We study the problem of decision-theoretic online learning (DTOL). Motivated by practical applications, we focus on DTOL when the number of actions is very large. Previous algorithms for learning in this framework have a tunable learning rate parameter, and a major barrier to using online-learning in practical applications is that it is not understood how to set this parameter optimally, particularly when the number of actions is large. In this paper, we offer a clean solution by proposing a novel and completely parameter-free algorithm for DTOL. In addition, we introduce a new notion of regret, which is more natural for applications with a large number of actions. We show that our algorithm achieves good performance with respect to this new notion of regret; in addition, it also achieves performance close to that of the best bounds achieved by previous algorithms with optimally-tuned parameters, according to previous notions of regret.

We present a new boosting algorithm, motivated by the large margins theory for boosting. We give experimental evidence that the new algorithm is significantly more robust against label noise than existing boosting algorithm.

We present a simple variant of the k-d tree which automatically adapts to intrinsic low dimensional structure in data.

We present a new online learning algorithm for cumulative discounted gain. This learning algorithm does not use exponential weights on the experts. Instead, it uses a weighting scheme that depends on the regret of the master algorithm relative to the experts. In particular, experts whose discounted cumulative gain is smaller (worse) than that of the master algorithm receive zero weight. We also sketch how a regret-based algorithm can be used as an alternative to Bayesian averaging in the context of inferring latent random variables.

A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent dimension of the space in which the data happen to lie.

We analyze the "query by committee" algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the two-member committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease holds for query learning of thresholded smooth functions.

We analyze the "query by committee" algorithm, a method for filtering informativequeries from a random stream of inputs. We show that if the two-member committee algorithm achieves information gainwith positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease holds for query learning of thresholded smooth functions.

We study a particular type of Boltzmann machine with a bipartite graph structure called a harmonium. Ourinterest is in using such a machine to model a probability distribution on binary input vectors. We analyze the class of probability distributions that can be modeled by such machines.

We study a particular type of Boltzmann machine with a bipartite graph structure called a harmonium. Our interest is in using such a machine to model a probability distribution on binary input vectors. We analyze the class of probability distributions that can be modeled by such machines.