Minimizing $f$-Divergences by Interpolating Velocity Fields

Many machine learning problems can be formulated as approximating a target distribution using a particle distribution by minimizing a statistical discrepancy. Wasserstein Gradient Flow can be employed to move particles along a path that minimizes the $f$-divergence between the \textit{target} and \textit{particle} distributions. To perform such movements we need to calculate the corresponding velocity fields which include a density ratio function between these two distributions. While previous works estimated the density ratio function first and then differentiated the estimated ratio, …

cs.lg distribution divergence fields flow gradient machine machine learning movements path statistical stat.ml