Markov random fields are a popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for provably learning them relied on exhaustive search, correlation decay or various incoherence assumptions. Bresler [4] gave an algorithm for learning general Ising models on bounded degree graphs. His approach was based on a structural result about mutual information in Ising models. Here we take a more conceptual approach to proving lower bounds on the mutual information.

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination.

While the field of statistical learning with sparsity [Hastie et al., 2015] has been steadily rising to

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We study the problem of learning overcomplete HMMs--those that have many hidden states but a small output alphabet.

Despite their wide success in a variety of domains, recurrent neural networks (RNNs) are often inhibited by the difficulty of learning an internal state representation.

A naive approach to an unknown model is the certainty equivalence principle .

These counts are then used to compute a reward bonus according to the classic count-based exploration theory. We find that simple hash functions can achieve surprisingly good results on many challenging tasks. Furthermore, we show that a domain-dependent learned hash code may further improve these results.

Exponential number of classes: this brings both additional computational and statistical challenges. By exponential, we mean exponentially large in the size of the natural dimension of output, e.g., the