Bias-Variance Decomposition for Boltzmann Machines

Mahito Sugiyama, Koji Tsuda, Hiroyuki Nakahara

Abstract: We achieve bias-variance decomposition for Boltzmann machines using an information geometric formulation. Our decomposition leads to an interesting phenomenon that the variance does not necessarily increase when more parameters are included in Boltzmann machines, while the bias always decreases. Our result gives a theoretical evidence of the generalization ability of deep learning architectures because it provides the possibility of increasing the representation power with avoiding the variance inflation.

TL;DR: We achieve bias-variance decomposition for Boltzmann machines using an information geometric formulation.

Keywords: Boltzmann machine, bias-variance decomposition, information geometry