Learning Exponential Families in High-Dimensions: Strong Convexity and Sparsity

The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions when the optimal parameter vector is sparse. This work characterizes a certain strong convexity property of general exponential families, which allows their generalization ability to be quantified. In particular, we show how this property can be used to analyze generic exponential families under L1 regularization.