Policy gradient Reinforcement Learning (RL) algorithms have received substantial attention,seeking stochastic policies that maximize the average (or discounted cumulative) reward. In addition, extensions based on the concept of the Natural Gradient (NG) show promising learning efficiency because these regard metrics for the task. Though there are two candidate metrics, Kakade's Fisher Information Matrix (FIM) for the policy (action) distribution and Morimura's FIM for the stateaction jointdistribution, but all RL algorithms with NG have followed Kakade's approach. In this paper, we describe a generalized Natural Gradient (gNG) that linearly interpolates the two FIMs and propose an efficient implementation for the gNG learning based on a theory of the estimating function, the generalized Natural Actor-Critic(gNAC) algorithm. The gNAC algorithm involves a near optimal auxiliary function to reduce the variance of the gNG estimates. Interestingly, the gNAC can be regarded as a natural extension of the current state-of-the-art NAC algorithm [1], as long as the interpolating parameter is appropriately selected. Numerical experimentsshowed that the proposed gNAC algorithm can estimate gNG efficiently and outperformed the NAC algorithm.

This paper presents a spike feature extraction algorithm that targets real-time spike sorting and facilitates miniaturized microchip implementation. The proposed algorithmhas been evaluated on synthesized waveforms and experimentally recorded sequences. When compared with many spike sorting approaches our algorithm demonstrates improved speed, accuracy and allows unsupervised execution. A preliminary hardware implementation has been realized using an integrated microchip interfaced with a personal computer.

We introduce a kernel-based method for change-point analysis within a sequence of temporal observations. Change-point analysis of an (unlabelled) sample of observations consists in, first, testing whether a change in the distribution occurs within the sample, and second, if a change occurs, estimating the change-point instant after which the distribution of the observations switches from one distribution to another different distribution. We propose a test statistics based upon the maximum kernel Fisher discriminant ratio as a measure of homogeneity between segments. We derive its limiting distribution under the null hypothesis (no change occurs), and establish the consistency under the alternative hypothesis (a change occurs). This allows to build a statistical hypothesis testing procedure for testing the presence of change-point, with a prescribed false-alarm probability and detection probability tending to one in the large-sample setting. If a change actually occurs, the test statistics also yields an estimator of the change-point location. Promising experimental results in temporal segmentation of mental tasks from BCI data and pop song indexation are presented.

The principles by which spiking neurons contribute to the astounding computational power of generic cortical microcircuits, and how spike-timing-dependent plasticity (STDP) of synaptic weights could generate and maintain this computational function, are unknown. We show here that STDP, in conjunction with a stochastic soft winner-take-all (WTA) circuit, induces spiking neurons to generate through their synaptic weights implicit internal models for subclasses (or causes") of the high-dimensional spike patterns of hundreds of pre-synaptic neurons. Hence these neurons will fire after learning whenever the current input best matches their internal model. The resulting computational function of soft WTA circuits, a common network motif of cortical microcircuits, could therefore be a drastic dimensionality reduction of information streams, together with the autonomous creation of internal models for the probability distributions of their input patterns. We show that the autonomous generation and maintenance of this computational function can be explained on the basis of rigorous mathematical principles. In particular, we show that STDP is able to approximate a stochastic online Expectation-Maximization (EM) algorithm for modeling the input data. A corresponding result is shown for Hebbian learning in artificial neural networks."

In this article, we propose fast subtree kernels on graphs.

The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a three-parameter generalization of the IBP exhibiting power-law behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the \emph{stable-beta process} and deriving the IBP corresponding to it. We find interesting relationships between the stable-beta process and the Pitman-Yor process (another stochastic process used in Bayesian nonparametric models with interesting power-law properties). We show that our power-law IBP is a good model for word occurrences in documents with improved performance over the normal IBP.

Query expansion is a long-studied approach for improving retrieval effectiveness by enhancing the user's original query with additional related words. Current algorithms for automatic query expansion can often improve retrieval accuracy on average, but are not robust: that is, they are highly unstable and have poor worst-case performance for individual queries. To address this problem, we introduce anovel formulation of query expansion as a convex optimization problem over a word graph. The model combines initial weights from a baseline feedback algorithmwith edge weights based on word similarity, and integrates simple constraints to enforce set-based criteria such as aspect balance, aspect coverage, and term centrality. Results across multiple standard test collections show consistent andsignificant reductions in the number and magnitude of expansion failures, while retaining the strong positive gains of the baseline algorithm. Our approach does not assume a particular retrieval model, making it applicable to a broad class of existing expansion algorithms.

Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al., 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al., 2008) in constrained clustering. Although in theory SDPs can be efficiently solved, the high computational complexity incurred in numerically processing the huge linear matrix inequality constraints has rendered the SDP approach unscalable. In this paper, we show that a large class of kernel learning problems can be reformulated as semidefinite-quadratic-linear programs (SQLPs), which only contain a simple positive semidefinite constraint, a second-order cone constraint and a number of linear constraints. These constraints are much easier to process numerically, and the gain in speedup over previous approaches is at least of the order $m^{2.5}$, where m is the matrix dimension. Experimental results are also presented to show the superb computational efficiency of our approach.

Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.

We propose in this paper RecLasso, analgorithm to solve the Lasso with online (sequential) observations. We introduce an optimization problem that allows us to compute an homotopy from the current solution to the solution after observing a new data point. We compare ourmethod to Lars and Coordinate Descent, and present an application to compressive sensing with sequential observations. Our approach can easily be extended to compute an homotopy from the current solution to the solution that corresponds to removing a data point, which leads to an efficient algorithm for leave-one-out cross-validation. We also propose an algorithm to automatically update the regularization parameter after observing a new data point.