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
- Category: 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
- Category: 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
- Category: 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.