# On parameters transformations for emulating sparse priors using variational-Laplace inference

## TL;DR

This paper introduces a parameter transformation technique that allows L2-norm regularization methods to emulate sparse priors, simplifying sparse estimation in Bayesian models.

## Contribution

The authors propose a novel parameter transform that mimics sparse priors within a Bayesian variational Laplace framework, avoiding direct L1 regularization.

## Key findings

- The transform effectively emulates L1 regularization using L2 norms.
- Monte Carlo simulations validate the approach.
- The method simplifies sparse Bayesian inference.

## Abstract

So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined, i.e. when number of model parameters is much higher than the number of data points. Typically, such constraints are enforced by minimizing the L1 norm, which yields the so-called LASSO estimator. In this work, we propose a simple parameter transform that emulates sparse priors without sacrificing the simplicity and robustness of L2-norm regularization schemes. We show how L1 regularization can be obtained with a "sparsify" remapping of parameters under normal Bayesian priors, and we demonstrate the ensuing variational Laplace approach using Monte-Carlo simulations.

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Source: https://tomesphere.com/paper/1703.07168