Agenda

Luca Martino (University of Catania) - On importance sampling and contrastive learning schemes

Abstract:

Energy-based model (EBM) are an important family of models where a piece of them is intractable, and hence unknown. This unknown part is often called partition function. Gibbs distributions, Markov random fields, and multi-layer networks are examples of models where analytical normalization is often impossible. The partition function normalizes the model so that it integrates to one for any choice of the parameters. However, it is often impossible to obtain it in closed form, i.e., is analytically intractable and unknown. For this reason, the parameter estimation in EBMs is a challenge for the standard estimation methods.  Nowadays, the most famous approaches for inference in EBMs are (in order of appearance): noisy gradient descent of C. Geyer - the Geyer's approach (GA) and  contrastive learning (CL). The noise gradient descent applied importance sampling (IS), for estimating the partition function (the estimation can be performed once, and it is amortized for different values of the parameters).  In this work, we present  a critical discussion on the relationships among these techniques. Some important connections have been somehow overlooked in the literature, specially between IS and CL.  We provide  different derivations and several practical suggestions for the choice of a proposal/reference density that is required.