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math.ST2026
Consistency of variational approximations under bounded Kullback--Leibler divergence
Hien Duy Nguyen, Jacob Westerhout, Thomas Guilmeau +1
Variational methods are widely used to approximate posterior distributions in Bayesian inference when exact computation is infeasible. We study when such approximations inherit pos…
math.ST2025
Optimal sub-Gaussian variance proxy for 3-mass distributions
Soufiane Atouani, Olivier Marchal, Julyan Arbel
We investigate the problem of characterizing the optimal variance proxy for sub-Gaussian random variables,whose moment-generating function exhibits bounded growth at infinity. We a…
math.ST2024
Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables
Mathias Barreto, Olivier Marchal, Julyan Arbel
This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optima…