Valiant's learnability model is extended to learning classes of concepts defined by regions in Euclidean space En. The methods in this paper lead to a unified treatment of some of Valiant's results,… (More)

We consider two algorithms for on-line prediction based on a linear model. The algorithms are the well-known gradient descent (GD) algorithm and a new algorithm, which we call EG. They both maintain… (More)

We generalize the recent relative loss bounds for on-line algorithms where the additional loss of the algorithm on the whole sequence of examples over the loss of the best expert is bounded. The… (More)

We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worst-case situations, i.e., we make no… (More)

We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an… (More)

We explore the learnability of two-valued functions from samples using the paradigm of Data Compression. A first algorithm (compression) choses a small subset of the sample which is called the… (More)

We present an on-line investment algorithm which achieves almost the same wealth as the best constant-rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm… (More)

We study online learning algorithms that predict by combining the predictions of several subordinate prediction algorithms, sometimes called “experts.” These simple algorithms belong to the… (More)