# Variational Inference for Bayesian Bridge Regression

arXiv: https://arxiv.org/abs/2205.09515 · HTML: https://mlsanity.com/paper/2205.09515/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 58 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Automatic Variational Inference in Stan](https://mlsanity.com/paper/1506.03431/) (2015)
- [Fast Approximate Inference for Arbitrarily Large Semiparametric Regression Models via Message Passing](https://mlsanity.com/paper/1602.07412/) (2016)
- [Variational Full Bayes Lasso: Knots Selection in Regression Splines](https://mlsanity.com/paper/2102.13548/) (2021)
- [Variational inference for count response semiparametric regression](https://mlsanity.com/paper/1309.4199/) (2013)

## Abstract (arXiv)

We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses ℓα norm, with α ∈ (0, +∞) to define a penalization on large values of the regression coefficients, which includes the Lasso (α = 1) and ridge (α = 2) penalizations as special cases. Full Bayesian inference seamlessly provides joint uncertainty estimates for all model parameters. Although MCMC aproaches are available for bridge regression, it can be slow for large dataset, specially in high dimensions. The ADVI implementation allows the use of small batches of data at each iteration (due to stochastic gradient based algorithms), therefore speeding up computational time in comparison with MCMC. We illustrate the approach on non-parametric regression models with B-splines, although the method works seamlessly for other choices of basis functions. A simulation study shows the main properties of the proposed method.