Multilevel Monte Carlo simulation of a diffusion with non-smooth drift

TL;DR

This paper compares Lasso and Bayesian Lasso in high sparsity and low noise settings, introduces a multivalued SDE approach for Bayesian Lasso, and analyzes the computational costs of various Monte Carlo methods.

Contribution

It presents a novel SDE-based method for Bayesian Lasso and provides cost analysis for MC, MLMC, and MCMC algorithms.

Findings

Lasso and Bayesian Lasso are closely related under certain conditions

Three discretization algorithms for the proposed SDE are developed

Cost estimation methods for MC, MLMC, and MCMC are introduced

Abstract

We show that Lasso and Bayesian Lasso are very close when the sparsity is large and the noise is small. Then we propose to solve Bayesian Lasso using multivalued stochastic differential equation. We obtain three discretizations algorithms, and propose a method for calculating the cost of Monte-Carlo (MC), multilevel Monte Carlo (MLMC) and MCMC algorithms.