# Posts tagged variational inference

## Pathfinder Variational Inference

Pathfinder [Zhang *et al.*, 2021] is a variational inference algorithm that produces samples from the posterior of a Bayesian model. It compares favorably to the widely used ADVI algorithm. On large problems, it should scale better than most MCMC algorithms, including dynamic HMC (i.e. NUTS), at the cost of a more biased estimate of the posterior. For details on the algorithm, see the arxiv preprint.

## Introduction to Variational Inference with PyMC

- 13 January 2023
- how-to, intermediate

The most common strategy for computing posterior quantities of Bayesian models is via sampling, particularly Markov chain Monte Carlo (MCMC) algorithms. While sampling algorithms and associated computing have continually improved in performance and efficiency, MCMC methods still scale poorly with data size, and become prohibitive for more than a few thousand observations. A more scalable alternative to sampling is variational inference (VI), which re-frames the problem of computing the posterior distribution as an optimization problem.

## Empirical Approximation overview

For most models we use sampling MCMC algorithms like Metropolis or NUTS. In PyMC we got used to store traces of MCMC samples and then do analysis using them. There is a similar concept for the variational inference submodule in PyMC: *Empirical*. This type of approximation stores particles for the SVGD sampler. There is no difference between independent SVGD particles and MCMC samples. *Empirical* acts as a bridge between MCMC sampling output and full-fledged VI utils like `apply_replacements`

or `sample_node`

. For the interface description, see variational_api_quickstart. Here we will just focus on `Emprical`

and give an overview of specific things for the *Empirical* approximation.

## Variational Inference: Bayesian Neural Networks

- 30 May 2022
- intermediate

**Probabilistic Programming**, **Deep Learning** and “**Big Data**” are among the biggest topics in machine learning. Inside of PP, a lot of innovation is focused on making things scale using **Variational Inference**. In this example, I will show how to use **Variational Inference** in PyMC to fit a simple Bayesian Neural Network. I will also discuss how bridging Probabilistic Programming and Deep Learning can open up very interesting avenues to explore in future research.

## GLM: Mini-batch ADVI on hierarchical regression model

- 23 September 2021
- intermediate

Unlike Gaussian mixture models, (hierarchical) regression models have independent variables. These variables affect the likelihood function, but are not random variables. When using mini-batch, we should take care of that.