The $f$-Divergence Expectation Iteration Scheme
| Autor: | Daudel, Kamélia, Douc, Randal, Portier, François, Roueff, François |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper introduces the $f$-EI$(\phi)$ algorithm, a novel iterative algorithm which operates on measures and performs $f$-divergence minimisation in a Bayesian framework. We prove that for a rich family of values of $(f,\phi)$ this algorithm leads at each step to a systematic decrease in the $f$-divergence and show that we achieve an optimum. In the particular case where we consider a weighted sum of Dirac measures and the $\alpha$-divergence, we obtain that the calculations involved in the $f$-EI$(\phi)$ algorithm simplify to gradient-based computations. Empirical results support the claim that the $f$-EI$(\phi)$ algorithm serves as a powerful tool to assist Variational methods. Comment: This content ended up being split into the papers arXiv:2005.10618 and arXiv:2103.05684, which correspond to two separate and more in-depth approaches |
| Databáze: | arXiv |
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