Trevor J. Hastie

Hristo S. Paskov, John C. Mitchell, Trevor J. Hastie

We propose `Dracula', a new framework for unsupervised feature selection from sequential data such as text. Dracula learns a dictionary of $n$-grams that efficiently compresses a given corpus and recursively compresses its own dictionary; in effect, Dracula is a `deep' extension of Compressive Feature Learning. It requires solving a binary linear program that may be relaxed to a linear program. Both problems exhibit considerable structure, their solution paths are well behaved, and we identify parameters which control the depth and diversity of the dictionary. We also discuss how to derive features from the compressed documents and show that while certain unregularized linear models are invariant to the structure of the compressed dictionary, this structure may be used to regularize learning. Experiments are presented that demonstrate the efficacy of Dracula's features.

Jason D. Lee, Trevor J. Hastie

We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of Gaussian graphical models and structure learning of discrete models. Our approach is a natural generalization of these two lines of work to the mixed case. The penalization scheme involves a novel symmetric use of the group-lasso norm and follows naturally from a particular parametrization of the model.