Learning Continuous Exponential Families Beyond Gaussian

TL;DR

This paper introduces a scalable, efficient method for learning continuous exponential family distributions, extending beyond Gaussian models to capture higher-order moments with improved runtime performance.

Contribution

We propose a novel Interaction Screening approach for learning continuous exponential families, offering better computational efficiency than existing methods.

Findings

Maintains similar accuracy and sample complexity as existing methods

Significantly faster runtime in numerical experiments

Effective for higher-order moment modeling beyond Gaussian assumptions

Abstract

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing general continuous exponential families modeling higher-order moments of the data beyond the mean and the covariance. Here, we introduce a computationally efficient method for learning continuous graphical models based on the Interaction Screening approach. Through a series of numerical experiments, we show that our estimator maintains similar requirements in terms of accuracy and sample complexity scalings compared to alternative approaches such as maximization of conditional likelihood, while considerably improving upon the algorithm's run-time.