New research compares MCMC, LA, and VI complexity for generalized linear models

A new arXiv paper explores the computational complexity of Markov Chain Monte Carlo (MCMC) methods for generalized linear models, comparing them to Laplace approximation (LA) and variational inference (VI). The research demonstrates that for linear, logistic, and Poisson regression, MCMC achieves complexity scaling comparable to first-order optimization algorithms when the sample size $n$ is roughly proportional to the dimension $d$. This finding suggests MCMC is competitive with LA and Gaussian VI in terms of computational cost under more general scaling conditions than previously established by Bernstein-von Mises theorems. AI

IMPACT Provides theoretical insights into computational trade-offs for Bayesian inference methods, relevant for developing more efficient AI models.

RANK_REASON The cluster contains a single academic paper detailing theoretical research findings. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• arXiv
• Bayesian inference
• Bernstein-von Mises theorems
• Gaussian VI
• Laplace Approximation
• linear regression
• logistic regression model
• Markov Chain Monte Carlo
• Martin Shakkum
• Poisson regression model
• Student's t-test
• Variational Inference

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