and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A

We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a

and computationally efficient algorithms for a wide range of problems such as classification, regression, and novelty detection. In addition to allowing the exploitation of the kernel trick in an online setting, we examine the value of large margins for classification in the online setting with a drifting target. We

per-pixel classification problem. Our large and highly varied training dataset allows the classifier to estimate body parts invariant to pose, body shape, clothing, etc. Finally we generate confidence-scored 3D proposals of several body joints by reprojecting the classification result and finding

, mixed, good). We begin by identifying the unique properties of this problem and develop a method for automatically distinguishing between positive and negative reviews. Our classifier draws on information retrieval techniques for feature extraction and scoring, and the results for various metrics

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade

In this paper we study online classification algorithms for multiclass problems in the mistake bound model. The hypotheses we use maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarity-score between each prototype and the input instance

In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding

Machine Learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (a) improving classification accuracy by learning ensembles of classifiers, (b) methods for scaling up

programming, discrete optimization, Monte Carlo sampling, Law of Large Numbers, Large Deviations theory, sample average approximation, stopping rules, stochastic knapsack problem AMS subject classifications. 90C10, 90C15