On the Difficulty of Unbiased Alpha Divergence Minimization
This addresses a fundamental limitation in probabilistic inference methods for researchers, showing incremental theoretical analysis of existing unbiased algorithms.
The paper tackled the problem of unbiased alpha-divergence minimization in approximate inference, finding that the Signal-to-Noise Ratio of gradient estimators worsens exponentially with dimensionality for non-zero alpha, casting doubt on practicality.
Several approximate inference algorithms have been proposed to minimize an alpha-divergence between an approximating distribution and a target distribution. Many of these algorithms introduce bias, the magnitude of which becomes problematic in high dimensions. Other algorithms are unbiased. These often seem to suffer from high variance, but little is rigorously known. In this work we study unbiased methods for alpha-divergence minimization through the Signal-to-Noise Ratio (SNR) of the gradient estimator. We study several representative scenarios where strong analytical results are possible, such as fully-factorized or Gaussian distributions. We find that when alpha is not zero, the SNR worsens exponentially in the dimensionality of the problem. This casts doubt on the practicality of these methods. We empirically confirm these theoretical results.