Unlearning for better mixing

Two learning algorithms were recently proposed–Herding and Fast Persistent Contrastive Divergence (FPCD)–which share the following interesting characteristic: they exploit changes in the model parameters while sampling in order to escape modes and mix better, during the sampling process that is part of the learning algorithm. We first justify such approaches as ways to escape modes while approximately keeping the same asymptotic distribution of the Markov chain. We then extend FPCD using an idea borrowed from Herding in order to obtain a pure sampling algorithm and show empirically that this FPCD-sampler yields substantially better samples than Gibbs sampling. Because these algorithms entangle the model and the sampling algorithm and we want to evaluate both (but particularly how well the sampling schemes mix), it is not always easy to evaluate them, so we propose a “black-box” approach based on how well and how quickly the samples generated by a model “cover” the test set examples. We empirically study these algorithms and variations with this perspective and these new evaluation tools in order to better understand their strengths and limitations.