Reinforcement learning by direct policy gradient estimation is attractive in theory but in practice leads to notoriously ill-behaved optimization problems. We improve its robustness and speed of convergence with stochastic meta-descent, a gain vector adaptation method that employs fast Hessian-vector products. In our experiments the resulting algorithms outperform previously employed online stochastic, offline conjugate, and natural policy gradient methods.

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion.

We define a probability distribution over equivalence classes of binary matrices with a finite number of rows and an unbounded number of columns. This distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features. We identify a simple generative process that results in the same distribution over equivalence classes, which we call the Indian buffet process. We illustrate the use of this distribution as a prior in an infinite latent feature model, deriving a Markov chain Monte Carlo algorithm for inference in this model and applying the algorithm to an image dataset.

We propose a simple information-theoretic approach to soft clustering based on maximizing the mutual information I(x, y) between the unknown cluster labels y and the training patterns x with respect to parameters of specifically constrained encoding distributions. The constraints are chosen such that patterns are likely to be clustered similarly if they lie close to specific unknown vectors in the feature space. The method may be conveniently applied to learning the optimal affinity matrix, which corresponds to learning parameters of the kernelized encoder. The procedure does not require computations of eigenvalues of the Gram matrices, which makes it potentially attractive for clustering large data sets.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learning result and works for hundred thousands of examples or hundreds of kernels to be combined.

We present a series of theoretical arguments supporting the claim that a large class of modern learning algorithms that rely solely on the smoothness prior - with similarity between examples expressed with a local kernel - are sensitive to the curse of dimensionality, or more precisely to the variability of the target. Our discussion covers supervised, semisupervised and unsupervised learning algorithms. These algorithms are found to be local in the sense that crucial properties of the learned function at x depend mostly on the neighbors of x in the training set. This makes them sensitive to the curse of dimensionality, well studied for classical nonparametric statistical learning. We show in the case of the Gaussian kernel that when the function to be learned has many variations, these algorithms require a number of training examples proportional to the number of variations, which could be large even though there may exist short descriptions of the target function, i.e. their Kolmogorov complexity may be low. This suggests that there exist non-local learning algorithms that at least have the potential to learn about such structured but apparently complex functions (because locally they have many variations), while not using very specific prior domain knowledge.

To escape from the curse of dimensionality, we claim that one can learn non-local functions, in the sense that the value and shape of the learned function at x must be inferred using examples that may be far from x. With this objective, we present a non-local nonparametric density estimator. It builds upon previously proposed Gaussian mixture models with regularized covariance matrices to take into account the local shape of the manifold. It also builds upon recent work on non-local estimators of the tangent plane of a manifold, which are able to generalize in places with little training data, unlike traditional, local, nonparametric models.

A dynamic texture is a video model that treats a video as a sample from a spatiotemporal stochastic process, specifically a linear dynamical system. One problem associated with the dynamic texture is that it cannot model video where there are multiple regions of distinct motion. In this work, we introduce the layered dynamic texture model, which addresses this problem. We also introduce a variant of the model, and present the EM algorithm for learning each of the models. Finally, we demonstrate the efficacy of the proposed model for the tasks of segmentation and synthesis of video.

Many real-world classification problems involve the prediction of multiple interdependent variables forming some structural dependency. Recent progress in machine learning has mainly focused on supervised classification of such structured variables. In this paper, we investigate structured classification in a semi-supervised setting. We present a discriminative approach that utilizes the intrinsic geometry of input patterns revealed by unlabeled data points and we derive a maximum-margin formulation of semi-supervised learning for structured variables. Unlike transductive algorithms, our formulation naturally extends to new test points.

Brain-Computer Interface (BCI) systems create a novel communication channel from the brain to an output device by bypassing conventional motor output pathways of nerves and muscles. Therefore they could provide a new communication and control option for paralyzed patients. Modern BCI technology is essentially based on techniques for the classification of single-trial brain signals. Here we present a novel technique that allows the simultaneous optimization of a spatial and a spectral filter enhancing discriminability of multi-channel EEG single-trials. The evaluation of 60 experiments involving 22 different subjects demonstrates the superiority of the proposed algorithm. Apart from the enhanced classification, the spatial and/or the spectral filter that are determined by the algorithm can also be used for further analysis of the data, e.g., for source localization of the respective brain rhythms.