Year: 2018
Type: preprint
Abstract: It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared to having only the Lasso point estimate. Traditionally, the Bayesian Lasso is implemented via Gibbs sampling methods which suffer from lack of scalability, unknown convergence rates, and generation of samples that are necessarily correlated. We provide a measure transport approach to generate i.i.d samples from the posterior by constructing a transport map that transforms a sample from the Laplacian prior into a sample from the posterior. We show how the construction of this transport map can be parallelized into modules that iteratively solve Lasso problems and perform closed-form linear algebra updates. With this posterior sampling method, we perform maximum likelihood estimation of the Lasso regularization parameter via the EM algorithm. We provide comparisons to traditional Gibbs samplers using the diabetes dataset of Efron et al. Lastly, we give an example implementation on a computing system that leverages parallelization, a graphics processing unit, whose execution time has much less dependence on dimension as compared to a standard implementation.
Source: arXiv (Cornell University)
Institution: University of California San Diego
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1513559549, G1957798471, G3112872626, Behavioral, Physiological, and Quantitative Models of Pro-Social Behavior, G408915191, G5382857288, G5385673730, Emerging Frontiers of Science of Information, G7452299184, SCH: INT: Collaborative Research: Replicating Clinic Physical Therapy at Home: Touch, Depth, and Epidermal Electronics in an Interactive Avatar System, G8257659198
OpenAlex ID: W2783582639