Empirical Evaluation of Biased Methods for Alpha Divergence Minimization

There has been great recent interest in methods to minimize other alpha-divergences, such as the "inclusive" KL divergence, KL(p‖q). Some methods employ unbiased gradient estimators (Dieng et al., 2017; Kuleshov and Ermon, 2017). These estimators often suffer from a high variance, difficulting optimization (Geffner and Domke, 2020). Another class of methods estimate a gradient using self-normalized importance sampling (Bornschein and Bengio, 2014; Finke and Thiery, 2019; Li and Turner, 2016). While these estimators may control variance, they do so at the cost of some bias.