In this paper we consider approximate policy-iteration-based reinforcement learning algorithms. In order to implement a flexible function approximation scheme we propose the use of non-parametric methods with regularization, providing a convenient way to control the complexity of the function approximator. We propose two novel regularized policy iteration algorithms by adding L2-regularization to two widely-used policy evaluation methods: Bellman residual minimization (BRM) and least-squares temporal difference learning (LSTD). We derive efficient implementation for our algorithms when the approximate value-functions belong to a reproducing kernel Hilbert space. We also provide finite-sample performance bounds for our algorithms and show that they are able to achieve optimal rates of convergence under the studied conditions.

Dimensionality reduction is commonly used in the setting of multi-label supervised classification to control the learning capacity and to provide a meaningful representation of the data. We introduce a simple forward probabilistic model which is a multinomial extension of reduced rank regression; we show that this model provides a probabilistic interpretation of discriminative clustering methods with added benefits in terms of number of hyperparameters and optimization. While expectation-maximization (EM) algorithm is commonly used to learn these models, its optimization usually leads to local minimum because it relies on a non-convex cost function with many such local minima. To avoid this problem, we introduce a local approximation of this cost function, which leads to a quadratic non-convex optimization problem over a product of simplices. In order to minimize such functions, we propose an efficient algorithm based on convex relaxation and low-rank representation of our data, which allows to deal with large instances.

This paper studies the general problem of learning kernels based on a polynomial combination of base kernels. It examines the corresponding learning kernel optimization problem, shows how that minimax problem can be reduced to a simpler minimization problem, and proves that the global solution of this problem always lies on the boundary. We give a projection-based gradient descent algorithm for solving the optimization problem, shown empirically to converge in few iterations. Finally, we report the results of extensive experiments with this algorithm using several publicly available datasets demonstrating the effectiveness of our technique. Papers published at the Neural Information Processing Systems Conference.

We introduce a new family of positive-definite kernel functions that mimic the computation in large, multilayer neural nets. These kernel functions can be used in shallow architectures, such as support vector machines (SVMs), or in deep kernel-based architectures that we call multilayer kernel machines (MKMs). We evaluate SVMs and MKMs with these kernel functions on problems designed to illustrate the advantages of deep architectures. On several problems, we obtain better results than previous, leading benchmarks from both SVMs with Gaussian kernels as well as deep belief nets. Papers published at the Neural Information Processing Systems Conference.

We present a novel and highly effective approach for multi-body motion segmentation. Drawing inspiration from robust statistical model fitting, we estimate putative subspace hypotheses from the data. However, instead of ranking them we encapsulate the hypotheses in a novel Mercer kernel which elicits the potential of two point trajectories to have emerged from the same subspace. The kernel permits the application of well-established statistical learning methods for effective outlier rejection, automatic recovery of the number of motions and accurate segmentation of the point trajectories. The method operates well under severe outliers arising from spurious trajectories or mistracks. Detailed experiments on a recent benchmark dataset (Hopkins 155) show that our method is superior to other state-of-the-art approaches in terms of recovering the number of motions, segmentation accuracy, robustness against gross outliers and computational efficiency.

This paper addresses the important tradeoff between privacy and learnability, when designing algorithms for learning from private databases. First we apply an idea of Dwork et al. to design a specific privacy-preserving machine learning algorithm, logistic regression. This involves bounding the sensitivity of logistic regression, and perturbing the learned classifier with noise proportional to the sensitivity. Noting that the approach of Dwork et al. has limitations when applied to other machine learning algorithms, we then present another privacy-preserving logistic regression algorithm. The algorithm is based on solving a perturbed objective, and does not depend on the sensitivity.

We investigate a topic at the interface of machine learning and cognitive science. Human active learning, where learners can actively query the world for information, is contrasted with passive learning from random examples. Furthermore, we compare human active learning performance with predictions from statistical learning theory. We conduct a series of human category learning experiments inspired by a machine learning task for which active and passive learning error bounds are well understood, and dramatically distinct. Our results indicate that humans are capable of actively selecting informative queries, and in doing so learn better and faster than if they are given random training data, as predicted by learning theory.

Speaker comparison, the process of finding the speaker similarity between two speech signals, occupies a central role in a variety of applications---speaker verification, clustering, and identification. Speaker comparison can be placed in a geometric framework by casting the problem as a model comparison process. For a given speech signal, feature vectors are produced and used to adapt a Gaussian mixture model (GMM). Speaker comparison can then be viewed as the process of compensating and finding metrics on the space of adapted models. We propose a framework, inner product discriminant functions (IPDFs), which extends many common techniques for speaker comparison: support vector machines, joint factor analysis, and linear scoring.

We study convex stochastic optimization problems where a noisy objective function value is observed after a decision is made. There are many stochastic optimization problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation for the joint distribution of state-outcome pairs to create weights for previous observations. Those similar to the current state are used to create a convex, deterministic approximation of the objective function.

We present a novel feature selection algorithm for the $k$-means clustering problem. Our algorithm is randomized and, assuming an accuracy parameter $\epsilon \in (0,1)$, selects and appropriately rescales in an unsupervised manner $\Theta(k \log(k / \epsilon) / \epsilon 2)$ features from a dataset of arbitrary dimensions. We prove that, if we run any $\gamma$-approximate $k$-means algorithm ($\gamma \geq 1$) on the features selected using our method, we can find a $(1 (1 \epsilon)\gamma)$-approximate partition with high probability. Papers published at the Neural Information Processing Systems Conference.