  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.
