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We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple assign-and-average approach. The components of the dataset posteriors are assigned to the proposed global model components by solving a regularized variant of the assignment problem. The global components are then updated based on these assignments by their mean under a KL divergence. For exponential family variational distributions, our formulation leads to an efficient non-parametric algorithm for computing the fused model. Our algorithm is easy to describe and implement, efficient, and competitive with state-of-the-art on motion capture analysis, topic modeling, and federated learning of Bayesian neural networks.
Renyi divergence is related to Renyi entropy much like Kullback-Leibler divergence is related to Shannons entropy, and comes up in many settings. It was introduced by Renyi as a measure of information that satisfies almost the same axioms as Kullback
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process, in its simp
This paper addresses a new interpretation of reinforcement learning (RL) as reverse Kullback-Leibler (KL) divergence optimization, and derives a new optimization method using forward KL divergence. Although RL originally aims to maximize return indir
We introduce hardness in relative entropy, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible entropy, two forms of com
Non-negative matrix factorization (NMF) approximates a given matrix as a product of two non-negative matrices. Multiplicative algorithms deliver reliable results, but they show slow convergence for high-dimensional data and may be stuck away from loc