On Using Control Variates with Stochastic Approximation for Variational Bayes and its Connection to Stochastic Linear Regression
By Tim Salimans, David A. Knowles. 2014
37 citations recorded by the source corpus.
Recently, we and several other authors have written about the possibilities of using stochastic approximation techniques for fitting variational approximations to intractable Bayesian posterior distributions. Naive implementations of stochastic approximation suffer from high variance in this setting. Several authors have therefore suggested using control variates to reduce this variance, while we have taken a different but analogous approach to reducing the variance which we call stochastic linear regression. In this note we take the former perspective and derive the ideal set of control variates for stochastic approximation variational Bayes under a certain set of assumptions. We then show that using these control variates is closely related to using the stochastic linear regression approximation technique we proposed earlier. A simple example shows that our method for constructing control variates leads to stochastic estimators with much lower variance compared to other approaches.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- David M. Blei
- Stephan Mandt
- Dustin Tran
- Rajesh Ranganath
- Michalis K. Titsias
- Qiang Liu
- Max Welling
- Sergey Levine
In Statistics and Probability
- Stephan Mandt
- Michalis K. Titsias
- David M. Blei
- Dustin Tran
- Rajesh Ranganath
- Alp Kucukelbir
- Danilo Jimenez Rezende
- Hedvig Kjellström
Citations in the corpus
- Variational Inference: A Review for Statisticians (2016, background): “As examples, see Kingma and Welling (2014); Rezende, Mohamed, and Wierstra (2014); Ranganath, Gerrish, and Blei (2014); Ranganath, Tran, and Blei (2016); Salimans and Knowles (2014); Titsias and Lázaro-Gredilla (2014); and Tran, Ranganath, and Blei (2016).”
- Automatic Differentiation Variational Inference (2016, background): “Ranganath et al. (2014) and Salimans and Knowles (2014) propose a black-box technique that only requires computing gradients of Algorithm 1: Automatic Differentiation Variational Inference Input: Dataset x = x1:N , model p(x ,θ ).”
- Stochastic Backpropagation and Approximate Inference in Deep Generative Models (2014, background): “…(Williams, 1992), since it is simple to implement and applicable to both discrete and continuous models , though control variate methods are becoming increasingly popular for variational inference problems (Hoffman et al., 2013; Blei et al., 2012; Ranganath et al., 2014; Salimans & Knowles, 2014).”
- Automatic Variational Inference in Stan (2015, methodology): “One way to automate vi is to use black-box variational inference [8, 9].”
- Simplified and Generalized Masked Diffusion for Discrete Data (2024, unknown): “To fix this, we used the REINFORCE leave-one-out estimator [53, 54] to compute low-variance unbiased gradients for optimizing w .”
- Local Expectation Gradients for Black Box Variational Inference (2015, methodology): “Therefore, we need to apply approximate inference and next we consider stochastic variational inference using the local expectation gradients algorithm and compare this with the method in [19] eq.”
- Stochastic Learning on Imbalanced Data: Determinantal Point Processes for Mini-batch Diversification (2017, background): “Several ways of variance reduction of stochastic gradient algorithms have been proposed, an important class relying on control variates [26, 31, 34, 43, 37].”