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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.ST2024
Regularized Rényi divergence minimization through Bregman proximal gradient algorithms
Thomas Guilmeau, Emilie Chouzenoux, VÃctor Elvira
We study the variational inference problem of minimizing a regularized Rényi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradie…
math.ST2024
On variational inference and maximum likelihood estimation with the λ-exponential family
Thomas Guilmeau, Emilie Chouzenoux, VÃctor Elvira
The λ-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of…