Minimizing_Convex_Functionals_over_Space_of_Probability_Measures_via_KL_Divergence_Gradient_Flow

This repository contains code of the experiments of AISTATS 2024 paper Minimizing Convex Functionals over Space of Probability Measures via KL Divergence Gradient Flow, Rentian Yao, Linjun Huang, and Yun Yang. We introduce an implicit scheme, called the implicit KL proximal descent (IKLPD) algorithm, for discretizing a continuous-time gradient flow relative to the Kullback–Leibler (KL) divergence for minimizing a convex target functional. We perform experiments to validate the effectiveness of our approach works in different scenarios.

Description

• Repository Gaussian_location contains code used in the experiments for the Gaussian location mixture model.
• Repository Gaussian_location_scale contains code used in the experiments for the Gaussian location scale mixture model.
• Repository Bayesian_sampling contains code used in the experiments for the Bayesian sampling.
• Repository Comparisons_with_WGF contains code used in the experiments for the Comparison with Wassersten gradient flows.
• Repository impact_of_tau_figure_5 contains code used in the experiments for figure 5 of the Impact of IKLPD Step Size in Appendix C.4.
• Repository impact_of_tau_figure_6 contains code used in the experiments for figure 6 of the Impact of IKLPD Step Size in Appendix C.4.
• Repository impact_of_tau_figure_7 contains code used in the experiments for figure 7 of the Impact of IKLPD Step Size in Appendix C.4.
• Repository NF_short_flows contains code used in the experiments for the Composition of Short Flows and Teacher-Student Architecture in Appendix C.5.

Dependencies

• We use the normflows package to implement the IKLPD algorithm.