October
This seminar is scheduled for 3PM
Differential Privacy of Markov Chains
Timothy JOHNSTON CEREMADE, Université Paris Dauphine–PSL
Joint work with Andrea Bertazzi, Alain Durmus and Gareth Roberts. Available on arXiv.
In this talk we shall discuss differential privacy, a framework for quantifying the extent to which a random output depends on the information used to produce it. After introducing several related definition of differential privacy, we shall discuss techniques used to show the differential privacy of both trajectories and single draws from Markov Chains. In doing so we shall touch on a perturbation technique which allows for Wasserstein type bounds to be converted into stronger distances like the KL and Renyi divergence.
Permutations accelerate Approximate Bayesian Computation
Antoine LUCIANO CEREMADE, Université Paris Dauphine–PSL
Joint work with Charly Andral, Christian P. Robert and Robin J. Ryder. Available on arXiv.
Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in hierarchical or high-dimensional models. In this paper, we introduce permABC, a new ABC framework designed for settings with both global and local parameters, where observations are grouped into exchangeable compartments. Building upon the Sequential Monte Carlo ABC (ABC-SMC) framework, permABC exploits the exchangeability of compartments through permutation-based matching, significantly improving computational efficiency. We then develop two further, complementary sequential strategies: Over Sampling, which facilitates early-stage acceptance by temporarily increasing the number of simulated compartments, and Under Matching, which relaxes the acceptance condition by matching only subsets of the data. These techniques allow for robust and scalable inference even in high-dimensional regimes. Through synthetic and real-world experiments – including a hierarchical Susceptible-Infectious-Recover model of the early COVID-19 epidemic across 94 French departments – we demonstrate the practical gains in accuracy and efficiency achieved by our approach.