Contrastive learning of strong-mixing continuous-time stochastic processes

TL;DR

This paper investigates contrastive learning for continuous-time stochastic processes, demonstrating how it can estimate transition kernels and providing theoretical bounds and insights into hyperparameter choices.

Contribution

It introduces a contrastive learning framework for strong-mixing continuous-time processes, with theoretical guarantees and practical insights for kernel estimation.

Findings

Contrastive learning can estimate transition kernels in diffusion processes.

Sample complexity bounds are derived for the learning task.

Guidelines for setting contrastive distribution and hyperparameters are provided.

Abstract

Contrastive learning is a family of self-supervised methods where a model is trained to solve a classification task constructed from unlabeled data. It has recently emerged as one of the leading learning paradigms in the absence of labels across many different domains (e.g. brain imaging, text, images). However, theoretical understanding of many aspects of training, both statistical and algorithmic, remain fairly elusive. In this work, we study the setting of time series -- more precisely, when we get data from a strong-mixing continuous-time stochastic process. We show that a properly constructed contrastive learning task can be used to estimate the transition kernel for small-to-mid-range intervals in the diffusion case. Moreover, we give sample complexity bounds for solving this task and quantitatively characterize what the value of the contrastive loss implies for distributional closeness of the learned kernel. As a byproduct, we illuminate the appropriate settings for the contrastive distribution, as well as other hyperparameters in this setup.