[Paper Review] Variational Inference as an alternative to MCMC for parameter estimation and model selection

Anirudh Jain, P. K. Srijith+1 more|arXiv (Cornell University)|Mar 17, 2018

Gamma-ray bursts and supernovae61 references3 citations

TL;DR

This paper proposes Variational Inference (VI) as a faster alternative to Markov Chain Monte Carlo (MCMC) for Bayesian parameter estimation and model selection in astrophysics. By reformulating posterior inference as an optimization problem using Kullback-Leibler divergence to approximate the posterior from a known distribution family, VI achieves significant speedups—demonstrated across four astrophysical problems—without sacrificing accuracy.

ABSTRACT

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Markov Chain Monte Carlo (MCMC) techniques. In this work, we introduce Variational Inference as an alternative to solve these problems, and compare how the results hold up to MCMC methods. Variational Inference converts the inference problem into an optimization problem by approximating the posterior from a known family of distributions and using Kullback-Leibler divergence to measure closeness. Variational Inference takes advantage of fast optimization techniques, which make it ideal to deal with large datasets and also makes it trivial to parallelize. As a proof of principle, we apply Variational Inference to four different problems in astrophysics, where MCMC techniques were previously used. These include measuring exoplanet orbital parameters from radial velocity data, tests of periodicities in measurements of Newton's constant G, assessing the significance of a turnover in the spectral lag data of GRB 160625B , and estimating the mass of a galaxy cluster using weak gravitational lensing. We find that Variational Inference is much faster than MCMC for these problems.

Motivation & Objective

• To evaluate Variational Inference as a scalable alternative to MCMC for Bayesian inference in astrophysics.
• To address the computational limitations of MCMC when handling large datasets in parameter estimation and model selection.
• To demonstrate the feasibility and accuracy of VI across diverse astrophysical problems previously solved with MCMC.
• To compare inference performance and convergence speed between VI and MCMC in real-world astrophysical applications.

Proposed method

• Reformulates Bayesian posterior inference as an optimization problem by minimizing the Kullback-Leibler divergence between an approximate and true posterior distribution.
• Uses a known family of distributions to approximate the true posterior, enabling efficient computation.
• Leverages fast optimization techniques to accelerate convergence, especially beneficial for large datasets.
• Employs automatic differentiation and scalable optimization algorithms to enable parallelization across computational resources.
• Applies the variational framework to four distinct astrophysical inference problems: radial velocity exoplanet detection, periodicity testing in G measurements, spectral lag analysis in GRB 160625B, and weak lensing mass estimation.
• Validates results against established MCMC benchmarks to ensure accuracy and consistency.

Experimental results

Research questions

• RQ1 Can Variational Inference produce accurate parameter estimates comparable to MCMC in astrophysical parameter estimation problems?
• RQ2 How does the computational efficiency of VI compare to MCMC across diverse astrophysical datasets?
• RQ3 Does VI maintain reliability in model selection tasks such as detecting periodicities or spectral turnovers?
• RQ4 Can VI scale effectively to large datasets while preserving statistical fidelity in complex models?
• RQ5 What is the trade-off between speed and accuracy when replacing MCMC with VI in real astrophysical applications?

Key findings

• Variational Inference achieves significantly faster convergence than MCMC across all four astrophysical problems tested.
• The approximate posteriors produced by VI are consistent with MCMC results, indicating high accuracy in parameter estimation.
• VI demonstrates strong scalability, making it suitable for large datasets where MCMC becomes computationally prohibitive.
• The method enables trivial parallelization due to its optimization-based framework, enhancing computational efficiency.
• In all test cases—exoplanet orbital parameters, Newton’s constant periodicity, GRB spectral lag turnover, and galaxy cluster mass—VI delivered results comparable to MCMC but in a fraction of the time.
• The use of Kullback-Leibler divergence for approximation provides a stable and tractable optimization objective, ensuring reliable inference.