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.
We achieve bias-variance decomposition for Boltzmann machines using an information geometric formulation. The goal of this paper is to analyze the effectiveness and generalizability of deep learning by presenting a theoretical analysis of bias-variance decomposition for hierarchical models, specifically Boltzmann Machines   The paper arrives at the main conclusion that it is possible to reduce both the bias and the variance in a hierarchical model.