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Abstract
In the realm of fast and scalable approximated Bayesian Inference, two highly sought-after approaches have traditionally been the Laplace Method and Variational Bayes. While standalone approximation methods often deliver results swiftly, they may not always prioritize the accuracy of the approximation. To tackle this challenge, we propose an innovative fusion of the Laplace Method with a Low-Rank Variational Bayes Correction (VBC). This novel approach not only refines the approximation of the posterior mean through low-rank corrections but also enhances the accuracy of the posterior variance estimation. Especially the variance correction particularly shines in scenarios with limited data, especially when dealing with fat-tail likelihoods.
In addition to refining the mean and variance, our approach extends its focus to address marginal skewness correction through VBC. In doing so, we break away from the constraints of Gaussianity inherent in the Laplace Method and introduce a novel distribution paradigm. Our method targets the skewness correction exclusively for user-specified covariates, allowing for tailored and precise adjustments. The enhancements, encompassing mean correction and variance correction have already been successfully integrated into the R-INLA software and the integration of marginal skewness correction in the R-INLA package is currectly underway.
We showcase the scalability of our method without incurring exorbitant computational costs, and we substantiate its efficacy through a series of experiments using simulated data examples.
Brief Biography
Shourya Dutta is a Ph.D. candidate In Statistics at KAUST, studying under the supervision of Professor Håvard Rue in his research group. He joined KAUST in Fall 2020 and mainly works on Bayesian and computational Statistics. Shourya obtained his Bachelor of Science in Statistics in 2017 from RKMRC, Narendrapur, Kolkata, West Bengal, India. Then, he graduated with a Masters of Science in Big Data Analytics from RKMVERI, Belur Math, Howrah, West Bengal, India in 2020.
