Learning Continuous Exponential Families Beyond Gaussian
This addresses a scalability bottleneck for researchers and practitioners working with non-Gaussian continuous data, though it appears incremental as an algorithmic improvement.
The paper tackles the problem of learning continuous exponential family distributions with unbounded support beyond Gaussian models, introducing a computationally efficient method based on Interaction Screening that maintains similar accuracy and sample complexity while significantly improving run-time compared to alternatives.
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.