Ratio Covers of Convex Sets and Optimal Mixture Density Estimation

ArXi:2602.16142v2 Announce Type: replace-cross We study density estimation in Kullback-Leibler divergence: given an i.i.d. sample from an unknown density $p^\star$, the goal is to construct an estimator $\widehat{p}$ such that $\mathrm{KL}(p^\star,\widehat{p})$ is small with high probability. We consider two fundamental settings involving a finite dictionary of densities: (i) model aggregation, where $p^\star$ belongs to the dictionary, and (ii) convex aggregation (mixture density estimation), where $p^\star$ is a mixture of densities from the dictionary.