We consider the problem of computing the maximum likelihood multivariate logconcave distribution for a set of points.

We propose the first reduction-based approach to obtaining long-term memory guarantees for online learning in the sense of Bousquet and Warmuth [8], by reducing the problem to achieving typical switching regret. Specifically, for the classical expert problem with K actions and T rounds, using our framework we develop various algorithms with a regret bound of order O( T (S ln T + n ln K)) compared to any sequence of experts with S 1 switches among n min{S, K} distinct experts. In addition, by plugging specific adaptive algorithms into our framework we also achieve the best of both stochastic and adversarial environments simultaneously.

We study the problem of properly learning large margin halfspaces in the agnostic PAC model.

We initiate a systematic investigation of distribution learning (density estimation) when the data is distributed across multiple servers. The servers must communicate with a referee and the goal is to estimate the underlying distribution with as few bits of communication as possible.

We investigate the problem of learning Bayesian networks in a robust model where an ɛ-fraction of the samples are adversarially corrupted. In this work, we study the fully observable discrete case where the structure of the network is given. Even in this basic setting, previous learning algorithms either run in exponential time or lose dimension-dependent factors in their error guarantees. We provide the first computationally efficient robust learning algorithm for this problem with dimension-independent error guarantees. Our algorithm has near-optimal sample complexity, runs in polynomial time, and achieves error that scales nearly-linearly with the fraction of adversarially corrupted samples. Finally, we show on both synthetic and semi-synthetic data that our algorithm performs well in practice.

We initiate a systematic investigation of distribution learning (density estimation) when the data is distributed across multiple servers. The servers must communicate with a referee and the goal is to estimate the underlying distribution with as few bits of communication as possible.

Neural Information Processing Systems http://nips.cc/