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

2009/10/31 by Sham M. Kakade, Ohad Shamir, Kakade, Sham M. +5 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #I.2.6 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.0911.0054

Errata added. Incorrect claim about cumulants of the Bernoulli distribution fixed

openalex publication_date 2009/10/31 · arxiv created 2015/05/16 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong convexity property of general exponential families, which allow their generalization ability to be quantified. In particular, we show how this property can be used to analyze generic exponential families under L₁ regularization.

Citations

• High-dimensional covariance estimation by minimizing ℓ₁-penalized log-determinant divergence

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