Contrastive learning of strong-mixing continuous-time stochastic processes
This work addresses theoretical gaps in contrastive learning for time series, which is incremental as it builds on existing methods but applies them to a new theoretical setting with specific processes.
The authors tackled the problem of theoretically understanding contrastive learning for time series data from strong-mixing continuous-time stochastic processes, showing that a properly constructed contrastive task can estimate transition kernels for small-to-mid-range intervals in diffusion cases and providing sample complexity bounds and quantitative characterizations of loss implications.
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.