The ability to quantify information transmission is crucial for the analysis and design of both natural and engineered systems. For systems driven by time-varying signals, the fundamental measure is the information transmission rate. However, due to the high dimensionality of signal trajectory space, this rate cannot be obtained directly from time-series data without approximations. Path Weight Sampling (PWS) is a computational technique that enables the exact calculation of the information rate for any stochastic model, raising the question of how this rate can be determined from time-series data in the absence of a prior model. Here, we present a method that combines machine learning (ML) with PWS: a generative model is learned from time-series data, to which PWS is applied to yield a rigorous lower bound on the information rate. We demonstrate the accuracy of this technique, called ML-PWS, by comparing its results on synthetic time-series data generated from several non-linear models against ground-truth results obtained by applying PWS directly to the same models. We illustrate the utility of ML-PWS by applying it to neuronal time-series data.

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