Machine Learning of Time Series Using Time-Delay Embedding and Precision Annealing.

Abstract

Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series and, using methods of nonlinear time series analysis, show how to produce a -dimensional time-delay embedding space in which the time series has no false neighbors as does the observed time series. In that -dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on -dimensional input and producing -dimensional outputs.