4 papers
Robust Bayesian Inference via Variational Approximations of Generalized Rho-Posteriors
EL Mahdi Khribch, Pierre Alquier
We introduce the -posterior, a modified version of the -posterior, obtained by replacing the supremum over competitor parameters with a softmax aggregation. This…
Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time
Geoffrey Wolfer, Pierre Alquier
The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often…
Convergence of Statistical Estimators via Mutual Information Bounds
El Mahdi Khribch, Pierre Alquier
Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This wor…
Dimension-free Bounds for Sum of Dependent Matrices and Operators with Heavy-Tailed Distribution
Shogo Nakakita, Pierre Alquier, Masaaki Imaizumi
We prove deviation inequalities for sums of high-dimensional random matrices and operators with dependence and {\rc heavy tails}. Estimation of high-dimensional matrices is a conce…