Due to linearity the PRG Pareto front is convex and easily constructed by visual inspection.

score 0.76 corresponds to β 2 = (1 − 0.76)/0.76 = 0.32 and score 0.49 corresponds to β 2 = 1.04, so the point closest to the Precision-Recall breakeven line optimises F β for 0.32 < β 2 < 1.04 and hence also F 1 (but note that the next point to the right on the convex hull is nearly as good for F 1 , on account of the connecting line segment having a calibrated score close to 1/2).


their method does not have an elegant Bayesian interpretation.


According to Lemma 1 a Newton update restricted to the fixed block does not result in any changes.

the main cost arises while computing the third term contributing to coefficient b, namely w T i Dw j .


( 4) and the definition of K * in  fact give a straightforward comparison between the proposed sufficiently scattered condition and the existing anchor-word assumption.

the anchor-word assumption requires that cone(C T ) fulfills the entire triangle, i.e., the nonnegative orthant, which is far more restrictive.


The effect of the split is then to separate out these two clusters.

in high dimension, the rate of decrease of the average diameter can be very slow.


Our method supports inequality, equality, and mixed constraints, and to our knowledge this updated ALBO procedure is unique in the BO literature in its applicability to the most general mixed constraints problem (1).

in the latter iterations stark distinctions emerge, with Slack-AL+optim and PESC, both leveraging L-BFGS-B subroutines, outperforming.


In this section we develop the search algorithm that guarantees the performance stated in Theorem 2.

this is developed in more detail in [3].


Thus one might expect the spectral method to produce cuts with fairly good balance, and this is what does happen for the class of spacelike graphs that inform much of our intuition.

moreover they seem to match the true dimensionality of simple spacelike graphs.


Whereas previous methods single out a single "best" correspondence across images, in a Bayesian framework we are interested in characterizing our knowledge about the unknowns conditioned on the data only, averaging over all possible correspondences.

the structure from motion problem is this: given a set of images of a scene, taken from different viewpoints, recover the 3D structure of the scene along with the camera parameters.


We have derived upper and lower bounds that are rather tight-with a polynomial gap of order four-and hold for the computation of a specific family of real-valued functions in one variable.

we obtain almost tight time bounds for real computation in recurrent neural networks.


The code to fit the models and reproduce the figures is available online at: https://github.com/david-klindt/NIPS2017

there is only one feature map in the convolutional layer (K = 1).


To demonstrate this, we adapt the proposed DirBN structure to the following models: PFA+DirBN Poisson Factor Analysis (PFA) is a popular framework for topic analysis (DPFA , DPFM , GBN (Zhou et al., 2016) can be viewed as a deep extension to PFA).

here DirBN is a new hierarchical approach of constructing WDs, detailed as follows.


The core result is that the manifold tangent plane at x is mostly defined by the near neighbors of x in the training set (more precisely it is constrained to be in the span of the vectors x − x i , with x i a neighbor of x).

we now proceed to the proof of the theorem.


We also provide it online on our project page.

the baseball player is not swinging a bate.


In these, child node information is either retrieved from the cache, if available, or initialized with an admissible heuristic function h. • Perform the backtracking test (lines 13-14 and 23-24).


For larger values of C, the algorithm changes action less frequently, hence, will play for a longer time period.

this is not an easy problem, because the future actions are not independent of the actions taken in the past (since the algorithm's choices of future actions depend on the random confidence set constructed from past data).


Furthermore, the conditional distributions of the stick lengths are quite involved so they tend to have slow running times.

a) σ-Stable Poisson-Kingman processes [23].


The last term in Eq.4 is nonnegative and integrates to one over R d , and is thus a proper probability distribution in Ω d . Furthermore, p is the fixed point of operator Φ g p,A , as Φ g p,A {p} = p. The following result shows that both Φ m A and Φ mg p,A are KL contraction operators, and that they are in a sense complementary to each other.


Reviewing the algorithm above, we see that EP costs are dominated by the O(M 2 ) Cholesky downdate at each site inclusion.

there is a computational price to pay for this robust framework: the time for training scales as N 3 for N data points, and the cost of prediction is O(N 2 ) per test case.


Here, we describe how a tremendous speed-up is acheived through the use of a variational technique for decoupling transformations, and a fast Fourier transform method for computing posterior probabilities.

the number of possible x-y translations in a 320 × 240 image is 76,800.


To achieve that goal, physicians took an interest in mathematical modeling.

such an approach cannot ensure the curve γ 0 to be at least continuous.


Suppose, for example, that very accurate surveys reveal the number of birds n t (i) in each location i at each time t, and these numbers are collected into a single vector n t for each time step.

let A be decomposable and let n A be consistent with A = V , so that each variable is part of an observed margin.


Indeed, for general online learning problems, this is the most one seems able to hope for.

the main open question posed by that paper is whether a better rate can be obtained.


We define z k (t) = 1 at spike times t of neuron k and z k (t) = 0 otherwise.

the constrained maximization problem q * (z|y) = arg max q∈Q F (V , q(z|y)) can be solved with the help of Lagrange multipliers (cf.


Step 4 is carried out in Corollary 2, which follows.

a careful reader may notice that the procedure for FREEREXMOMENTUM involves computing argmin W √ 5ψ(at(w−wt) atηt + g 1:t • w , which may not be easy if the solution w t+1 is on the boundary of W . When the w t+1 is not on the boundary of W , then we have a closed-form update: when w t+1 lies on the boundary of W , it is not clear how to compute it for general W . In this section we offer a simple strategy for the case that W is an In this setting, we can use the standard trick (e.g.


If it is positive definite, then a learning machine can be understood as a Riemannian manifold.

(1) If the prior is positive, then 0 <).


Markov Decision Processes (MDPs) have been extensively studied in the context of planning and decision-making.

we should make a call to the above function passing in the conservative policy ⇧ m and starting from the first state-action pair: getOptimal(⇧ m , 0, ✏).


We expect pooling methods one and two to be more powerful than the third pooling method used in the current study, since the Bonferroni and Hommel tests are conservative compared to using  We showed that multivariate K-sample and independence tests can be performed by comparing the univariate distributions of the distances from center points, and that favourable properties of the univariate tests can carry over to the multivariate test.

as an interesting example we discuss the energy test of ( 25) and ( 1) for the two-sample problem.


For the sequence of dependencies model, there are a small number of good permutations which mix very quickly compared to the other permutations and random scan.

this experiment illustrates that random scan and a good systematic scan move to the other island quickly, while a bad systematic scan requires many more iterations.


This variant is meant to evaluate whether any performance benefit is due to the form of the features or due to the addition of new timestamps.

a timeline tree may also establish new timestamps in the past and is able split on features of observations surrounding those events as well.


These challenges motivate the design decisions of our soft-to-hard annealing approach, described in the next section.

the above treatment would stay the same if z is the concatenation of multiple feature outputs.


Our work, presented in Section 2, focuses on unexpected events which are indicated by the incongruence between prediction induced by prior experience (training) and the evidence provided by the sensory data.

the classifier of the parent object accepts the new observation, but all the children object classifiers reject it.


For each of the three methods, we have also included a variant that incorporates a flat component in the dictionary that can account for noise or non-harmonic components.

best overall performance is obtained with OST e +noise with an average ∼10% performance gain over PLCA and ∼750× speedup.


The exploring on the attention in ConvLSTM leads to a new variant of LSTM, which is different from the FC-LSTM and ConvLSTM.

the lower accuracy may be due to the additional optimization difficulty caused by the extra multiplication operations in the attention mechanism.


2 Our implementation allows for the usage of arbitrary higher-order graphical models, and it allows for an arbitrary composition of graphical models within the H vector specified previously.

we use a more direct way of modeling structure and a more global approach to inference by predicting all variables together.


For another example, in protein interaction networks, two proteins may be connected only when they belong to the same or correlated gene ontology terms.

hence, when either of r and r is zero, D(r, r ) = 0.


. . , π K } that is shared for all {x i } i=1,N B , it is expected that there may be a mixture of π vectors, corresponding to different segments in the image.

note that the model in (2) may be employed for unlabeled data, and the extension above may be employed for the available labeled data; consequently, all data (labeled and unlabeled) may be processed jointly to infer D. In the above discussion, we implicitly assumed all data D = {x i , y i } i=1,N are used together to infer the dictionary D. in some applications N may be large, and therefore such a "batch" approach is undesirable.


In SVMs, approaches based on optimizing generalization bounds [4], such as the radius/margin-bound [15] or maximal discrepancy criterion [2] have been proposed.

the partial derivative of 1 2 w T Cw + ℓ T (w) with respect to w i vanishes when w = w ⋆ , so where C T i denotes the ith row of the C matrix.


We say Q(Z; q) is unique if there exists a unique z such that P(Z ≤ z) = q.

commonly used elliptical distributions include Gaussian distribution and t-distribution.


The formal definition is a bit tricky, because one has to be careful about scaling issues.

the intention is to capture the property that if the ratios d Y (f (u), f (v))/d X (u, v) are close to 1 for many pairs of points u, v, then the distortion is small.


Under our learning problem setup, after nearly log(km) initial time steps, the proposed algorithm achieves near-optimal performance relative to an oracle algorithm that recommends all likable items first.

instead of maximizing the expected reward r (T ) , we aim to maximize the expected number of likable items recommended up to time T : where X ut is the indicator random variable for whether the item recommended to user u at time t is likable, i.e., X ut = +1 if p uπut > 1/2 and X ut = 0 otherwise.


To deepen the LSTM, the popular Stacked LSTM (sLSTM) stacks multiple LSTM layers [20]; however, runtime is proportional to the number of layers and information from the input is potentially lost (due to gradient vanishing/explosion) as it propagates vertically through the layers.

during the online inference when the input presents sequentially, temporal computations can no longer be parallelized and will be blocked by deep computations of each timestep, making these methods potentially unsuitable for real-time applications that demand a high sampling/output frequency.


Larger coefficients implies stronger local phase coherence.

( 5) and the phase coherence relationship of Eq.


In an ambient space Ω, we say that a set C separates the sets A and B if any continuous path in Ω with endpoints in A and B intersects C. Theorem 3.3.

in each case, our result prescribes conditions on the initialization pattern.


The fractional power estimator d(α),fp can be treated as a linear estimator in because the power 1/λ * is just a constant.

our additional simulations (not included in this paper) indicate that d(α),fp still has comparable tail probability behavior as the geometric mean estimator, when α ≤ 1.


This is in analog to structured output learning (e.g.

we can train the LSVM by an iterative algorithm that alternates between inferring h on positive examples and optimizing the model parameter w. Dual form with fixed h on positive examples : Due to its nature of non-convexity, it is not straightforward to derive the dual form for the general LSVM.


Our contributions are the following: (i) we design a randomized hierarchical data structure with which we can do NN search using the comparison oracle (ii) we develop the first lower bound for the search complexity in the combinatorial framework of [1,12], and thereby demonstrate the importance of combinatorial disorder.

the main question we ask in this paper is to design a (approximate) nearest neighbor retrieval algorithm while minimizing the number of questions to such an oracle.


We use the same observations as used in prior work which includes joint positions, joint velocities, and for some tasks, information related to contacts.

this indicates that careful design of initial state distributions are crucial for generalization, and to enable the agent to learn a wide range of skills.


The first is a function which is a measure of the distance of the current state ω from the solution state ω * (in the next section we will require ω * = arg min ω D(P 0 (x)||P (x|ω))).

younes [7] gives convergence results when the gradient of the energy ∂E(x; ω)/∂ω is bounded by a term that is linear in ω (and hence unbounded).


More statistics of the dataset can be found in the supplementary material.

the model needs to predict much fewer tokens for a CoffeeScript program than a JavaScript program, so that even seq2seq models can achieve a reasonably good accuracy.


The authors thank Yevgeny Seldin for finding a bug in an earlier version of the paper.

y, s(f ) 2 {0, 1} d is an indicator vector whose i th component indicates whether f is sensitive to its i th input (in particular, s i (f ) = 0 by definition when f (x 1 , .


At this point, X i sends the resulting table to its distinguished neighbor N * (X i ).

x i and N * (X i ) could together decrypt the value in column d + 1, use this value in order to sample X i 's new value according to the appropriate distribution, and distribute the new value between themselves.


First, recall that Lemma 3 argues that the regret of just the A(Σ) ∩ B(Σ) game is infinite.

this paper is concerned with the minimax strategy s * , which is the strategy that minimizes the worst case regret over all possible covariate and outcome sequences in some constraint set, i.e.


We can generalize it to fractional counts as follows.

instead, the structure of the relationship between the contexts should be harnessed.


By blocking the information exchange between channels, the accuracy drops.

the effectiveness of BN would diminish with the scenario of micro-batch (e.g.


Indeed, we observe this in our experiments as well and either of the two classifiers can be used for test time predictions.

[8] used the idea of co-training for semi-supervised domain adaptation (assuming a few target labeled examples are available) by finding a suitable split of the features into two sets based on the notion of -expandibility [1].


Comparing the IQRP to the current state-of-the-art randomized algorithms that were reviewed in Section 2.2 we observe that the IQRP is competitive in terms of the number of passes and appears to outperform these algorithms in terms of the number of IO-passes.

it is based on the following two ideas: 1.


. . , µ K , and second, construct a ray emanating from a (weighted) center of the polytope and extending through each of the centroids µ k until it intersects with a sphere of radius R k or with the simplex ∆ V −1 (whichever comes first).

the connection between extension parameters and the thresholding is the following: if the cluster centroid assigns probability to a word smaller than the whole data does on average, this word will be excluded from topic k with large enough m k . the extension parameters can as well be used to control for the sparsity of the inferred topics.


On another hand, maximizing the mean value (Sec.

pS(d µ,π * ) and RPS(d µ,π * ) are compared in Fig.


From the results, we find that the performances of the methods with attention mechanism are much better than those without attention mechanism on both CUB and NABird datasets, which verifies the effectiveness of the attention mechanism.

we directly copy the performance results of the competitors from [6] and [33].


We do this by showing something much stronger, namely that LLR guarantees a so-called second-order bound (a concept introduced in [7]).

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


We defined the distance between a prediction (p) and an observation (y) as the difference between the log-likelihoods of y assuming θ=p and θ=y.

in both our Bayesian and fast-and-frugal analyses, the prediction task is decomposed into two inference procedures.


We prove that the difference in the tightness of the bound on the likelihood of a document decreases as O(k − 1) + log m/m, where k is the number of topics in the model and m is the number of words in a document.

(Some topic models, such as LSI and pLSI, are not fully generative.)


Larger values of r and K enable better approximation to the unknown signals.

we further use the notation svd(X; r) to denote computation of the rank-r singular value decomposition (SVD) of X and the arrangement of its singular vectors into a set of up to r rank-1 matrices.


In this graph, one host is "connected" to another host if there is at least one link from a web-page in the first host to a web-page in the other host.

if, while ascending from v i we enter a vertex c which has previously been visited during the ascent from another vertex w (line 6) then we compute r T (v i , w) as r T (v i , c)+r T (c, w).


Here, we take a pragmatic approach, and constrain ourselves to solutions of the form μ(y , where b µ : R !

thus our model is misspecified in the sense that there is no function f such that a current prediction y(t) i increased the log-odds of the next prediction by f (y (t) i ), and so this example can be taken as a stretch case for our method.


While the normalized Laplacian L is commonly adopted for M , there are several other choices [9,10,11].


7 Conclusions We studied learning to rank methods for global ranking problem, in which we use both content information of objects and relation information between objects for ranking.

to our knowledge, this is the first time such kind of CRF model is proposed.


The decomposition of relations over latent factors allows a significant reduction of the number of parameters and is motivated both by computational and statistical reasons.

for instance, (divide,split) is labeled 4, while (postpone,show) has a score of 0.


Several recent papers [6,10,9,11] have considered the problem of recovering the connected components of {x : f (x) ≥ λ} for a user-specified λ: the flat version of our problem.

the collection of all such clusters forms an (infinite) hierarchy called the cluster tree (Figure 1).


If the index is built to highlight differences in locations, one would naturally favor mergers between neighboring indexes.

their computational cost can be prohibitive when dealing with large datasets, and can only be applied to sequential data.


In our case, the attention mechanism is only guides the learning procedure, and not used by the model for inference.

while such methods have demonstrated positive results on a number of tasks, their performance can significantly vary based on the setting of their hyper-parameters.


This yields to two fundamental questions: First, can we construct a multi-layered model with non-differentiable components, such that the outputs in the intermediate layers are distributed representations?

when F i is non-differentiable or even non-parametric, back-prop is no longer applicable since calculating the derivative of loss function with respect to its parameters is impossible.


Observation To visualize word embeddings, we reduce their dimensionalities by SVD and plot two cases in Figure 1.

it has been demonstrated that word representations learned from one task can be transferred to other tasks and achieve competitive performance [3].


We generated a sampling distribution s correlated with target distributions.

the methods of the previous two approaches do not apply directly to density estimation where the setup is "unconditional", i.e.


The trademark of a good model selection procedure, then, is its ability to satisfy two opposing goals.

use of such a measure can result in the choice of a model that over-fits the data, one that captures idiosyncracies in the particular data set (i.e., noise) over and above the underlying regularities of interest.


We refer to this network as WRN-22-5.4×2.


Although effective, some issues, including high resemblance in model-gerenated captions, are observed [1] on models learned by MLE.

compare Model Choices To study the generalization ability of CL, AdaptiveAttention and Neu-raltalk2 are respectively chosen as both the target and the reference in CL.


We adopt this position because we could derive a method that minimizes the residual T * v π − v π 1,ν over policies and compare to other methods that usually maximize the mean value.

1.a and 1.b, it appears clearly that RPS(µ) is less efficient than PS(µ) for decreasing the error.


Building on the Sparse Subspace Clustering (SSC) algorithm [26], we cast the problem as finding a completion of the data so that each complete point can be efficiently reconstructed using a few complete points from the same subspace.

in the low-rank regime, while LRMC and SSC-lifting have almost zero error for ρ ≤ 0.35, the performance of LRMC quickly degrades for larger ρ's, while SSC-lifting performs well for ρ ≤ 0.6.


In our application, the x n are one-dimensional time indices.

the expectation connecting the alignments and the pseudo inputs is given by where ˆ ni is the combined length scale corresponding to the same kernel as σni .


In general, hierarchies can be represented as directed graphs.

in comparison with most existing work on novelty detection, one new and important characteristic of our approach is that we look for a level of description where the novel event is highly probable.


An analog Gilbert multiplier computes the product of each pixel of the input image, represented as a differential voltage, and the local synaptic weight.

as Section 5 shows, this error does not translate into a large degradation in the face classification performance.


Nevertheless, it has to be said that in some of our experiments the model selected by the bounds resulted as accurate as the ones selected by ten-fold cross-validation in terms of test error rate on a separate test.


One possible approach is to formulate a stochastic neural network that samples from a probability distribution in which the correct solutions have higher probability [2].

at a local optimum, the ongoing perturbation of constraint strengths will eventually lead to a configuration that de-emphasizes the currently satisfied constraints and emphasizes the unsatisfied constraints.


The posterior distribution of x for given observed syndrome z is derived from the prior p(x) and the conditional p(z | x) by applying the Bayes formula, and the result is where we let The objective of decoder of Gallager codes is to obtain the marginal-posterior-mode (MPM) estimate based on the posterior p(x|z): The MPM estimation provides the Bayes-optimum decoder minimizing expected bit-error probability of the decoding results.


For this model, the theoretical receptive field of the top convolutional layer units is quite big at 505 × 505.

if we make an extra simplifying assumption that the gradients σ are independent from the weights and g in the upper layers, we can simplify the variance as Var 2 ] = Var[σ p i,j ] = 1/4 is a constant factor.


In comparison, VIME leads to a more diffused visitation pattern, exploring the states more efficiently, and hence reaching the goal more quickly.

this can be explained as both variants are locally equal when introducing small changes to the parameter distributions.


. . , p n are consistent, mutually exclusive and exhaustive.

the PSDD only maintains enough parameters to represent the resulting distribution, which further explains the size differences.


If not specified otherwise, x next = argmax x a(x) is computed using gradientbased search with multiple restarts (see supplementary material for details).

for a fully-Bayesian treatment of hyperparameters (summarized here by θ alone), it is desirable to marginalize over hyperparameters and compute the integrated acquisition function: where a(x) depends on θ and all of the observations.


the second Universum U nm is physiologically motivated.


We are given a fixed set of sequentially labeled data pairs (so D 0 = ∅), where each x (n) ∈ R V0 is a data point, and each y (n) is a label taken from a binary set Y ⊂ {−1, +1} V L . For brevity, we will sometimes suppress the sample index n, where it is clear from the context.

in order to reduce the computational complexity in cases that Σ m is not diagonal, we will approximate the distribution of u m with its factorized ('mean-field') version.


Since the original work in [4], multiple studies have highlighted the theoretical and practical importance of the IB method, in particular in the context of cluster analysis [2,5,6,7,8].

as already mentioned, the matrix partition itself may be described by nI(X; C) + mI(Y ; D) bits.


Denote by z t the point played by Algorithm 3 in round t. Suppose we set ⌘ = ↵ 4/3 LRT 2/3 , ✏ = ↵R T and = 2/3 d T 1/3 in Algorithm 3 (assuming T > 2 d 3 so < 1).

recent advancements on black-box online-to-offline reductions were made in (Kakade et al., 2009;Dudík et al., 2016;Garber, 2017).


Assume H 1 and H 2 hold and that X ∞ ≤ γ.

we need to control deviations of the sampling mechanism from the uniform distribution and therefore we consider the following assumptions.


The allowable drift is restricted by ensuring that consecutive probability distributions are close in total variation distance.

[Bar92,BL97] study the problem of learning a subset of a domain from randomly chosen examples when the probability distribution of the examples changes slowly but continually throughout the learning process; they give upper and lower bounds on the best achievable probability of misclassification after a given number of examples.


Many scoring functions have been proposed for use in search algorithms.

furthermore, we show that XCorr p-values are also made more accurate by training the underlying scoring function for which p-values are computed.


From practical standpoint, it is hard to achieve high quality partitions on all types of graphs using a single algorithm.

vanishing moments: The wavelets should have vanishing dual and primal moments -two independent conditions due to biorthogonality of our wavelets.


Despite these advances, the work possesses a number of limitations.

. . , β M } with m β m = 1 be a set of associated probabilities.


Bottom,left: A clusterable data set, described in the Experiments section 6, (n = 1024) with a stable and nearly optimal clustering C w.r.t the K-means loss.

a good clustering C has low Loss(D, C), in a way that will become precise later.


It turns out that the ideas used in wavelet based signal denoising (see for example [10] and references therein), are applied to signal separation from noisy mixtures.

the same arguments are valid for the second source.


The question of whether the nervous system produces movement through the combination of a few discrete elements has long been central to the study of motor control.

this analysis assumed that the muscle synergies consisted of a set of muscles which were activated synchronously.


( 1) can be rewritten as the Bellman equation The advantage of using the Bellman equation is that it describes the relationship between the value function at one state s and its immediate follow-up states s ∼ p(s |s, a).

hence, DSDP can be regarded as a special case of NPDP for discrete state systems.


A larger training set typically gives better test performance.

this will be demonstrated with some numerical examples in §4.


( 11), and that the decoder knows CA, CB and R C of eq.

in our more general setting, there may be more than one encoder-decoder pair for which each is optimal given the other.


Besides, kernel methods have the important computational advantage that no nonlinear optimization is involved.

the basic idea is to map data in the input space X to a feature space via some nonlinear map ϕ, and then apply a linear method there.


For this reason, during training we saturated the running sums ζ to allow some units to be always active.

pre-processing consisted of dividing each pixel value by 255.


This ordering can be chosen according to some heuristic along with a mechanism to cut down some parts of the search space.

funding was provided by the National Institutes of Health (grant R21 DA019800) and the NSERC Discovery Grant program.


Equipped with this abstraction, a second network observes the world and decides how to act to retrace the path under noisy actuation and a changing environment.

this touches on classical work in robotics and recent works learning-based efforts.


This is precisely the opposite of what one may have expected in this limit, namely the complete graph corresponding to the unregularized maximum likelihood estimate (MLE).

with a finite data set and a large number of joint configurations, only the typical limit in Proposition 2 is possible.


We described a factor-graph-based model to encode observational, temporal, and spatial dependencies observed in EEG-based brain activity analysis.

this epoch length was chosen because it would likely accommodate at least one abnormal neural event that could be associated with the SOZ [6].


Here, it can be easily checked that A is a consistently ordered, 2-cyclic matrix.

in this paper, we provide examples and more generally problem classes for which CCD (or CD with any deterministic order) is faster than RCD in terms of asymptotic worst-case convergence.


We have shown so far that our trained policies outperform appropriate baselines for the task when tested on novel environments.

we do this by testing the policies trained in the 'Base Setting', in different settings in novel environments.


Since the present work pertains to pre-processing and not modeling, balanced error rates and predictive bias are less relevant criteria.

in this paper, we focus on pre-processing since it is the most flexible in terms of the data science pipeline: it is independent of the modeling algorithm and can be integrated with data release and publishing mechanisms.


We currently lack an accurate meta-inference algorithm for MCMC samplers that do not employ annealing, and therefore AIDE is not yet suitable for use as a general MCMC convergence diagnostic.

it is typically intractable to compute output probabilities for sampling-based inference algorithms like MCMC and SMC, because that would require marginalizing over all possible values that the random variables drawn during the algorithm could possibly take.


• At iteration k, each of the link functions {σ i } m i=1 maps β Qmax Q k+1 and the dictionary B k B k to an element of the space of vector-valued Q max -bounded measurable functions X × A → R |A| .

revealing the full power of VPI remains as future work.


Following Friedman [7], we capture robustness by computing the ratio bm of its error rate em and the smallest error rate over all methods being compared in a particular example: bm = emf minl<k<8 ek.

severe bias can be introduced under these conditions when using the nearest neighbor rule.


5 Simulations and experiments Our synthetic simulations consider both matrix sensing and matrix completion, but with an emphasis on matrix completion.

there are also a few key differences between Theorem 3.4 and our results for matrix completion.


Concerning ⇤ (c) , rather than explicitly imposing a sparse diagonal via b, we may also draw , with shrinkage priors employed on the ck (i.e., with the ck drawn from a gamma prior that favors large ck ; which encourages many of the diagonal elements of ⇤ (c) to be small, but typically not exactly zero).

recall that G (c) In the original construction, (4) and ( 5), in which refractory-time violations are not account for, the Gibbs update equations for {U (c) ji } are analytic, due to model conjugacy.


Note that if f φj were known in advance, we could simply use the greedy algorithm.

our goal is to select a subset S j ⊆ Ω for each function f φj that maximizes its corresponding utility f φj (S j ).


Without losing any generality, we assume the instances are arranged in the order of [U, L], such that The instance selection problem formulated in (6) selects a subset of b instances indexed by Q from U and moves them into the labeled set L. This problem is actually equivalent to partitioning matrix Σ into submatrices Σ L L , Σ U U , Σ L U and Σ U L by reordering the instances in U .

a kernel function is first learned from a mixture of labeled and unlabeled examples, and then is used to effectively identify the informative and diverse instances via a min-max framework.


We set k = 200, and each block contains approximately 237 coordinates.

recent work has corroborated the empirical advantage of RBCD methods over the proximal gradient method [4,20,8].


In theorem 2 we show that for a fixed t, as the number of points |X| = N tends to infinity, with probability 1, β(t, X) tends to α(t).

even more importantly, this paper establishes an explicit connection between the point-cloud Laplacian applied to such characteristic functions (weighted graph cuts) and a geometric quantity, which is the weighted volume of the cut boundary.


Learning algorithms for this purpose have been explored previously, and the claim has been made that every set of locally consistent marginals can arise from belief propagation run on a graphical model.

in this paper, we prove that some sets of marginals simply cannot be achieved by belief propagation.


Since e ✓ is obtained via a model selection procedure, it is irregular and its asymptotic distribution cannot be estimated [14,22].

an estimator b ✓ obtained in this way can be shown to be asymptotically consistent [9], however, in general it will not be efficient [8].


In discriminative methods one attempts to generate a decision boundary appropriately enclosing the high density regions of the training set [11].

note that this assumption still leaves us with an infinite game because the learner's pure strategy space, R δ (P ), is infinite.


In this case, we can still expect an accurate estimate of µ π E (s, π E (s)), but there is little hope for µ π E (s, a = π E (s)).

sCIRL relies on an estimate μπ E of the expert feature expectation.


This pattern has a manifold structure where distances are locally but not globally Euclidean, due to the curved arms.

at h =10 all points have paths to labeled points but the Markov process has not mixed well.


When used with GANs, it results in our AdaGAN algorithm, detailed in Section 3 .

on each step AdaBoost adds new predictor to the current composition, which is trained to minimize the binary loss on the re-weighted training set.


Note that the boundedness condition of the kernel gives that k) .

although AMP is computationally quite efficient, as shown in Fig.


Under the first noise model, each pixel was corrupted via i.i.d.

in this algorithm the messages are not guaranteed to be bounded.


A value of 30 on this plot corresponds to a p-value of 10-30 .

further, in many multiple regression analyses, frequency is not found to be significant when AoA is controlled for (Brown & Watson, 1987; Carroll & White, 1973; Morrison et al.


In general, as with the forward-backward algorithm, the N -dimensional Viterbi search requires O(T N D N +1 ) operations.

we must estimate the likelihoods in order to determine which states to retain.


In the SIS model, node i will become susceptible to infection again at time τ i + r i .

these nodes w i can then buy the product (with the option to recommend it to others).


It is noteworthy that our method performs better on objects of small sizes (defined by [14]).

our R-FCN system has significantly better accuracy (Table 2).


An alternative hypothesis is overfitting to the training data.

the only stochasticity is the initial draw of a new sentence to be parsed.


For this purpose we define the sets A = {X 1 ≤ r 1 , .

we give an informal introduction to copulas and apply the concept to a pair of neurons from our data which are described and fully analyzed in Section 4.


(Please see the supplementary material.)

it is not clear whether there is an upper bound for the linear coefficients that is sufficiently good for our purpose.


The latent SMM represents each word as a latent vector, and each document to be classified as a distribution of the latent vectors for words appearing in the document.

medLDA and SVD+SMM often could not display their own abilities when the latent dimensionality was low.


Since the mix of content in the available pool already incorporates constraints like voice, topicality, etc., we focus on choosing articles to maximize overall click-through rate (CTR), which is the total number of clicks divided by total number of views for a time interval.

whenever polar articles were in the pool of candidate articles, there was usually a non-polar one in the pool that was more popular than the polar ones across all segments.


Consider a model M with k parameters, summarized in the parameter vector θ = (θ 1 , θ 2 , .

models should be penalized for their complexity when their adequacy is measured.


Then, there is a single solution to q l log q l PS l + (1 − q l ) log 1−q l PS h = Λ, where q l and 1 − q l are the probabilities that Q assigns to the events from S l and S h , respectively.

let P (x) be the underlying distribution of the target class, defined over some space Ω.


We used the FSS tools to gain insight into consumer preferences.

this is a metric-based method that selects one from a nested sequence of complexity-increasing models.


The hybrid method consisting of SVRG interleaved with Oja's algorithm for Hessian descent also improves upon SGD but does not match the performance of our method or AdaGrad.

in the limit where ✏ is small the result simplifies: o , then under the settings of Theorem 1 we can conclude that Algorithm 1 will output an ✏-second-order stationary point of f with probability at least 1 within total stochastic gradient and Hessian-vector product evaluations.


Note that in evaluating λ(Y, ȳ) one has access to the whole set Y , not just single elements.

object detection can be solved as a structured prediction problem where natural images are the inputs and coordinate tuples of bounding boxes are the outputs.


Here we report new EEG data from experiments in which we explore stimulus types and codebooks in a within-subject design, finding an interaction between the two factors.

the codes with a larger d min are characterized by an increased weight compared to the RC code, i.e.


Thus, we see that our optimization approach generally achieves competitive results with random features at lower computational costs, and it offers the most improvements when either the base kernel is not well-suited to the data or requires a large number of random features (large D) for good performance.

in under 0.2 seconds, we whittle down the original feature space to 379 important features.


The study shows each user on an average took 3 rerank and 2 zero-G feedbacks to train Baxter (Table 2).

step 3: The robot now updates the parameter w of s(x, y; w) based on this preference feedback and returns to step 1.


Our search space size is on the order of 10 11 and we adopt the random search algorithm implemented by Vizier [30], which basically employs the strategy of sampling points b uniformly at random as well as sampling some points b near the currently best observed architectures.

1) -largely focused on the heavily-studied problem of scene labeling.


The number of function evaluations required by the algorithm to achieve this ε-approximation of the maximum defines the sample-complexity.

a necessary condition for an interval [a, b] to be split is that max(W (a), W (b)) ≥ M − η which means that either a or b or both are η-near-optimal which is the key point of Lemma 2.


Suppose that we are given a hierarchical decomposition of a control task in the form of two MDP\Rs -a low-level and a high-level MDP\R, denoted M = (S , A , T , H , D ) and M h = (S h , A h , T h , H h , D h ) respectively -and a partitioning function ψ : S → S h that maps low level states to high-level states (the assumption here is that |S h | |S | so that this hierarchical decomposition actually provides a computational gain).

often the reward function R can be represented more compactly as a function of the state.


To derive the submodularity cut, we use the following definition: Definition 3 (γ-extension) Let g : R n → R be a convex function, x ∈ R n , γ be a real number satisfying γ ≥ g(x) and t > 0.

as stated below, this approach is inefficient even for moderate problem sizes.


First, the fixed objective f gives us a more direct way of tracking the change in comparator through f (u t ) − f (u t+1 ), which might often be milder than u t − u t+1 .

statistically, using stages guarantees that the monomials added in the previous stage have an opportunity to have their corresponding parameters converge.


We provide a sound termination condition for the algorithm based on the criterion proposed by Perkins et al.

this method was designed for the log-likelihood objective.


In our case, we define importance by separability-or a gap-rather than simply variance.

each group g is characterized by a latent variable f g which contains the formula associated with the group g. In this work, we only consider the formulas f g = or, f g = and and constrain each dimension to belong to only one group.


In both cases, we assume that the models of the dynamics (state, observation) are known.

such particle-based approaches have been used in many applications (see e.g.


In the presence of gross errors, the classical Principal Component Analysis (PCA) method, which is probably the most widely used tool for data analysis and dimensionality reduction, becomes brittle -A single gross error could render the estimate produced by PCA arbitrarily far from the desired estimate.

capital letters such as M are used to represent matrices, and accordingly, [M ] ij denotes its (i, j)th entry.


Given the tighter ELBOs in ( 6) and ( 7), we develop a distributed algorithm to optimize the latent factors U, the inducing points B, the variational parameters λ (for binary data) and the kernel parameters.

our algorithm can fully exploit the memory-cache mechanism to achieve fast inference.


We examine two special cases: (1) MNNs with real weights (2) MNNs with binary weights (and real bias).

the output of the network is therefore We assume that the weights are constrained to some set S, with the specific restrictions on each weight denoted by S ij,l , so W ij,l ∈ S ij,l and W ∈ S. If S ij,l = {0}, then we say that W ij,l is "disconnected".


The maximal cliques of the graphical model are the fully connected nodes (f (x 1 ), .

we propose a Bayesian undirected graphical model for co-training, or more generally for semi-supervised multi-view learning.


One possible method is to divide the variables into smaller blocks and quantize them separately.

the computational complexity of this source coding method is exponential in n. like the Shannon random codebook, this is a demonstration of the asymptotic achievability of the lower bound (3), rather than a practical scheme to be implemented.


To detect density ridges from data, [22] proposed the 'Subspace Constrained Mean Shift (SCMS)' algorithm.

the coverage plot reveals the quality for representation.


Such models take the form where, for FilterBoost, f t (x) = α t h t (x).

on each round, a boosting-by-filtering algorithm draws a set of examples from D t via the filter, trains the weak learner on this set, and receives a weak hypothesis h t . Though a batch booster would estimate t using the fixed set S, filtering boosters may use new examples from the filter.


After learning, at test-time we replaced back σ(x; a c ) with h(x; a c ) to obtain binary descriptors.

in contrast to previous work in the domain of object recognition, we do not choose an arbitrary intermediate representation, but explicitly learn short codes.


One stochasticity comes from sampling data points as in stochastic gradient descent.

the data are represented by sorted Coulomb matrices of size 75 × 75 [14].


In general, these matrices describe how the state of a dynamical system autonomously evolves with time, A; how inputs affect system states, B; how states are mapped into outputs, C; and how inputs instantaneously affect the system's output D (Astrom and Murray, 2012).

in order to generate optimal eligibility traces, synapses must include a forward model of the controlled subsystem.


We only describe and relate some of the existing literature briefly in this section since each of the four problems are already well explored separately on their own.

we relax the boolean constraints, allowing y and z to take any value between 0 and 1.


The number of iterations needed to find an optimal result on the development set is smallest for Algorithm PR(cont), compared to Algorithms EL and CE.

the out-of-domain baseline model has around 200k active features.


This work was supported in part by NSF under award IIS-0931463.

we show that the likelihood ratio policy gradient estimate is equivalent to the gradient of an importance sampled estimate of the expected return function estimated using only data from the current policy.


Freund and Schapire [10] showed that MW updates converge to NE empirically in any two-person zero-sum game using the notion of regret; their analysis also yields a simple and beautiful proof of John von Neumann's Minimax Theorem.

such bad accumulation exists even when ε is arbitrarily tiny, which might be surprising to people not familiar with numerical methods, since they might have the misconception that once the step-size ε is sufficiently small, the discretization would always yield a good approximation of its continuous counterpart.


Smoothness is captured by a low pass filter with only lower frequencies passing through.

with a similar generation procedure as in 1dimensional experiment, a 2-dimensional w is generated with analogical properties as the regression weights in fMRI data.


To overcome this √ d gradient evaluation barrier, we therefore need to control the change in the Hessian with respect to a norm which does not grow as quickly with the dimension as the Euclidean norm for a random N (0, I d ) momentum vector.

in this paper, we show that the conjecture of [11], which says that HMC requires O * (d 1 4 ) gradient evaluations, is true when sampling from strongly log-concave targets satisfying weak regularity properties associated with the input data.


Figure 3 shows objective vs. time plots for the three ML algorithms, over several machine configurations.

any number of read row() and inc() calls can be made in-between calls to clock().


Another benefit is that they require very little processing of the visual signal (some of them operating on raw pixel values [10]).

finally, we show how to incorporate auditory information using our visual-only model as a training signal.


In the rest of this paper, we shall assume that the cost function takes the following form: where β is the fixed cost of maintaining a neuron, and γ is the cost of a spike (c.f.

adopting a control policy that minimizes a variational upper bound on surprise will lead to optimal behavior.


In these work, different tree-structured encoders are proposed for embedding the input data, and different tree-structured decoders are proposed for predicting the output trees.

one approach is to model the problem as a machine translation problem between two languages, and thus numerous neural machine translation approaches can be applied.


We analyze the correctness and convergence time of A ⇤ Sampling and demonstrate empirically that it makes more efficient use of bound and likelihood evaluations than the most closely related adaptive rejection sampling-based algorithms.

the distribution over the number of iterations is distributed as a Geometric distribution with rate parameter µ(R d )/(exp(M )⌫(R d )).


4A), and the extrinsic curvature κ(θ) of the curve is defined as κ(θ) = 1/R(θ).

case of a sigmoidal nonlinearity, φ(h) = tanh(h).


From this literature has emerged the notion of brain modules specialized to a task, such as the celebrated fusiform face area (FFA) dedicated to face recognition [1].

cogPO focuses on the description of the experimental conditions characteristics, namely the explicit stimuli and their modality, the instructions, and the explicit responses and their modality.


It was seen that the order in which the inputs are presented to the encoder during inference affects its performance.

in fact, the Delaunay Triangulation for a given set of points triangulates the convex hull of these points.


The CVP implements the-rich-get-richer dynamics as an interplay of these two preferential reinforcements, learning latent qualities of individual responses as inspired in Table 1.

3 max The {q T j } in the Table 3 shows the result from solving (1) up to T -th votes for each j 2 {1, 2}.


1 i,j is an indication function, which will be 1 if R i,j is observed and 0 otherwise.

as analyzed in this paper, submatrices with different ranks could coexist in the rating matrices and only adopting a fixed rank cannot achieve optimal matrix approximation.


Meanwhile, artificial neural networks have been used in computer music [4,12].

the first, third, fifth, and seventh notes of a major scale are the major seventh chord.


This is drastically lower than the best known bound of O m 2 n/ on the number of iterations required by convex methods, and just a factor r away from the complexity of vanilla PCA.

we implemented our method in Matlab and used a Matlab implementation of the IALM method by [LCM10].


If one visualizes the learned deep features in the high-dimensional space, the learned deep features of refined face image set form several compact clusters and each cluster may be far away from others.


The 2N distances can determine the location of the vertices along the dimension up to a shift, through use of the law of cosines: For each subsequent dimension, two new vertices are chosen and new dissimilarities (δ ai , δ bi ) are computed by Dijkstra's algorithm.

an MDS algorithm needs to be tested on distance matrices that are computed from distances between real points, in order to verify that the algorithm quickly produces sensible results.


Proteins are produced through translation of mRNA with a rate proportional to the mRNA abundance.

this simple network motif is one of the most important building blocks of the transcriptional regulatory networks found in cells because of its ability to increase robustness in the face of fluctuation in external signals [10].


The results that we presented here are promising, but it remains for future work to more fully explore the relation between the failures exhibited by this model and those exhibited by humans.

humans must of course be extremely flexible in their behavior.


By Lemma 4, after t = 4(q−H(0)) r + 1 steps of the MW updates, H(t) > q, a contradiction.

a mixed strategy of a Player i is a probability distribution over her strategy set, represented by a vector x i ∈ R ni with j∈Si x ij = 1, where x ij is the probability density that strategy j is chosen.


Extension to other cases, such as the restricted iGaP model of Example 2, are straightforward.

the fraction of documents for which the correct labels is one of the n most likely.


For example, locality is not satisfied by the spectral clustering functions ratio-cut and normalized-cut.

outer consistency is defined in the same way consistency, except that (C, d)-consistent is replaced by (C, d)-outer consistent.


For convenience, lets restrict the memory of player 2 to be 1.

then let µ b0∶t be the distribution obtained by conditioning µ on the actions of player 2 being b 0∶t .


following ideas from [18], we can find a simple relaxation by considering the following constraints: (a) for all i 6 = j, for all i 6 = j, Y ij 6 inf{y i , y j }, which corresponds to x i x j 6 inf{x i , x j } for any x 2 [0, 1] n , (c) for all i, Y ii 6 y i , which corresponds to x 2 i 6 x i , and (d) for all (i, j) .


Usually, it is feasible to find only the most likely or maximum a-posteriori (MAP) assignment (structure) rather than sampling from the full Gibbs distribution.

when the random perturbations follow the Gumbel distribution (cf.


as the algorithm progresses down the tree it prunes all the nodes that cannot be prefixes of heavy hitters, hence leaving Õ( √ n) nodes in every depth.


Our algorithm is based on alternated minimization and a greedy coordinate descent solver that leads to state-of-the-art running time on long time series.

greedy selection is more efficient iteration-wise (Nutini et al., 2015).


When learning a function f , we may have access to not only the output values f (x i ) for training points x i , but also the values of its j-th order derivatives with respect to the input, D j x f (x i ).

the stark difference in approximation error is highlighted in Figure 3, where we show the Styblinski-Tang function and its approximations with both regular and Sobolev Training.


Moreover, the curves with plus marks representing ROGD-f does not drop down but even go up instead, which is also reasonable because it is fixed and if there are some recovering errors, it will perform worse.

the steps in Algorithm 3 on rounds 1, . . . , T 1 is the same as that in Algorithm 2.


On the surface, our network appears similar to AC-GAN [24], where the only difference is the separation of the classifier network from the authenticator network.

variants of GAN have been proposed to improve the quality of the synthetic images [22,3,23,24].


Next, in §3 we formulate its kernel variant, and in §4 we discuss classification with aligned data.

table 1 features results from a 7-label classification experiment.


The corpus has a high percentage of stops and fricatives in the initial and final consonant positions.

the STI does not accurately model intraband masker non-linearities, phase distortions or the underlying auditory mechanisms (outside of independent frequency bands) We therefore sought to extend the AI/STI concepts to predict intelligibility, on the assumption that the closest physical variable we have to the perceptual variable of intelligibility is the auditory nerve response.


We consider the problem of approximate joint matrix triangularization when the matrices in M are jointly diagonalizable and real, but we only observe a set M' of noise perturbed versions of the matrices in M. Our main result is a first-order upper bound on the distance between any approximate joint triangularizer of the matrices in M' and any exact joint triangularizer of the matrices in M. The bound depends only on the observable matrices in M' and the noise level.

the parameter σ can often be bounded by a function of the sample size, as in problems involving empirical moment matching [4].


Observed vs. unobserved denotation sets.

the focus of these QA approaches is understanding natural language, whereas we focus on queries that are in logical form.


(taken from [16]) For a given sequence of Erdös-Rényi networks G(n, c n ), we have: As previously stated, our results hold for any given graph, and not only asymptotically.

the first bound (Proposition 1) applies to any set of influencers A such that |A| = n 0 .


We analyzed the results in two ways: by counting each suffix once for each word type it was associated with, and by counting once for each word token (thus giving more weight to the results for frequent words).

we will focus on a different preferential attachment scheme, based upon the two-parameter species sampling model [4,5] known as the Pitman-Yor process [6].


For example, in Figure 1, it is seen that for recognizing a character, not all of the context are useful.

the GRCL is a generalization of RCL and it can adjust context modulation dynamically.


Indeed, iterative regularization algorithms are classical in inverse problems [15], and have been recently considered in machine learning [36,34,3,5,9,26], where they have been proved to achieve optimal learning bounds, matching those of variational regularization schemes such as Tikhonov [8,31].

this excludes the choice t ⇤ (n) = 1 for all n 2 N ⇤ , namely considering only one pass over the data.


On the WMT'14 English to French translation task, we obtained a BLEU score of 34.81 by directly extracting translations from an ensemble of 5 deep LSTMs (with 380M parameters each) using a simple left-to-right beam-search decoder.

the right plot shows the LSTM's performance on sentences with progressively more rare words, where the x-axis corresponds to the test sentences sorted by their "average word frequency rank".


Second, it enjoys significant variance reduction over the unbiased estimates, smaller bias than averaged gradients, and leads to smaller mean-squared error against the full gradient.

every few hundred iterations, an entire pass through the data set is necessary, which makes the performance and expenses of the method depend on the size of the data set.


We designed the classifier for use in a clinical setting, where physicians have little time to label beats, let alone tune classifier parameters.


But instance E only having tag MAGA (indicated by the dotted line) produces a more complex example which there is no feasible solution.


according to our analysis, Double Q-learning sometimes underestimates the action values, but does not suffer from the overestimation bias that Q-learning does.


The minimization of the tr(WG) term forces the weights of the instances to reflect their local properties.

at each iteration, the main computations are in the gradient and the objective value with complexity O(nmd + n 2 m).


To overcome this limitation it has been proposed to smooth the dual objective using a soft-max function [7,8].

( 3) is a smooth function with Lipschitz constant L = 1 P r V r [see 24].


Object tracking requires some assumptions about how objects evolve over time.

we can modify our model to track in feature space by adding new dimensions corresponding to the features being tracked.


We found the binomial approximation to yield the most accurate predictions in parameter ranges of interest to us, namely 500-4000 total units and connectivities ranging from .05-.15 (see Figure 2).

in the presence of noise the same input applied multiple times to the same network will produce divergent trajectories , hence different final conditions, thus making the use of DALs for pattern classification problematic.


A focus on exploitation n of local optima.

although we did not observe a statistically significant improvement at the inferred optimum compared to sensible alternative policies, the results are consistent with our inferred optimum being an improvement over the type of policies one might have proposed a priori.


A challenge in implementing this solution lies in the enormity of the data space, which may contain a truly astronomical number of patterns.

also, in many cases a learning (i.e., model-Þtting) algorithm for Þnding optimal parameter values is not proposed along with the model, further complicating matters.


As mentioned earlier, most computation for the inside-outside algorithm is spent on the tensor calculation of T a→b c on the intermediate inside/outside quantities.

finally, for vectors x, y, z ∈ R m , xy z is the tensor D ∈ R m×m×m where D i,j,k = x i y j z k (this is analogous to the outer product: [xy ] i,j = x i y j ).


We then make the following assumption about the noise distribution:  This assumption enforces three constraints.

suppose that the most likely label for a particular input x n is y n = l. Because p(y n |x n ) is a multinomial distribution, a different label y n = l might be assigned to x n by the labeling process.


(A2) Bounded Potentials: The edge potentials θ := {θ i,j } of the Ising model are bounded, and let Similarly assume bounded node potentials.

intuitively, local neighborhoods of G can be constructed through latent tree methods.


Although drawing tutoring has a larger network than mortgage underwriting, POLARIS consumes less time on it.

[14] assign importance values to features for a particular prediction.


The standard view of perceptual decision making across psychology and neuroscience is of a competitive process that accumulates sensory evidence for the choices up to a threshold (bound) that triggers the decision [1,2,3].

a single-trial learning rule performs like stochastic gradient ascent averaged over many trials.


In the worst case, Algorithm 3 is not polynomial time, as N v is not upper bounded by a constant in general.

it turns out that every match (X, Y ) can be decomposed as a union of simple matches, where a simple match is an atomic match that cannot be decomposed any further.


Indeed, it is this approximate nature of our reflexive controller that allows the physical properties of the robot itself to contribute implicitly to generation of overall gait trajectories.

θ ES is the threshold of the extensor reflex and α ES a positive constant.


This is reflected by a subtle rise in some of the Cramer-Rao bounds at very low values of ∆t.

in addition, there is evidence that timing mechanisms are distributed [9] but subject to local (e.g.


For the latter, after training a classifier H on Z (figure 1, step 1) we fixed different margin thresholds considering the lowest and the highest output values of H over the labeled training examples.


Pakman and Paninski [11,10] present an algorithm to exactly solve these dynamics for quadratic U .

though traditional Hamiltonian Monte Carlo can in principle be used on such functions, the fact that the Hamiltonian will often be dramatically changed by the dynamics can result in a very low acceptance ratio, particularly in high dimensions.


The rest of the components in the vector (98 altogether) were generated independently using the normal distribution with a zero mean and a standard deviation of 0.05.

first note that given the vector v we can compute the norm of w as follows, Next, given two vectors x i and x j the value of their inner-product is, although we cannot compute the vector w explicitly we can still compute its norm and evaluate any of the kernels from the class C. Synthetic data: We generated binary-labelled data using as input space the vectors in 100 .


We consider a multi-armed bandit problem where there are two phases.

regime 2: Soft experimentation deadline, adaptive.


The gap between VCL and batchnorm is larger for SELU and the lowest for ReLU, which is also consistent with the results in Tab.

we are interested in distributions p ρ such that the quantity E[(σ 2 − σ 2 s ) 2 ] is minimized under the constraint that the variance is fixed, i.e., σ 2 = α.


We demonstrate the effectiveness of our approach by providing a comparison with state of the art methods and learning pictorial structures [6] for face recognition.

in order to facilitate their use, we consider the problem of learning them by approximating an observed distribution.


In the stereo-matching task subjects were presented with two target objects and a larger surrounding circle (25.2 degrees diameter) paired with one of the targets.

the difference between uncertainty conditions was only significant for two surround depths (0.6 and 1.0 degrees, one-sided paired t-test p=0.004, p=0.0281) and not significant as a main effect (2-way ANOVA p=0.3419).


In the best sparsity case, Δ = 1 /n and we get the condition τ ≤ √ n /10.

the average of a vector or matrix is denoted α := 1 n � n i=1 α i .


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

[5] proposed "labelled LDA," which is also a joint topic model, but for genes and protein function categories.


On the other hand VI is subject to bias on account of the introduction of the approximating variational distribution.

the following proposition shows that if each forward transition and backward transition are locally optimal, the result is globally consistent, which means the marginals r ⇤ t (z t ) and q ⇤ t (z t ) constructed by locally optimal transitions match the intermediate target f t (z t ).


These two steps are iterated until some level of accuracy is reached.

the definition of the Bayes' rule (4) clearly shows that the estimation of P(Y = 1|X = x) does not have to be accurate everywhere, but only in the vicinity of p + and p − .


Hence, Quartz is much better in the large τ regime.


Then, the new proof state constructed by unify is: Thus, the output score of the neural network S 0 ⇢ will be high if the subsymbolic representation of the input s is close to grandpaOf and the input i is close to BART.

in addition, we constrain proofs to be cycle-free by checking whether a variable is already bound.


This perhaps suggests that it is only the exact mapping of the models to the neural substrate that holds any remaining theoretical interest.

first the 'local field' is calculated as 3 + Input, then the output of the neuron is calculated as a threshold linear function of the local field: Thr and x i := 0 otherwise, where g := 0.53 a/ (1 − a) is the gain parameter, and h Thr := 0 is the threshold, and the value of k is set by iterative search to optimize performance.


We also trained our system using a larger dataset, Librispeech Corpus [33].

to overcome this problem, we add a depth-wise 1-D convolutional layer at the input of each recurrent layer.


The training network forward pass is a probabilistic representation of the deployment network forward pass.

the specific networks employed here, and associated parameters, are shown in Figure 3A.


Since the latent generalized correlation matrix encodes marginal uncorrelatedness while the latent generalized concentration matrix encodes conditional uncorrelatedness of the variables, the analysis of the population models are orthogonal and complementary to each other.

the final data matrix we obtained is X ∈ R n×d .


An overall very accurate approximation is then obtained if the subspaces are well selected and if they do contain the large majority of posterior mass.

for a given observed data point, all except for a very small fraction of the latent components can be assumed to be non-causal or irrelevant, hence the corresponding latent space can be neglected for the integration over � s. For a sparse initiation (i.e., π � 1) of the spike-and-slab model ( 1) to (2), we consider such low dimensional subspaces to be spanned by a few (approximately πH) of the H latent space coordinates.


Additionally, cross-entropy can be used as an auxiliary loss for in-distribution data.

this technique has been successfully applied to tasks in computer vision [19,20].


The success of the streamlining constraints is strongly governed by the literals selected for participating in these added disjunctions.

streamlining takes smaller steps in reducing the search space (as opposed to decimation) and hence are less likely to make inconsistent variable assignments.


Here 200 examples were drawn from the target distribution with label noise applied at various levels.

such a view neglects the possibility of reformulated training methods that can yield practically solvable alternatives.


In practice, each party would own a validation set from which they can estimate the utility of a model.

the model is optimized using stochastic gradient descent with a learning rate of 0.01 and momentum of 0.5.


In practice, we use the TCP trace computation algorithm (Equations 4 and 5) unless otherwise noted.

we observed that performance decreases as the number of neighbours increases.


this prior is much more realistic than a smooth one, as it allows only a small number of odors (out of ∼10,000) to be present in any given olfactory scene.


Quantization methods: Following [23] we used the GEMMLOWP quantization scheme as decribed in Google's open source library [1].

our simulations show that Range BN is equivalent to the traditional batch norm if a precise scale adjustment, which can be approximated analytically, is applied.


Progressively, the RNN4 and RNN8 seem to generalize well on chairs with longer predictions (t = 6 for RNN4 and t = 12 for RNN8).

3D view synthesis can be cast as pose manifold traversal where a desired rotation can be decomposed to a sequence of small steps.


We argue that Gaussianization density estimation indeed alleviates the problem of the curse of dimensionality.

therefore one can also view practically that at each iteration, the data is linearly transformed to the most marginally non-Gaussian coordinates and then each coordinate is marginally Gaussianized.


In most works, the variables are either discrete or the distribution is assumed to be Gaussian .

the middle panel shows a Gaussian distribution constructed only over the two variables and is thus an upper bound on the quality that we can expect from a linear Gaussian BN.


This novel hybrid use of 2D and 3D filters is suited for the highly anisotropic nature of serial section EM images.

during training, an output patch of specified size is randomly drawn from the training stacks at the beginning of each forward pass.


This association significantly broadens recent work connecting elementary, one-step iterative sparsity algorithms like (1) with simple recurrent or feedforward deep network architectures [20,30,34,38].

one popular non-trivial instantiation of this approach assumes g(u) = i log (u i + ) with > 0 a user-defined parameter [10].


This is referred in the literature as homophily.

we define the Markov chain Y * → A → Ŷ .


Therefore, during training we are masking the calculation of the unification success of a known ground atom that we want to prove.

the constructed neural network allowed us to compute the gradient of proof successes with respect to vector representations of symbols, and thus enabled us to train subsymbolic representations end-toend from facts in a KB, and to induce function-free first-order logic rules using gradient descent.


The static strategy p t = 0 witnesses 0, T ∈ G T for every horizon T . To ensure R 1 T < T , any strategy will have to play p t > 0 at some time t ≤ T . But then it cannot maintain R 0 t = 0.

suppose toward contradiction that R k t > r k at some t < T . An adversary may set all The two extreme trade-offs 0, T and T, 0 are Pareto optimal.


This can be done by sliding a cuboid (whose dimensions match our cuboid model) in 3D to best fit the 2D bounding box.

note however, that [1] returns only 2D boxes and hence a direct comparison is not possible.


There has so far been work in exploring Decision Tree (DT) language models [2,3], which attempt to cluster similar histories together to achieve better probability estimation.

the purpose of a language model is to estimate the probability of a word string.


The PASCAL dataset contains 2,051 training images and 5,011 testing images, belonging to 20 different categories.

among 100 classes, our model learned that there are 28 and 37 classes that can borrow from other classes without and with transformations, respectively.


Similar results were obtained if we restricted our sample to geniculate centers overlapped with the dominant subregion of the simple cell (n ϭ 31).

they predict temporal receptive fields of two different types resembling so-called lagged and non-lagged cells in the LGN.


Figure 2 shows the results of applying our SDPP sampling algorithm to this setting.

more generally, we consider modeling distributions over sets of structures (e.g., sequences, trees, graphs) where the total number of possible structures is exponential.


More precisely, we wish to map from a (small) support set of k examples of input-label pairs S = {(x i , y i )} k i=1 to a classifier c S (x) which, given a test example x, defines a probability distribution over outputs ŷ.

we compared our one-shot matching model to an oracle LSTM language model (LSTM-LM) [30] trained on all the words.


The learning rate is set heuristically to 0.01(λ −1 ) during the pretraining phase and modified to 0.01 min(1, λ −1 ) when training on the final objective.

wasserstein training can be seen as a more direct approach to density estimation than regularized KL training.


From our simulated data, we found that parameters of the noise (σ and ρ) can be recovered reliably with small variance.

this can be the major determinant of the bias structure in cases such as [8].


Note the extreme example of the stochastic oscillator, where the optimal encoder is concentrating all the resources in one dimension, essentially ignoring the second dimension.

this standard view, however, ignores the fact that sensors, controllers and actuators are often distributed across multiple sub-systems, and disregards the communication channels between these sub-systems.


A natural candidate for the optimal function f is the optimizer obtained from Lebesgue measure in Eq.

let d denote the ambient dimension, 0 denote the origin in R d and ) denote the complex-valued function on R d which are respectively continuous, absolutely integrable, square integrable, measurable and essentially bounded.


And what is the optimal sample complexity for each of these tasks?

namely that the variance in our estimator for F 3 (p) depends on the values of F 4 (p) and F 5 (p).


The latent group lasso predicts with a mixture of group sparse weights [see also 1,3,12].

it would be interesting to explore various extensions, such as, using the overlapped S 1 /∞-norm instead of the S 1 /1-norm or a non-sparse tensor decomposition.


Note that since the mutual information term is upper bounded by a constant (log N ), we are still maximizing a lower bound on the log-likelihood of data.

we can adopt the ODM idea for semi-supervised learning by assuming D 1 is the image domain and D 2 is the label domain.


To instantiate a complete ancestor, after sampling the alleles in the ancestor corresponding to the segment according to Eq.

due to space limit, we left out some details of the algorithms and more results of our experiments, which are available in the full version of this paper [Xing and Sohn, 2006].


We hypothesize that a simple fixed architecture of excitatory and/or inhibitory connections is sufficient to account for the cyclic trends in discrimination thresholds.

discrimination thresholds were obtained across eight 'test' motions corresponding to expansion, contraction, CW and CCW rotation, and the four intermediate spiral motions.


Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist.

lemma 3 (Bound mismatch in total reward).


Deep structure is included in order to capture the long-time dependence.

we believe this problem is caused by MF-variational inference used in our model and we hope it can be solved if we try other inference methods.


The R.EM 1110del of the \~lord-frequency effect described by Shiffrin and Steyvers [13,18,19] is a member of this class of models, as \ve describe next.

hirshnlan et a1 found that the difference in the LF and H'F FA.Rs \¥as not affected b:y 1\1idazolam.


(4) What is the most likely sequence of poses interpolating any two states?

key to the method is the assumption that features arise from potentials that vary only in low dimensional subspaces.


This can take Ω(n) time because regardless of where u is in the network, there always is another node v at distance Ω(n) from u.

suppose that g decomposes into a product of simpler functions, g(X) = j f j (X j ), for some collection of real-valued functions f j , called factors, whose arguments are (index-ordered) sets X j ⊆ X.


Theorem 2 provides a natural interpretation of the proposed approach.

as µ is varied, this leads to a trade-off between precision and recall.


An early work that formally motivates various negative dependence conjectures is [41].

a measure µ over 2 [n] is Exponentiated Strongly Rayleigh (ESR) if there exists an SR measure ν over 2 [n] and a power p ≥ 0 such that µ(S) ∝ ν(S) p . The parameter p serves to control the quality/diversity tradeoff by sharpening (p > 1) or smoothing out (p < 1) the variations of the ground SR measure (see Figure 1).


If we did know |H 1 | (and equivalently know |H 0 | = n |H 1 |) then a FWER+FWPD algorithm is equivalent to the so-called top-k multi-armed bandit problem [9,8] and controlling FWER would be relatively simple using a Bonferroni correction:  Because we only know |S t | and not its expectation, the extra factors in the surrogate expression used in R t are used to ensure correctness with high-probability (see Lemma 7).

[3,10]) we show that FDR is controlled for all times using the Benjamini-Hochberg procedure [11] (see Lemma 1), and also provide an anytime high probability bound on the false discovery proportion (see Lemma 2).


The breadth-first property ensures that the length of the path from u to i within T u is equal to the length of the shortest path from u to i in G 1 .

it seems plausible that the technique employed by [2] could be used to design a modified algorithm which does not need to have prior knowledge of the spectrium.


A major challenge in forming models based on the Bayesian hypothesis is the correct selection of two main components: the prior distribution (belief) and the likelihood function.

it might provide a new explanation for perceptual biases that are hard to reconcile with traditional Bayesian approaches [5].


Results: Our results, summarized in Table 1, show that our proposed methods substantially outperform all baseline methods.

. . ), they sample c i ∼ U{1, C} separately for each anchor node v i and potential context nodes, and only keep context nodes that are within c i -steps of v i .


Most of these semi-supervised learning algorithms are applicable only to multiclass classification problems [1,10,32], with very few exceptions that develop discriminative models suitable for structured prediction [2,9,16,20,21,22].

they proposed to minimize the following objective where the first term is the negative log conditional likelihood of the labeled data, and the third term is the conditional entropy of the CRF model on the unlabeled data.


This sPDE formulation has two chief advantages: it allows for a real-time synthesis using an AR recurrence and it allows one to recast the log-likelihood of the model as a generalization of the classical motion energy model, which in turn is crucial to allow for a Bayesian modeling of perceptual biases.

observers sat 57 cm from the screen in a dark room.


Articles that are currently the best are shown in the serving bucket; others are explored in the random bucket until their scores are better than the current best articles; at this point they get promoted to the serving bucket.

a data-driven machine learning approach can help with the scale issue, and we seek to blend the strengths of the editorial and algorithmic approaches by algorithmically optimizing content programming within high-level constraints set by editors.


Our analysis in Section 6 of the full paper predicts that, once is small in comparison to the gap σ k σ k+1 − 1, we should see much more rapid convergence since q will depend on log(1/ ) instead of 1/ .

as predicted, because its additional memory overhead and post-processing costs are small compared to the cost of the large matrix multiplication required for each iteration, Block Krylov Iteration outperforms Simultaneous Iteration for small .


[2015] also used the truncated SVD estimator for matrix completion.

it has wide applications in machine learning, especially in online recommendation systems.


In this section, we conduct simulations to verify the robustness of RoLR along with its applicability for robust binary classification.

the proposed RoLR can be easily adapted to solving binary classification problems where corrupted training samples are present.


Let G be any compact group with identity e and ρ : G → C dρ×dρ be a unitary representation of G. Then given an array of possibly noisy and unsynchronized group elements, (g ji ) i,j and corresponding positive confidence weights (w ji ) i,j , the synchronization loss (assuming g ii = e for all i) To synchronize putative matchings between images, we instantiate this proposition with the approriate unitary representation of the symmetric group.

the proposed model can easily generalize to other applications, outside computer vision, involving multi-matching problems.


here we revisit the recently proposed partially absorbing random walks (PARW) [23], which generalizes absorbing random walks by allowing partial absorption at each state.


All that remains is to decide on a heuristic used to select the parameter to be optimised in each step.

the most striking aspect of the comparison is that the Bayesian regularisation scheme is typically around two orders of magnitude faster than the cross-validation based approach, with SBMLR being approximately five times faster in the worst case (COVTYPE).


Consequently, recent work has considered normalizing flows [28], in which random variables from (for example) a Gaussian distribution are fed through a series of nonlinear functions to increase the complexity and representational power of the encoder.

considering Figure 2, note that VAE significantly underestimates the variance of the posterior (examining the marginals), a well-known problem of variational Bayesian analysis [7].


Future work can go in different directions.

the highest degrees of occurrences, e.g., for convolutional matching pursuit [31] seems to be assigned exclusively to Gabor features.


The only obstacle for using this new technique is the complexity of the corresponding inference problem, since it is considerably slower algorithm than the method of Batra et al.

the set {θ f : f ∈ F} of all potentials is referred by θ.


This can be done using methods such as Ksubspaces [2], an extension of Kmeans to the case of subspaces, or Expectation Maximization for Mixtures of Probabilistic PCAs [3].

the case in which n(t) = 1 and there are ρ 1 > 0, S ∈ N and i ∈ {1, . . . , N } such that for all m m+S t=m corresponds to the case of data that is rich in time.


(2009) who proposed an algorithm ("Exploratory FPL") for this setting and have shown an o(T ) almost sure bound on the regret.

no statistical assumptions are made about the choice of this sequence.


The affinity between two nodes is computed as W ij,ij = exp( −|pi−p ′ j | 0.05 ), where p i is the orientation of normal vector at the sampled point (node) i to the contour, similarly to p ′ j .

it can be obtained by setting the first derivative to zero ( ∂Φ(x,x) ∂x kl = 0), which gives we obtain the update rule in Eq.


The proof of proposition 5.1 can be found in the supplementary material.

the practical impact of OT is still limited because of its computational burden.


These predicates are useful for giving partial credit; for instance, it is easier to satisfy mod(y, 6) = 0 than y = 1296, but many programs that satisfy the former will have pieces that are also in the correct z.

in the relaxed case, the Fisher information can be written to first order as I β , to first order, is the covariance of the penalty −β ψ with the second-order statistics of φ.


Since the movie was taken while the cells were under drug treatment conditions, the properties of these calcium waves are important features of interest.

we expect a certain degree of smoothness among spatially adjacent warping functions.


In the experiments we discuss in the following, we set the hyperparameters as u The Bayesian method calculates p(θ, Z|X, M ), which is a posterior of unknown parameters and hidden variable set Z = (Y, S) given the data and model structure, M (in our case, this indicates the number of hidden states, and correlation structure).


The D problem can be optimized by introducing a variable S: The optimal solution of ( 11) can be obtained by the ADMM algorithm: When the difference between the energy in two adjacent iterations is less than 0.01, the iteration stops.

the atoms in the structured dictionary have class labels, and the class-specific representation residual can be computed for classification.


Separate experiments showed that the chip could also adapt rapidly to changes in the ISI within this range after initial learning.

cS related parallel fiber (pf) and US related climbing fiber (cf) signals converge at Purkinje cells (PU) in the cerebellum (Steinmetz et al.


To ask the adequate question, deep learning and reinforcement learning have been recently applied.

significant research on goal-oriented dialog has tackled this problem using from the rule-based approach to the end-to-end neural approach [1][2][3].


Accumulating statistics over the 50 runs we obtain the distributions reported in figure 3.

once one accepts that a synaptic element can neither have an unlimited dynamic range (i.e.


Each sweep lasts a total of one second, and data is sampled at 110Hz.

a biophysically-realistic embodied model of the whisker array is a critical first component of any model of the vibrissal system.


All three cases (a)-(c), are polynomial optimization problems which we solve by first applying the sparse SDP relaxation of first order [19] with SDPA [20] as the SDP solver, and then applying IPOPT [21]  The results for the deterministic case (a) show that the optimal setting and the overall pressure sum i∈V1 w i differ even when the demand at only one node changes, as reported in Table 1.

probability density functions can be readily estimated using a variety of data-driven methods, e.g., empirical histograms, kernel-based [8,9], and orthogonal basis [10] estimates.


The leading eigenvalue of its covariance matrix Σ is set as λ 1 = 100, and its corresponding eigenvector is sparse in the sense that only the first s = 5 entries are nonzero and set be to 1/ √ 5.

for synthetic dataset II, we set s = 10 and k = 5.


We show how this improves the running time of gradient descent and SVRG.

the worse-case time complexities of first-order methods are usually proportional to a fixed parameter times T . In large-scale settings, however, if we have already spent time computing the (full) gradient at x, perhaps we can use such information to reduce the time complexity to compute full gradients at other points near x.


The positive class is formed by 100 randomly chosen samples representing a number 0, and 100 representing a 1; the negative class by 100 samples representing a 2 and 100 representing a 3.

in this section, we will gradually derive a relaxed version of the transductive SVM formulation.


In experiments on simulated dynamic systems, comparing our Gaussian approximation to Monte Carlo simulations, we found that the propagation method is comparable to Monte Carlo simulations, and that both approaches achieved more realistic error bars than a naive approach which ignores the uncertainty on current state.

the iterated method provides any -step ahead forecast, up to the desired horizon, as well as the joint probability distribution of the predicted points.


We address this issue by introducing the notion of coset based multiresolution analysis (CMRA) on the symmetric group, find the corresponding wavelet functions, and describe a fast wavelet transform for sparse signals.

this instance of L-CMRA is an exact analog of Haar wavelets: V k will consist of all functions that are constant on each left S n−k -coset.


Their solution minimizes the worst-case loss over all possible choices of the data in these intervals.

an individual game may still possess a unique Nash equilibrium, and we can derive an algorithm that identifies it whenever it exists.


The lower bound quantifies directly how information constraints in online learning degrade the attainable regret, independent of the problem semantics.

the limitations shown in these works apply when the required precision exceeds the amount of memory available.


We describe the basic ideas of LP in Section 2, show how it applies to Gaussian Processes (in particular the Bayes Committee Machine of [9]) in Section 3, prove that SVM chunking is a special case of LP in Section 4, and finally demonstrate in experiments the feasibility of LP (Section 5).

we thank Nir Friedman, Zoubin Ghahramani and Adam Kowalczyk for useful suggestions and discussions.


Such a local analysis, however, quickly becomes impractically expensive when dealing with networks with millions of parameters.

we observed empirically that adding this weight decay prevents the weights to overly grow between every two computations of the proximity operator.


If the estimate, θ 02 , is eight instead of the true value, two, the efficiency of the optimal design at θ 0 is 36% of the optimal design at θ.

the resulting robust design spreads some experiments across the menu, but also concentrates on experiments that will help minimize the variance of the parameter estimates.


We additionally incorporate a bias term for each aspect, b a , to make the scores of multiple aspects comparable when we combine them into full cuboid model.

our 3D bed model was trained with two parts per face.


Each neuron in the optimal network will seek to reduce this loss function by firing a spike.

( 5) can be found by reversing the previous membrane potential analysis.


We conclude that the mixing time is around 100 iterations 5 .

optimize the hyper-hypers, ¡ & ¢ , for each of the variance parameters.


The consistency problem has been studied before as the membership problem for the marginal polytope (see Related Work); in the case of inconsistency, the closest consistency problem seeks the minimal perturbation to the data necessary to recover coherence.

by strong duality, the corresponding "reduced primal linear program," obtained from the linear program in Lemma 3.2 by retaining only the decision variables corresponding to the K 1.


The stimulus filter had 10 weights governing 10 basis functions, the post-spike and coupling filters each had 5 weights governing 5 basis functions, and a bias parameter was included.

we use systems of orthogonal Chebyshev polynomials to compute polynomial approximations.


Then, Algorithm 1 (where OPTCARD is replaced with Approximate OPTCARD, Algorithm 2) runs in at most log(k) + log(Q)/λ + 1 rounds and produces a solution of size at most 2k + 2 log(Q)k/λ .


To do so, we define the regularized empirical risk R n (w) := L n (w) + (cV n /2)kwk 2 and the corresponding optimal argument and attempt to minimize R n with accuracy V n . Since the regularization in ( 4) is of order V n and (3) holds, the difference between R n (w ⇤ n ) and L(w ⇤ ) is also of order V n -this is not immediate as it seems; see [16].

this bound not only improves the bound O(N 1+↵/2 ) for Ada AGD, but also enhances the complexity of SVRG for reaching the same target accuracy which is given by O In this section, we compare the adaptive sample size versions of a group of first-order methods, including gradient descent (GD), accelerated gradient descent (AGD), and stochastic variance reduced gradient (SVRG) with their standard (fixed sample size) versions.


These results thus fall in line with prior work demonstrating consistency of resting state networks across subjects [35,12], and reveal that feature-driven activity during natural viewing induces a similar functional clustering as that occurring during rest.

figure 1 shows the weights for the motion variable, Figure 2 for the human body variable, and Figure 3 for the language variable.


The double sampling structure suits the nature of dueling bandits and leads to more extensive usage of TS, which significantly reduces the regret.

the simplicity, good performance, and robustness of D-TS and D-TS + make them good algorithms in practice.


The purpose is to confirm that when the pairwise interactions of the underlying graphical models are highly nonlinear and unknown a prior, our additive estimator will be significantly superior to existing parametric/semi-parametric graphical models for inferring the structure of graphs.

where q and r are the truncation order parameters.


Integrating out the parameters in any HMM induces long range dependencies between states.

an advantage of this is that it is no longer necessary to constrain the HMM to have finitely many states and observation symbols.


Let Θ 0 be a positive definite matrix supported on ∆ ∪ E 0 .

minimizing the EBIC can be viewed as a data-driven method of tuning ρ, one that does not require creation of test data.


Before STDP, spike timing among neurons was highly variable (except for the very highest input rate).

we characterized PEP's pattern-recall performance as a function of the probability that the pattern in question's neurons are activated (Figure 6C).


We start by analyzing (4) in greater detail, and give tools for computing the regret value V T in such games.

that is, the Regret when we fix the plays on the first t rounds, and then assume minimax optimal play for rounds t +1 through T . following the approach of Rakhlin et al.


Apparently, the weights learned by CrowdSVM are also better than those learned by the other MV estimators.

crowdSVM jointly considers these two factors when estimating true labels.


For multimodal queries, the model trained with ML objective performed the best, although the performance gain was incremental.

the theorem holds under two assumptions, consistency of density estimators and ergodicity of transition operators.


The linear spatial model uses a set of spatial filters (vectors) w 1 , ..., w K to relate input to output.

instead of deriving an objective function from first principles, we derived an objective function heuristically, and verified through simulations that the objective function is capable of estimating the two-layer model.


The strength of such a fully Bayesian approach lies largely in its extensibility to allow for more accurate signal and noise models; in this vein work is continuing on the development of appropriate conditional prior structures for audio signals, including the formulation of Markov random field models.

consider a function ¡ whose time-frequency support is centred about the origin, and let ¡ ¡ ¢ £ denote a time-shifted (translation by ¤ ¦¥ ) and frequency-shifted (modulation by § ¨) version thereof; such a collection of shifts defines a sampling grid over the time-frequency plane.


Theorem 1.1 (Lyapunov's theorem [6, page 368]) If for some δ > 0, we have the condition: as n → ∞ where d −→ denotes convergence in distribution, and we denote by N (a, σ 2 ) the normal distribution with mean a and variance σ 2 .

our result provides for the first time a rigorous solution of the mean filed equations for the standard Hopfield model and is in contrast to the mathematically unjustifiable replica technique that has been used hitherto for this derivation.


For the stochastic approximation procedure, the total number of parameter updates was 100,000, so the learning took about 25.6 minutes on a Pentium 4 3.00GHz machine.

3 for fully visible discrete MRF's, if one uses a Gibbs transition operator and the learning rate is set to is the largest magnitude of the gradient, and C 1 is the maximum variation of φ when one changes the values of a single component only: The proof of convergence relies on the following simple decomposition.


The proposed algorithm is an extension of the one proposed by Olshausen & Field.

only images from T to P-T+l are reconstructed -since the assumed length of the bases is T, those images contain only the bases whose other parts are also contained in the sequence.


First assume that the function comparison oracle makes no errors.

the semi-distance satisfies =: 2s T . Applying Theorem 4 we have where the final inequality holds since M 2 and a = 1/16.


We evaluate hierarchical matching pursuit for scene recognition on the MIT-Scene dataset [20].

single layer sparse coding heavily depends on hand-crafted SIFT features.


Four of the twelve examples of higher oppsex are given below: 1.

the gradient optimization gets stuck in poor local minima.


Recently, it has been suggested to consider a Bayesian inference approach [16] to (discreet) optimal control problems formalised in Section 2.

note that although with a fixed, long duration (e.g., AICO with duration T=0.41) the control and error costs are reduced for short movements, these movements necessarily have up to 4× longer durations than those obtained with AICO-T. For example for a movement distance of 0.2 application of AICO-T results in a optimised movement duration of 0.07 (cf.


I-SSGPR differs from LGR and LWPR in that it is a global method and does not learn the distance metric online.

for both robots, learning the inverse dynamics involves learning a map from the joint positions q (rad), velocities q ( rad s) and accelerations q ( rad s 2 ), to torques τ (Nm) for each of 7 joints (degrees of freedom).


The conceptual similarity to our approach is the idea of performing an image-wide clustering step.

the lower value for the image optimal setting of 18.2 compared to 25.