.1 and Assumption 3.2: Definition 3.1 (Multivariate sub-Gaussian distribution, [15]).


1 defines the likelihood maximization problem, which is iteratively solved using EM.

an approach for exploiting embedded structure in the transition and observation functions is to replace the exact forward-backward message computations with exact forward filtering and backward sampling (FFBS) [11] to obtain a sampled reverse trajectory consisting of �s T , n T i,l , a T i �, �n T −1 i,l , a T −1 i , o T i , n T i,l �, and so on from T to 0.


It is therefore important to develop theoretical tools to analyze the spectra of these matrices.

as a first step in that direction, we focus on the properties of the layer-wise block structure in the Fisher induced by the neural network architecture.


The image-level feature is the concatenation of feature representations of all detected regions from the corresponding image.

when a template model is matched to a given image, not all templates within the model are necessarily used.


The dataset used for these experiments is already larger than those used for published results for genre and artist classification.

these CF recommenders (CFRs) harness the "wisdom of the crowds" to recommend music.


We used mini-batches of size 100 and the step-size of 10 −α , where α is an integer between 0 and 10.

to see this, we consider the vector π(w), the path vector, where the number of coordinates of π(w) is equal to the total number of paths from the input to output units and each coordinate of π(w) is the equal to the product of weights along a path from an input nodes to an output node.


Our results were produced using an active set size M = 60.

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


So we simplify the dataset slightly by normalizing the lighting variations across images.

the M-step also changes the mixing proportions of the component models to match the proportion of the training data that they are responsible for.


In recent years, there has been a trend towards unified statistical analyses that provide statistical guarantees for broad classes of models via general theorems [12].

given the joint distribution in (10), the conditional distribution of X s given the rest of the nodes is given by: Let θ * \s = {θ * st } t∈V \s ∈ R p−1 be a zero-padded vector, with entries θ * st for t ∈ N (s) and θ * st = 0, for t ∈ N (s).


4(a) and 4(d) show that for this dataset our algorithm does not get trapped when initialization is poor (as in Fig.

3.2 bring the associated update cost to O(zn) by updating L z rather than recomputing it.


All participants worked on all four of the memory tasks, with interference avoided with the use of semantically distinct category pairs across the four conditions.

this affects recall, but not recognition for the same reasons the list strength effect does.


We would like to differentiate W U with respect to U .

we now derive formulas for the first and second order derivatives of f . In deriving these formulas, it is useful to note that, for a suitably smooth mapping g, grad X → 1/2 g(X) 2 where Dg(X) * is the adjoint of the differential of g at X.


6 For each of these datasets we trained a logistic regression model, and evaluated using the logistic loss (LogLoss).

this leads to very bad performance for standard AdaGrad DA and GD as D gets large.


A common assumption in supervised learning is that training and test samples follow the same distribution.

following this spirit, the kernel mean matching (KMM) method has been proposed recently [6], which directly gives importance estimates without going through density estimation.


The rank-differentiable property is defined on the space of multi-level ratings while the orderpreserving property is defined on the permutation space.

in the proof of [11], they do not take the constraint of multi-level ratings into consideration, thus deduce contradict results.


The exact solution to this problem would require, in the worst case, the solution of |Γ a | × |Γ a ′ | LPs of the form (11) for every pair of actions with conflicting value bounds.

the resulting equation can be rewritten as: with β ∈ R n , γ ∈ R m and δ ∈ R. By maximizing (or minimizing) the terms associated with the potentially free variables, we can use this form to establish the maximum (and minimum) value that can be attained at b L . Theorem 1. . . , m and β ∈ R m : β i = min j∈Ii β j , i = 1, . . . , m. The maximum achievable value for a local belief point, b L , according to α, is: Analogously, the minimum achievable value is Proof.


Benefits of this untying are twofold: (1) Now the weight matrices W xh • , and W hh • are of size |h| × |x| and |h| × |h| which means that we can use large pretrained word vectors and a small number of hidden units without a quadratic dependence on the word vector dimensionality |x|.

number of hidden units in a single hidden layer).


In this limit, recovering the ground truth Z from noiseless measurements is as easy as solving a system of linear equations.

good initializations are highly problem-specific and difficult to generalize.


Formally, a set function , where the marginal gain F (i | X) is defined as F ({i} ∪ X) − F (X).

as a concrete example, the graphic matroid of a graph G = (V, E) is generated by the (arbitrarily oriented) edge-vertex incidence matrix U ∈ {0, ±1} (|V|−1)×|E| of G after removing an arbitrary vertex.


First, the trace and 1 terms that are involved in the objective of (3) can be calculated with respect only to the entries in the columns I j (the rows are taken into account by symmetry).

[20,12] consider block-coordinate-descent methods where in each step t a subset J t of variables is updated.


Different loss functions lead to different learning algorithms.

to our knowledge, few learning algorithms and applications have been studied along this line from a unified RKHS regularization point of view, or investigated for empirical evaluations.


Finally, we encode and align pairs of profiles using the learned classes, comparing the results to those obtained both with the full profiles and with just the original sequences.

the latter is important because the best path can be very sensitive to small changes in the sequences or scoring matrix; if two radically different alignments have similar scores, neither is clearly "correct".


Once our model is trained, we can obtain a compact network for faster and more memory-efficient inference by making use of a post-processing step.

in essence, and by contrast with methods that aim to learn uncorrelated units to prevent overfitting [5,54,40], we seek to learn correlated ones, which can then easily be pruned in a second phase.


More importantly, for the robust matrix decomposition problem considered [1], only the sum of error bound of two matrices (low-rank matrix and the sparse corruption matrix) can be obtained under the assumption of restricted strongly convexity.

in this paper, we focus on the following questions: under what conditions for the size of the tensor, the rank of the tensor, and the fraction (sparsity level) of the corruption so that: (i) ( 2) is able to recover W * and V * with small estimator error?


Since the trajectories of the output of a linear dynamical system live in the so-called observability subspace, the intensity trajectories of pixels associated with a single dynamic texture lie in a subspace.

in addition the fixed projection and the recursive estimation of the polynomial coefficients make our method much faster than GPCA.


To derive an estimator of the parameter β * , we place ourselves in the Bayesian framework.

this investigation is left for future research.


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

contain the full information needed to attend to the regions within the image and answer the question accurately.


Also, as the results show, learning a purely discriminative model at the top level of a DBN gives much worse performance.

the two types of update for the c th slice of the tensor W •,•,c are then combined by a weighted sum: where λ is a parameter that sets the relative weighting of the generative and discriminative updates, and η is the learning rate.


Problems may arise if the search engine deploys the classifier, and starts featuring search results that are predicted to be newsy for some queries: promoting the search result may lead to a higher CTR, which in turn leads to higher newsiness predictions, which makes the result be featured even more.

much of the work on model feedback in fields like finance, education, or macro-economic theory has focused on negative results: there is an emphasis on understanding when feedback can happen and promoting awareness about how feedback can interact with policy decisions, but there does not appear to be much focus on actually fitting feedback.


Our result supports the use of a local approximation based on representative states spread over the state space S. This is in line with the quantization strategies used in batch-mode kernel-based reinforcement learning to define the states s j [4,5].

we compare iKBSF with fitted Q-iteration using an ensemble of 30 trees generated by Ernst et al.


Meanwhile, by (b) and (c), 2 i,⌘ (t) stays at 1 for i < q because of the vanishing drift.

recall that we choose the block size h of downsampling to be h . the asymptotic sample complexity satisfies .


When there is an intensity boundary, the flow boundary in the same orientation becomes more likely.

the summary of our results are shown in figure 2 where we show the mean log likelihood on the Sintel test set.


The non-trivial problem is to detect the correct structure despite the disturbing influence of 5 un-informative kernels.

it lacks a means to control the sparseness of the coefficients α α α.


Our model assumes that (in expectation) only one node changes its cluster at every time step.

without loss of generality, throughout the paper we assume α 1 ≥ .


A problem encountered when working with operator-valued kernels in infinite-dimensional spaces is that of solving the system of linear operator equations (8).

our multiple operator-valued kernel learning formulation can be seen as a way of learning simultaneously input and output kernels, although we consider a linear combination of kernels that are fixed in advance.


RSALP outperforms established policies: Approaches such as the Max-Weight or 'parametric' ADP with basis spanning polynomials have been previously shown to work well for the problem of interest.

a non-parametric approach would, in principle, permit the user to select a rich, potentially full-dimensional architecture (e.g., the Haar basis).


Unlike most psychological models of categorization, the DP mixture model reserves some probability mass for outcomes that have not yet been observed.

we focus on problems where the number of objects must be inferred and where identity uncertainty arises from partial observability rather than noise.


In absence of such an oracle, we face the additional challenges of evaluating f , both statistical and computational.

as a result, the presented approach unleashes the powerful toolkit of stochastic gradient based approaches to discrete optimization problems.


singular value thresholding [3] for nuclear norm minimization).

the first gradient term term is much harder to evaluate because Θ λ (•) is an optimization procedure.


We propose to overcome this limitation by using likelihood-free inference approaches (also known as Approximate Bayesian Computation, ABC) to perform full Bayesian inference on single-neuron models.

many models of interest -such as multi-compartment biophysical models [2], networks of spiking neurons [3] or detailed simulations of brain activity [4] -have intractable or computationally expensive likelihoods, and statistical inference has only been possible in selected cases and using model-specific algorithms [5,6,7].


In comparison to [2], we look at the number of iterations to reach ρ for SGD in Table 2.

since we draw c i at random we need to show that a mixture of such mappings is a contraction, too.


Finally, alterations in resting state activity patterns have recently been shown to be diagnostic for clinical conditions such as neuropsychiatric disorders [18], and have been shown to alter with increasing age [34].

experimental results show that one of the primary assumptions of semi-supervised learning, the manifold assumption, holds well for this data, and that the marginal distribution of unlabeled resting state data is observed to augment that of labeled data to consistently improve regression performance.


Due to the very high computational cost for various methods in high dimensions, for each simulation example, we set the number of repetitions to 20.

to resolve this issue, we propose a new DNN architecture named DeepPINK (Deep feature selection using Paired-Input Nonlinear Knockoffs).


It will be interesting to extend the perturbative framework for the computation of corrections to inference approximations to other, more complex models.

the right panel shows that the lowest order term ∆F 1 accounts for a major part of the true correction when µ < 3.


1C-H except for the crucial change that all simulation results in Fig.

many large random measurement matrices A which violate sufficient conditions proven in the literature still nevertheless typically yield perfect signal recovery.


Special cases When r = 2, the SD is an instance of a kernel Stein discrepancy (KSD) with base reproducing kernel k(x, y) = R (x, z) (y, z) dz.

moreover, the underlying principle used to generalize the KSD could also be used to develop fast alternatives to maximum mean discrepancies in twosample testing applications [6,13].


For each block sub-problem, a proximal Newton method is applied, requiring a solution of a LASSO problem to find the descent direction.

it solves the problem by iterating and updating the matrix block by block, where each block is chosen as a subset of columns and respective rows.


Suppose each player i at every time-step t is characterised by an unknown skill s t i ∈ R and a player-specific draw margin ε t i > 0.

the second problem is addressed by performing inference for TrueSkill through time (TTT), i.e.


Tsybakov and collaborators replace global restrictions on η by restrictions on η near ∂G * .

as j increases, A grows additively with j, but p A decays at a multiplicative rate.


Constant memory backprop through reversibility Recent work developed reversible versions of residual networks (Gomez et al., 2017;Chang et al., 2017), which gives the same constant memory advantage as our approach.

for reference, a neural net with a single hidden layer of 300 units has around the same number of parameters as the ODE-Net and RK-Net architecture that we tested.


With the added layers for the classifier, the conjugate-exponential character of the model is retained, sustaining the ability to perform VB or MCMC inference with analytic update equations.

for Gibbs rounds 16, 32 and 64 the corresponding PSNR values were 26.78 dB, 28.46 dB and 29.31 dB.


This can be computed by projected gradient, as described by Bertsekas [3].

in future work, we would like to evaluate the usefulness of these sparser annotations for downstream tasks, for example determining whether Sparse POS tags are better for unsupervised parsing.


Of course, if the target dataset is very large, there would be little need to transfer because the lower level filters could just be learned from scratch on the target dataset.


Smoothing Parameter (Estimated) L1 Coverage Risk q q q q q q q q q q q q q q q q q q q q 0.0 0.

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


Bandit learning is characterized by the tension between long-term exploration and short-term exploitation.

this suggests that in slightly perturbed environments, exploration and exploitation need not be in conflict in the linear setting.


In the code-based approach, we simply ignore the fact that the quantized data actually intervals and them precisely in same way as full-precision Recovery of cosine similarity is performed by means of the estimator in §2 with z, z replaced by q, q .

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


A portfolio is characterized by a vector of investment allocations, w = (w 1 , .

under this model, the covariance matrix of the stock returns is given by ) where B = [b jk ] is a d × 3 matrix consisting of the factor loadings, Σ f is the covariance matrix of the three factors, and σ 2 j is the variance of the noise ε i .


( 6) is then solved by a standard 'relaxation' (or Newton) method of iterative improvements to a guessed solution [13] (the target precision is always 10-5 ).

monte Carlo averagings given here are only over 500 runs, fluctuation determinants are calculated according to Eq.


To simplify expressions, we will often omit the arguments from φ(x, z) and ψ(z, y), and use S and ¬S for the events [S(z, y) = 1] and [S(z, y) = 0].

the relaxation parameter β provides a trade-off between faithfulness to the original objective (large β) and tractability (small β).


For a semi-deterministic approach, when the dynamics matrix A is block-diagonal, a simple heuristic is given in Remark ??

there are two key challenges with these approaches: the first is ensuring the scalability of the model to large scale phenomena, which manifests due to the fact that the hyperparameter optimization problem is not convex in general, leading to methods that are difficult to implement, susceptible to local minima, and that can become computationally intractable for large datasets.


This procedure forms a homogenous Markov chain and its stationary distribution is exactly the joint posterior.

each inequality constraint has the form By rearranging terms and combining the N Q constraints in matrix notation, we may write from which it is clear that the constraints are linear in a.


not only does the reverse-bound have to upper-bound the log-sum, it should also have the same form as the Jensen-bound above, i.e.


Not long after our paper first appeared, this issue was also answered.

each device computes the batch norm statistics using only its samples (i.e., part of the whole mini-batch).


Gaussian mixture models with diagonal covariance marices were trained on the PCA features, while exponential mixture models (as in eq.

it is worth comparing these multiplicative updates to others in the literature.


For the fly and the optimal lifting algorithms, the output dimensions are set to d = 20 × k and d = 2, 000 respectively.

we had an experiment to illustrate the effectiveness of the optimal sparse lifting (ref.


We are interested in deriving the FIM, J(s), for our correlated neural population encoding the stimuli s. The significance of the FIM is that the inverse of the FIM provides a lower bound on the covariance matrix of any unbiased estimator of s and also expresses the asymptotic covariance matrix of the maximum-likelihood estimate of s in the limit of large K 1 .

[3] found that subjects' performances were significantly better in the minimal color change condition than in the single probe condition.


Neural activity in motor cortex has been shown to be related to the movement kinematics of the animal's arm and, in particular, to the direction of hand motion [3,6].

the design of the experiment and data collection is described in detail in [12].


The main insight behind our robust estimation framework is that the signals present in imaging data are the superposition of many positive amplitude sources, and a lower amplitude noise component which could be well modeled by a normal distribution.

since we constrain S and T to be nonnegative matrices, the fixed-point solver cannot be used without constraints that enforce non-negativity.


We will seek an interval regression tree model T : R p → R that minimizes the total hinge loss on data set S: where ∈ R + 0 is a hyperparameter introduced to improve regularity (see supplementary material for details).

in the typical supervised regression setting, we are given set of learning examples, each associated with a real-valued output.


The main technical contribution of this paper is a class of GMMs for parameter estimation under the PL model, which generalizes BTL and the input consists of full rankings instead of pairwise comparisons as in the case of BTL and RC algorithm.

the corresponding GMM seeks to minimize GMM g F satisfies Condition 1.


As for parameter τ , it can be seen as an upper bound for P x∼P [x ∈ supp R] since in this case, we have supp R ⊂ {R(x) = 1}.

we further focus solely on the last two terms and, similar to the previous case, provide a result based on both the L 1 and χ 2 distances.


We introduced the teaching risk, a quantity that depends on the worldview of the learner and the true reward function and which (1) measures the degree to which policies which are optimal from the point of view of the learner can be suboptimal from the point of view of the teacher, and ( 2) is an obstruction for truly optimal policies to look optimal to the learner.

the discussion in the last section shows that, under our assumptions on how L learns, a teaching scheme in which T solely provides demonstrations to L can generally, i.e., without any assumption on the teaching risk, not lead to reasonable guarantees on the learner's performance with respect to the true reward.


• We numerically demonstrate the effectiveness and robustness of our algorithms in recovering the minimizer of ridge logistic regression on several real datasets (Figures 1 and 2).

the following theorem indicates that if the blocks of the augmented matrix of {A i (w)} (see Assumption 3) are sampled based on block norm squares or block partial leverage scores with large enough sampling size, (C1) or (C2) holds, respectively, with high probability.


The computational cost of bootstrapping weighted v-statistics is the same level as that of permutation statistics.

to date, there is no systematic and efficient solution to the issue of exact calculation of resampling statistics.


This makes it difficult to directly incorporate images, depth maps, and other high-dimensional observations.

our state estimation task is meant to reflect some of the typical challenges in visual state estimation: the need for long-term tracking to handle occlusions, the presence of noise, and the need to process raw pixel data.


Sections 4 and 5 give precise statements and proofs of the results in Section 3.

our estimator undersmooths the density, and converges at a slower rate of O n −β/(β+d) when β < d (and the parametric rate O n −1/2 when β ≥ d), but obeys an exponential concentration inequality, which is not known for the estimators of [8].


We report the per-class average Top-1 accuracies of different approaches in Table 1.

[6] proposed to learn region-specific classifier to connect text terms to its relevant regions and suppress connections to non-visual text terms without any part-text annotations.


We can infer the parameters α, γ, d by maximizing the marginal likelihood [22].

define c j to be the number of previous items in the stream that have also hashed to j, i.e., c j = .


Under the functional point of view, each 2D image is a function defined on the regular 2D lattice, so all images are functions over a common underlying parameterizing domain.

each shape has up to 10 keypoints, while most of the shapes have missing keypoints.


The complete proof of Theorem 6, the proofs of Theorem 7 to 9 and Corollary 2 are given in the supplementary file.

the number of these queried labels, which is necessary and sufficient for obtaining a good leaner, is well-known as the sample complexity of active learning.


We used linear SVMs as the basis for our active learning procedure.

in many situations, training data may actually arise from a different distribution than test data.


In general the values will differ because PBHT sets P X = I n×n , but HJ does not.

the fact that the above μj , ηj , γi , ¯ i are identical to those of HJ depends crucially on the fact that span(U S ) ⊆ span(U A ).


By 100,000 iterations of learning, this three-layer neural network achieves a prediction error rate of 0.31%.

these additional matrices can be considered as the mask matrices.


A particularly surprising result is that the minimax strategy is identical in either case; that is, the the recursive definition of w i (ρ) is the same whether the player is maximizing or minimizing.

at the beginning of each round the player is presented with a cost vector, describing the cost of occupying each point in the metric space.


As shown in the figure, the reverberation of the signal was effectively reduced, and the formant structure of the signal was restored.


Imagine, for instance, a traffic engineering application where each traffic signal may independently decide when to switch colors, and performance is measured by aggregating the throughput at all traffic stops.

such algorithms do not scale well to large numbers of agents.


Given a proposal q(θ |θ), the MH algorithm starts its chain at a user-defined θ 0 , then at iteration k + 1 it proposes a candidate state θ ∼ q(•|θ k ) and sets θ k+1 to θ with probability while θ k+1 is otherwise set to θ k . The core of the algorithm is thus to draw a Bernoulli variable with parameter α = α(θ, θ ) for θ, θ ∈ R d . This is typically implemented by drawing a uniform u ∼ U [0,1] and checking whether u < α.

such a process is called the determinantal point process associated to kernel L and base measure µ.


The analysis then proceeds by giving an upper bound b t (η) ≥ δ η t and choosing η to balance the two terms ln(K)/η and t b t (η).


For 50-dimensional ToP represented data, we compare SCA (SCA) and SCA-DIAG to SVM/LOGIT, information-theoretical metric learning (ITML), and large margin nearest neighbor (LMNN).

embedding documents using their topic representations does not reveal clear clustering structures such that network links can be inferred.


Thus this simple reinforcement learning modol has three meta-paramters, α,β and γ Such a reinforcement learning model does not only predict subject's actions, but also predicts internal process of the brain, which may be recorded as neural firing or brain imaging data.

here we assume that meta-parameters are constant with small drifts.


It posits that for every task the true label is always most commonly given.

and there are 165 workers involved in these tasks.


We let kwk denote the Euclidean norm of w, and supp(w) denotes the support of w. For any vector w 2 R p , [8] defined the overlapping group norm as We also introduce the notion of "group-support" of a vector and its group-`0 pseudo-norm: where a Gi satisfies the constraints of (2).

our result holds for arbitrarily large , and arbitrary group structures.


7  Spectral algorithms for Kalman filters typically use the left singular vectors of the covariance between history and future features as a basis for the state space.

to address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L 1 regularization.


. . , cm, ym if there exists a threshold Θ such that yi = sign(ci • w − Θ) for i = 1, . . . , m. We define sign(z) = 1 if z ≥ 0 and sign(z) = 0 otherwise.

we say that a vector w ∈ R n linearly separates the list c1, y1 , .


As one would expect, the higher the population frequency an ancestor is, the better its reconstruction accuracy.

the average reconstruction errors of HMDP for each of the five ancestors are 0.026, 0.078, 0.116, 0.168, and 0.335, respectively.


Although implemented in a possibly unbounded domain, Theorem 3 shows that {w t } t∈N by (2.2) falls into a bounded ball (up to a logarithmic factor) with high probabilities.


Following the usual set-up of composite optimization [10], no smoothness assumption is made on M and hence on f or g. Many learning problems are formulated as convex optimization problems, and hence by duality as saddle-point problems.

. . , i m ∈ I from the probability vector (π i ) i with replacement end for end for Output: Approximate solution (x, y) (x old(i) , y old(i) ), and we consider the estimate of B(x, y): πi B i (x, y) − 1 πi g i , which has the correct expectation when i is sampled from I with probability π.


The robots interact through resource constraints: the instantaneous production and consumption of each resource must balance exactly.

the addition of coordination (via our factored planning algorithm) significantly improved the performance.


Consider the following class of exchangeable ranking functions f (x) where the score for the ith document is given by: where b(x i ) is the score provided by the base ranker for the i-th document, and S k are pairwise functions ("kernels") applied to x i and x j .

in the following, we extend the theory above to the partially symmetric case (proof in Appendix B).


Similarly, the presented bound for r ∞ also implies sparsity, though it is the sparsity of w k − w. In fact, this is directly related with the sparsity of w k , considering that the classifiers can be postprocessed to subtract their average simultaneously whilst the classification decision won't change for any possible input.

within each iteration, a portion (ρ) of nonzero entries of w, whose magnitudes are relatively small in comparison with the others, will be directly set to zero and shall never be activated again.


Since σ i ( Xk ) > 0 for all k ≥ 0, we have σ i (− Ḡ) = τ by (23).

the inequality (15) then follows from Assumption 2.1(b).


Semi-Supervised Smoothness Assumption (SSS): The regression function m(x) = EY | X = x is very smooth where the density p(x) of X is large.

we now show that, in fact, one can skip the step of estimating d. Let E 1 , .


, the shortest-distance from the initial states of to its final states using the shortest-distance algorithm described in the previous section. .

the -sum and ¡ -multiplications of two transducers c g and c w are defined for each pair E 4 ¤ ~7 R by: This section introduces rational kernels, presents a general algorithm for computing them efficiently and describes several examples of rational kernels.


Our new methods subsume a variety of existing spectral algorithms as special cases.

ψ t must be a sufficient statistic for ) for a known function f predict .


The LabelMe dataset [14] is well-suited for this task, having a large number of images and labels spanning hundreds of object categories.

notice that the retrieved images generally belong to similar scene categories.


System 1 is a fast, unconscious and automatic mode of thought, also known as intuition or heuristic process.

because the apprentice network has effectively generalised our policy, it gives us fast evaluations of action plausibility at the start of search.


A further open problem is to prove lower bounds, even in the special case when n Mn is bounded by a constant.

this time we control the large deviations of the on-line process using Bernstein's maximal inequality rather than the Azuma-Hoeffding inequality.


Then we construct a 5-NN graph and use the cosine distance to measure the similarity between data points throughout of our experiments.

standard active learning is not very practical in this case.


As a consequence of Theorem 1 and Proposition 1, strong kernels according to Definition 1 are indeed valid kernels.

there is a unique vertex b, such that B are the leaves of the subtree rooted at b, cf.


One MRI image is decomposed into overlapping 8 x 8 blocks to form 15,625 training vectors; a second image is used for testing.


The pricing of digital good in repeated auctions has been considered by many other authors, including [1,10,3,2,5,11].

the proof of Proposition 2 is moved to the appendix (Section A.7) in interest of space.


We can also show that combining graphs improves labelled sample complexity (Claim 7, Suppl.).

we investigate LS labelling [16]; given a graph G, LS labelling K LS ∈ K(G) is defined as LS labellinghas high Rademacher complexity on a large class of graphs, in particular Corollary 4.3.


Recent studies modeled exposure, a latent missingness variable which indicates whether an item is exposed to a user, to give each missing entry a confidence of being negative feedback.

besides, it is originally proposed for next-basket recommendation.


3(b), we added a curve labeled squared MLP with Ensemble, which appears to be better than the MLP ensemble though it is the same curve with softmax scores scaled by simply squaring them.

second, we expand this loss into the Objectosphere loss, which requires the samples of D c to have a magnitude above a specified minimum while driving the magnitude of the features of samples from D b to zero, providing a margin in both magnitude and entropy between known and unknown samples.


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

hsu and McIlraith [11] give an intuitive explanation of the behavior of SP and BP from the perspective of traditional local search methods.


Color constancy methods perform worst on images that are dominated by a small number of materials with ambiguous chromaticity, and our results indicate that end-to-end training increases the reliability of our estimation method in these cases.

while pschophysical experiments have demonstrated that the human visual system is remarkably successful at achieving color constancy [1], it remains a challenging task computationally.


A learning algorithm can be viewed as an instance of a policy.

this will require, however, that we restrict our attention to games where there exist a Nash equilibrium in which the agents' expected payoffs are higher than their probabilistic maximin values.


By scalability we imply that a main goal is to develop a system more or less automatically, using machine learning approaches, with minimal human intervention and handcrafting.

in our experience, these approaches do not scale up well to larger board sizes.


The straddle score for a point may be negative, which indicates that the model currently estimates the probability that the point is on a boundary is less than five percent.

the ideas of root bracketing and function transversal are not well defined [2]; given a particular bracket of a continuous surface, there will be an infinite number of solutions to the equation f ( x) − t = 0, since the solution in multiple dimensions is a set of surfaces, rather than a set of points.


Note that If d + d 0  1 2 (n 1) then C d,d 0  3.

our situation is very different, our matrices are low rank because they are sparse -not sparse and simultaneously low rank as in their case.


While it may be possible to apply dimensionality reduction methods directly in alternating minimization methods for solving tensor regression, unlike our method, such methods do not have provable guarantees and it is not clear how errors propagate across iterations.

this motivates us to consider data dimensionality reduction techniques, also called sketching, for the tensor regression problem.


on the Long-Servedio dataset observe the 4 distinct spikes.


how to generate rich multi-scale representations and optimally fuse them.

the results of this comparison are shown in Table 1 and Fig.


It only requires adding the term to the subgradient.

our FW algorithm converges orders of magnitude faster and finds a high quality solution (for runtime comparison see Appendix G).


In this section, we study the infinite horizon LQR problem specified by where toeplitz(r, c) denotes the Toeplitz matrix with first row r and first colum c. This is the same problem studied in [17, §6] (for n x = 3), where it is noted that such dynamics naturally arise in consensus and distributed averaging problems.

though better suited to optimization than (2), which is almost surely infinite, this integral cannot be evaluated in closed form, due to the complexity of J(•|✓) w.r.t.


Therefore, it is not surprising to see that multi-view MNs inherit the widely advocated property of EFH that the model distribution can be constructively defined based on local conditionals on each view.

for example, topics 3 and 4 are discriminative in predicting the categories hawk and whales, respectively.


We conclude that stability remains a meaningful cluster validation criterion over finite samples.

( 1) as: the clustering distance is the probability that two independently drawn instances from D will be in the same cluster under one clustering, and in different clusters under another clustering.


The first approach reduces graph noise simply by deleting edges between pairs of clusters.

non-contextual stochastic bandits in social networks were studied in a recent independent work [20].


We evaluate deep metric learning algorithms on fine-grained object recognition and verification tasks.

now, we introduce an effective batch construction to avoid excessive computational burden.


Thus if 1 − µ < 2 n−t , it is preferable not to explore new arms and to play the best known arm, with mean reward µ, until time n. A fortiori, the best known arm is played until time n whenever its parameter is larger than 1 − 2 n . We denote by A n the first arm whose parameter is larger than 1 − 2 n . We have K n ≤ A n (the optimal policy cannot explore more than A n arms) and The parameter θ An of arm For all k = 1, 2, . .

[2] and applied in [11,4,5,7] to various mean-reward distributions are variants of the 1-failure strategy where each arm is played until the first failure, called a run.


In any stochastic setting satisfying the (B, κ)-Bernstein Condition 1, the guarantees (1) for Squint and (2) for MetaGrad imply fast rates for the respective algorithms both in expectation and with high probability.

theorem 19 in Appendix D shows how to deal with this case.


It represents the "distributed feature vector" associated with each word in the vocabulary.

a weight decay ).11()11 2 , that penalizes slightly the norm of ().


They conclude from a study of a number of trials, including IST, that heparin provides little therapeutic benefit, with the caveat that the trial evidence base is lacking for the highest-risk patients where heparin may be of benefit.

in our framework, appropriate choice of is both important for ensuring that we avoid harm and will be context-dependent.


[6] cluster in the image domain and use a small validation set to select a single positive component.

the terms are generated by appending the polysemous word to its synonyms and first-level hypernyms.


In practice, sEM can take a minibatch of data instead of a single datum per iteration, but we stick to a single datum for cleaner presentation.

var t [μ t ] is always quadratic with respect to the step size ρ t , so we divide it by ρ 2 t to cancel the effect of the step size, and just study the intrinsic variance.


[4] for linear Support Vector Machines (SVM)) and thus applicable to large data sets.

moreover, in [44], a greedy reconstruction technique has been developed for regression by empirically fitting squared error residuals.


For all x ∈ U ∩ {x : Finally, we note that the required number of iterations per-stage t for finding an accurate solution depends on an unknown constant c and sometimes θ.

by adding a strongly convex prox function in terms of u with a smoothing parameter µ into the definition of f (x), one can obtain a smoothed approximation of the original objective function.


A third type aims to uncover the dynamics of the interaction between different brain regions by approximating the underlying neural activity (see Breakspear [2017] for review).

the above loss function can be thought of as the logarithm of a Gaussian likelihood function.


In this paper we take a different perspective and present a unified framework, which treats [14,6] as special cases, for learning the parameters of SPNs.

although the difference seems to be small, there is a huge difference between GP and SP from the computational perspective.


The purpose of this work is the study of generalization properties of classifiers trained using a possibly dependent training data, but in the special case where the latter is deterministically generated from the input data.

we recover the results of [2] obtained in a specific framework of algorithmic stability.


We are interested in situations where ||f || ν is much smaller than ||f || ∞ .

. . , X n ) and the function we want to control by .


We apply this logic to all comparisons, where the goal is to determine the heaviest path edge e and to compare it to the candidate e. If we are lucky enough that all of these comparisons are conclusive, the amount of work we save is related to how much data was used in computing the confidence intervals -the rest of the data for the attribute-pair that is represented by the eliminated edge can be ignored.

we then proceed to describe its use in the case where some edge weights are known not exactly, but rather only to lie within a given interval.


From just a glance, humans can make rich predictions about the future of a wide range of physical systems.

of particular note is the performance of the VIN on the invisible dataset (spring system with random invisible object), where its performance is comparable to the fully visible 3-object Spring system.


1 can be computed in parallel for each node i, because they depend only on the parameters from the previous iteration.

to incorporate the potential functions θ's of the MRF and achieve equivalence between the likelihood and MAP value, a special binary reward variable θ is introduced with its conditional distribution proportional to potentials θ.


given Ξ i , and the null matrix of size n × k. Moreover, by singular value decomposition, we , for i = 1, . . . , n. Using the fact that V (p) T V (p) = I, and combining the above equations, we get ) T V (p) Λ (p) −1 .

we start by factorizing Ξ using SVD, obtaining Ξ = VΛU T where V ∈ R n×n is an unitary matrix, Λ ∈ R n×s is a rectangular diagonal matrix with nonnegative real numbers on the diagonal with λ 1,1 ≥ λ 2,2 ≥ • • • ≥ λ n,n (the singular values), and U T ∈ R s×n is a unitary matrix.


We then created a training set in which we "hid" one variable.

finally, we are considering approaches for dealing with sparse data, when the structural signatures do not manifest.


We also mention that computational performance may improve if our scheme is used as core for the optimization step of active set methods, such as [23].

sacrificing theoretical convergence for speed may be mandatory in large scale applications.


These results suggest minimizing a biasvariance tradeoff that we discuss and that leads to several algorithmic ideas.

we also present a general lower bound indicating the key role played by the Rényi divergence of P and Q in this context.


AC and RS's data suggest three corner detectors and a top-bottom contrast detector.

each class contained one or more target stimuli.


Much like the emphasis algorithm, this fitness function encourages the two thresholds to come together.

the ROC curve is anchored at (0,1) and (1,0), and is monotonically nonincreasing.


By zooming in and drawing many more samples we would see the same behavior in both plots.

at any location x, the latent function f (x) conditioned on past observations D n is then Gaussian with marginal mean µ n (x) and variance v n (x) given by where k n (x) is a vector of cross-covariance terms between x and {x 1 , .


The parameter σ is set to 200 according to [1] in order to fit human cognition, which favors basic level hypotheses [15].

in addition to the quantitative precision-recall curves, we perform a qualitative per-level analysis similar to previous word learning work [1].


By comparison, applying [2] to the same model yields an accuracy of 74.5% for a compression rate of 17%.

in this section, we introduce our approach to explicitly encouraging compactness while training a deep neural network.


This dimension for representing analogue uncertainty is coupled to that of the firing rate for representing binary uncertainty, since neurons have to fire multiple times in a cycle to have a measurable lack of concentration.

the joint Figure 1: Representing uncertainty.


p k can be identified with a probability distribution on Ω, because l p l k = lm γ lm k = 1, and γ k can be viewed as a joint probability distribution on Ω 2 with marginal distributions Q k and p k . We can eliminate variables p 1 , p 2 by substituting p k with γ k using the last constraint, so that γ 1 , γ 2 are the only decision variables.

note that ω l are parameters, but not decision variables, thus ω l − ω m can be computed before solving the program.


We hypothesize that a lot of the complex structure in the fMRI volumes is relevant to early vs. late classification, but that most of it is irrelevant to finger vs. wrist classification.

it is been shown before that generative training can make use of unlabelled data to improve discriminative performance [7] [6].


Therefore, ∆-GAN provides a natural way to perform semi-supervised learning, since the conditional GAN part and the BiGAN part can be used to account for paired and unpaired data, respectively.

all the network architectures are provided in the Appendix.


3c), which is reminiscent of experimentally observed dendritic non-linearities [11] (Fig.

when storing actual patterns drawn from the prior, performance becomes extremely poor, and often worse than the control (Fig.


3(a)-(c) that the posterior over the warping functions is highly peaked, so a maximum likelihood approach makes sense.

the standard ARD SE covariance function [4] plus noise was used for the underlying GP in all models.


For this purpose, we adopt the accelerated gradient method due to its light computation per iteration, and refer the obtained algorithm as TopPush.

in the literature, bipartite ranking has found applications in many domains [32,25], and its theoretical properties have been examined by several studies [2,6,20,26].


Interestingly, all methods quickly found good configurations of the hyperparameters as shown in Figure 2(left), with BOHAMIANN reaching the validation performance of the manually-tuned baseline ResNet after 104 function evaluations (or approximately 27 hours of total training time).

obs ) and n k = |D k | points have already been evaluated for function f k . BO then requires a probabilistic model p(f | D) over the K functions, which can be used to transfer knowledge from related tasks to the target task t (and thus reduce the required number of function evaluations on t).


from D, the goal is to find a maximally correlated subspace of D, i.e.

we consider a first-order oracle that provides inexact estimates of the gradient with a norm bound on the additive noise, and focus on inexact proximal gradient descent algorithms for CCA.


Perhaps surprisingly, we show that even if the treatment effect sizes of the actual positives are identical, adaptive measurement allocation can still substantially improve statistical power.

these previous works mostly focused on the asymptotic regime as n !


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

similarly, for the OCR problem we extend code from [20], kindly provided by the authors.


This modification enables to train very deep convolutional networks without suffering as much from the vanishing gradient problem.

noticeably, MODERN modulates the entire visual processing pipeline and therefore backpropagates through all convolutional layers.


In the proposed framework, modal decomposition is first obtained in terms of learned observables g; thus, the values of g must be back-projected to the space of the original measurements y to obtain a physically meaningful representation of the dynamic modes.

we focus on a (possibly nonlinear) discrete-time autonomous dynamical system where M denotes the state space and (M, Σ, µ) represents the associated probability space.


Though an improvement upon the naive message passing scheme, backpropagation remains biologically implausible because it would require rapid transmission of information backwards along the axon, which has not been observed [8,28].

we assume that a critic exists that broadcasts the TD error, so a module's local information would consist of its input x i , which is not necessarily a Markov state representation, its output a i , and the TD error.


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

1 Note that the BN scale and bias parameters are also dataset-dependentas noted in the experiments, this alone provides a certain degree of model adaptation.


Theoretically, we analyze the behavior of a resulting two-stage relaxation scheme for the capped-L 1 regularization.

we assume that there exists a function ḡh (u) defined on Ω such that g(w) = ḡh (h(w)) holds.


At the root of the generalization graph of Power(U) is the hypothesis u∈U u and at the leaf is the empty hypothesis.

a key step in planned exploration is designing appropriate planning problems.


Notice that, in this case, the optimizing variable is "f E ~Nz +N y instead of a E ~n.

in this paper we show how such a minimax programme can be carried out in the setting of binary classification.


The correlation For instance, for the 5 instances of the N, I, P, S, characters, the correlation is systematically higher with the four other examples of the same character.

further studies are required to evaluate the quality of recognition in larger training and test sets -what we wanted to demonstrate is the ability for recognition without any specific system tuning or sophisticated classification algorithm.


This will limit interpolation complexity.

this approach was first explored in [5], where subject cortices were registered by maximizing the inter-subject correlation of the functional response elicited by a common stimulus (a movie viewing).


Two variables are called equivalent if there is a bijection from Unify(X) to Unify(Y ) such that for any Z 1 ∈ Unify(X) and its image Z 2 ∈ Unify(Y ), Z 1 and Z 2 always occur together.

we define a set of rules that look only at the logical representation to identify models for which exact efficient inference is possible.


We have to generate a prior over φ c and δ 1 = x 1 − x c and δ 2 = x 2 − x c based on the principle of smoothness.

we faithfully model recent results showing that confidence in estimation can be systematically affected by the same aspects of images that affect bias.


This parametrization results in the new objective function: In the objective function, although we minimize the discrepancy between the transformed labels and the predicted labels for only the labeled points in the test domain, we put a regularization term on the transformation for all X te to ensure overall smoothness in the test domain.

sMS with active selection is better than SMS with random selection, especially in the Active Learning result.


The main difference is that MP solves a slightly different problem, where the 1 regularization is replaced with an 0 constraint.

while the patterns recovered with one channel are very noisy, the multivariate model with rank-1 constraint recovers the original atoms accurately.


For these experiments, we initialize both the methods with an initial labeled dataset of 100 points and then after each active learning round we seek all the labels for the selected training data point.

first, consider the simpler scenario where the training data set only consists of fully labeled instances X L with labels Y L . Thus our aim is to infer p(Y U |X, Y L , Φ), the posterior distribution over unlabeled data.


Each segment is represented by a 30-dimensional feature vector describing color and texture attributes of the segment and its neighbors.

in the present work, we focus on the second formulation above, where the learner queries selected unlabeled instances from labeled, positive bags.


We develop a method for comparing hierarchical image representations in terms of their ability to explain perceptual sensitivity in humans.

we compared all of these predictions to a baseline model (MSE), where the image transformation, f ( x), is replaced by the identity matrix.


If all that is needed for learning and classification are the inner products (., .

bayesian algorithms based on sampling and voting are more flexible and have the so-called "anytime" property, providing a relatively good solution at any point in time.


The parameters of generative models such as ARIMA are typically estimated via the maximum likelihood technique, which often leads to non-convex optimization problems.

we consider the following general time series prediction setting where the learner receives a realization (X 1 , Y 1 ), .


We have incorporated population information into the AFHMM by employing the latent Bayesian melding approach.

the new posterior distribution of LBM thus has the form where Σ represents the collection of all the noise variances.


In the following, we refer to Φ, defined by parameters (α, p), as the true stochastic model under which all the observed random labels are generated, and denote by ) the corresponding probability measure (resp.

we can relate I to D(α, p): Claim 5 In the LSBM with K clusters, if p = o(1), and for all i, j, such that i = j, α i = 1 K , p(i, i, ) = p( ), and p(j, k, ) = q( ), we have: Again from this claim, the results derived in [13] are obtained by applying Theorem 3 and Claim 5.


For a restricted third-order model with N v visible units, N h hidden units and N l class labels, the distribution P (l|v) can be exactly computed in O(N v N h N l ) time.

note that we could have assigned the jittered images the same class label as their source images.


1), which serves as a baseline for our classification framework.

elements of these architectures are similar to standard hand-crafted representations used in computer vision.


Furthermore, Lemma 2 in the supplementary material gives an existence proof for such an γ 1 to exist.

their algorithm is centralized and it is unclear whether their approach is readily applicable to the multi-agent setting.


[1,2]), the label is predicted by judging each topic's relevance to the text.

x(∈ R d ) A document vector t 1 , t 2 , .


These hubs rarely link exclusively to pages of a single category-instead the hubs will contain a number of additional links, such as links back to a home page and links to related hubs.

builders support a certain set of operations relative to L B , in particular, the least general generalization (LGG) operation.


The widely used margin-based selection criterion of [8,9,10] seeks those points that are nearest to the current support vector machine's hyperplane decision boundary, and can substantially reduce total human annotation effort.

we demonstrate our algorithms' significant practical impact for large-scale active learning with SVM classifiers.


For global descriptors, we used the color correlogram for image texture representation, and the edge histogram descriptor.

the choice of M * is purely motivated by convenience of presentation since similar performance was reported for higher values of M * .


Theorem 4.2 Let F ∶ X → R + be monotone and weakly DR-submodular with parameter γ and assume K ⊆ X is a convex set.

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


Their use of an auxiliary sample set and the notion of average distance between partitions makes their bounds conceptually different from our work.

we have the following upper bounds on gen(µ, P W |S ) and gen + (µ, P W |S ) based on the mutual information between the training set S and the discretized output of the learning algorithm, where each of these mutual information terms is multiplied by an exponentially decreasing weight 2 −k , in which the exponent measures how finely the output W of the learning algorithm is discretized: Theorem 3.


For example, Wilson and Nickisch [27] proposes to space the inducing points on a multidimensional lattice, so the time and space complexities of using a product kernel becomes O(N + DM 1+1/D ) and O(N + DM 1+2/D ), respectively.

algorithm 1 summarizes the online learning procedure used by all stochastic algorithms, 12 where each learner has to optimize all the parameters on-the-fly using i.i.d.


By the bounded difference inequality, with probability 1  The right hand side is just the Rademacher complexity of G , .

each triplet t = (i, j, k) has an associated probability p t satisfying Let S denote a collection of triplets drawn independently and uniformly at random.


Surveys by Argall et al [26] and Chernova et al [27] provided a comprehensive review of techniques built upon these works as applied to robotics.

ω i was associated with the i th dinner piece, and encoded whether it was at its correct and final position.


Here Q(t), R(t) are positive semi-definite matrices which parameterize the reward function.

the first iteration's control policy (designed for the time-varying linearized models along the target trajectory) was unstable in the non-linear model and DDP failed to converge.


2) exhibit a strong selectivity to static disparity, but no specific tuning to motion-in-depth.

l. The predominance of one measure on the other one corresponds to different hypotheses on the architectural solutions adopted by visual cortical cells to encode dynamic 3-D visual information.


It is often claimed that small saccades are necessary to refresh neuronal responses and prevent the disappearance of a stationary scene, a claim that has remained controversial given the brief durations of natural visual fixation (reviewed in [16]).

it is difficult, however, to envision how such steady-states could occur under natural viewing conditions, given that the projection of the visual scene on the retina is never stationary.


We examine the approximation error of PMD on a toy dataset.


The terms of the conjugate distribution can also be derived easily.

the corresponding matrix for the BPM model, whose values are restricted to [0,1], is the partial membership of each data point and represents the extent to which each data point belongs to each of the K clusters.


This material is based upon work supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216, and the Italian Institute of Technology.

it is clear from definition (1) that an exact leverage scores computation would require the same order of computations as an eigendecomposition, hence approximations are needed.The accuracy of approximate leverage scores is typically measured by t > 0 in multiplicative bounds of the form Before proposing a new improved solution, we briefly discuss relevant previous works.


Unfortunately, none of these approaches strictly enforce prior logical relationships between label predictions.

for example, s might decompose as s(x, y) = c∈C s(x, y c ) over a set of cliques C that form a junction tree, where y c denotes the portion of y covered by clique c. Y might also encode constraints to aid tractability, such as y forming a consistent matching in a bipartite graph, or a consistent parse tree [28].


This function has parameters that can be iteratively tuned in order to maximize the log-likelihood of the training data or a regularized criterion, e.g.

n-gram models construct tables of conditional probabilities for the next word, for each one of a large number of contexts, i.e.


We consider as manifold the space of probability distributions over m points, that is the m-dimensional simplex ∆ m endowed with the Fisher information metric [3].

in this paper we consider a structured prediction approach to manifold valued regression following ideas in [13].


At each iteration, it halves the value of used in the previous iteration, calls an LP oracle, and checks whether the basis of the solution obtained is also a basis of an optimal solution when ↓ 0.

we will focus on extensive-form games with perfect recall, that is, where no player forgets what the player knew earlier.


Thus a first-order HMM for an alignment between e ≡ e 1:I and f ≡ f 1:J is defined as: where p(a j |a j−1 ) is the state transition probability; J and I are sentence lengths of the French and English sentences, respectively.

the English topics (represented by the topic-specific word frequencies) can be directly read-off from HM-BiTAM parameters β.


Note that T is a parameter, which could depend on the available resource of the user.

in this paper, we present the generalized subset selection problem that can be applied to arbitrary criterion evaluating the selection.


Therefore, we describe the effective input to a neuron via the following feature-map: where ψ sp represents the spike time history and ψ st the possibly nonlinear feature map for the stimulus.

we would like to thank Günther Zeck and Nicole Rust for generously providing their data and for useful discussions.


[12] proposed an active search scheme to sequentially evaluate selective search object proposals based on spatial context information.

states: At each step, the state of MDP is the concatenation of three components: the feature vector of the current window, the feature vector of the whole image and the history of taken actions.