Ron Meir

The kernel recursive least-squares algorithm

We present a nonlinear version of the recursive least squares (RLS) algorithm. Our algorithm performs linear regression in a high-dimensional feature space induced by a Mercer kernel and can therefore be used to recursively construct minimum mean-squared-error solutions to nonlinear least-squares problems that are frequently encountered in signal processing applications. In order to regularize solutions and keep the complexity of the algorithm bounded, we use a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be sufficiently well approximated by combining the images of previously admitted samples. This sparsification procedure allows the algorithm to operate online, often in real time. We analyze the behavior of the algorithm, compare its scaling properties to those of support vector machines, and demonstrate its utility in solving two signal processing problems-time-series prediction and channel equalization.

Reinforcement learning with Gaussian processes

Gaussian Process Temporal Difference (GPTD) learning offers a Bayesian solution to the policy evaluation problem of reinforcement learning. In this paper we extend the GPTD framework by addressing two pressing issues, which were not adequately treated in the original GPTD paper (Engel et al., 2003). The first is the issue of stochasticity in the state transitions, and the second is concerned with action selection and policy improvement. We present a new generative model for the value function, deduced from its relation with the discounted return. We derive a corresponding on-line algorithm for learning the posterior moments of the value Gaussian process. We also present a SARSA based extension of GPTD, termed GPSARSA, that allows the selection of actions and the gradual improvement of policies without requiring a world-model.

Semantic-oriented 3d shape retrieval using relevance feedback ∗

Shape-based retrieval of 3D models has become an important challenge in computer graphics. Object similarity, however, is a subjective matter, dependent on the human viewer, since objects have semantics and are not mere geometric entities. Relevance feedback aims at addressing the subjectivity of similarity. This paper presents a novel relevance feedback algorithm that is based on supervised as well as unsupervised feature extraction techniques. It also proposes a novel signature for 3D models, the sphere projection. A Web search engine that realizes the signature and the relevance feedback algorithm is presented. We show that the proposed approach produces good results and outperforms previous techniques.

Sparse Online Greedy Support Vector Regression

We present a novel algorithm for sparse online greedy kernel-based nonlinear regression. This algorithm improves current approaches to kernel-based regression in two aspects. First, it operates online - at each time step it observes a single new input sample, performs an update and discards it. Second, the solution maintained is extremely sparse. This is achieved by an explicit greedy sparsification process that admits into the kernel representation a new input sample only if its feature space image is linearly independent of the images of previously admitted samples. We show that the algorithm implements a form of gradient ascent and demonstrate its scaling and noise tolerance properties on three benchmark regression problems.

Nonparametric Time Series Prediction Through Adaptive ModelSelection

We consider the problem of one-step ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and adapt the uniform convergence framework of Vapnik and Chervonenkis to the problem of time series prediction, obtaining finite sample bounds. Furthermore, by allowing both the model complexity and memory size to be adaptively determined by the data, we derive nonparametric rates of convergence through an extension of the method of structural risk minimization suggested by Vapnik. All our results are derived for general L error measures, and apply to both exponentially and algebraically mixing processes.

Reinforcement Learning, Spike-Time-Dependent Plasticity, and the BCM Rule

Learning agents, whether natural or artificial, must update their internal parameters in order to improve their behavior over time. In reinforcement learning, this plasticity is influenced by an environmental signal, termed a reward, that directs the changes in appropriate directions. We apply a recently introduced policy learning algorithm from machine learning to networks of spiking neurons and derive a spike-time-dependent plasticity rule that ensures convergence to a local optimum of the expected average reward. The approach is applicable to a broad class of neuronal models, including the Hodgkin-Huxley model. We demonstrate the effectiveness of the derived rule in several toy problems. Finally, through statistical analysis, we show that the synaptic plasticity rule established is closely related to the widely used BCM rule, for which good biological evidence exists.

Explicit learning curves for transduction and application to clustering and compression algorithms

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapniks basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapniks transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space.

Towards Behaviometric Security Systems: Learning to Identify a Typist

We consider the problem of identifying a user typing on a computer keyboard based on patterns in the time series consisting of keyboard events. We develop a learning algorithm, which can rather accurately learn to authenticate and protect users. Our solution is based on a simple extension of the well known Lempel-Ziv (78) universal compression algorithm. A novel application of our results is a second-layer behaviometric security system, which continually examines the current user without interfering with this user’s work while attempting to identify unauthorized users pretending to be the user. We study the utility of our methods over a real dataset consisting of 5 users and 30 ‘attackers’.

Greedy algorithms for classification—consistency, convergence rates, and adaptivity

Many regression and classification algorithms proposed over the years can be described as greedy procedures for the stagewise minimization of an appropriate cost function. Some examples include additive models, matching pursuit, and boosting. In this work we focus on the classification problem, for which many recent algorithms have been proposed and applied successfully. For a specific regularized form of greedy stagewise optimization, we prove consistency of the approach under rather general conditions. Focusing on specific classes of problems we provide conditions under which our greedy procedure achieves the (nearly) minimax rate of convergence, implying that the procedure cannot be improved in a worst case setting. We also construct a fully adaptive procedure, which, without knowing the smoothness parameter of the decision boundary, converges at the same rate as if the smoothness parameter were known.

The Consistency of Greedy Algorithms for Classification

We consider a class of algorithms for classification, which are based on sequential greedy minimization of a convex upper bound on the 0 - 1 loss function. A large class of recently popular algorithms falls within the scope of this approach, including many variants of Boosting algorithms. The basic question addressed in this paper relates to the statistical consistency of such approaches. We provide precise conditions which guarantee that sequential greedy procedures are consistent, and establish rates of convergence under the assumption that the Bayes decision boundary belongs to a certain class of smooth functions. The results are established using a form of regularization which constrains the search space at each iteration of the algorithm. In addition to providing general consistency results, we provide rates of convergence for smooth decision boundaries. A particularly interesting conclusion of our work is that Logistic function based Boosting provides faster rates of convergence than Boosting based on the exponential function used in AdaBoost.