Context Based Predictive Information

Abstract

We propose a new algorithm called the context-based predictive information (CBPI) for estimating the predictive information (PI) between time series, by utilizing a lossy compression algorithm. The advantage of this approach over existing methods resides in the case of sparse predictive information (SPI) conditions, where the ratio between the number of informative sequences to uninformative sequences is small. It is shown that the CBPI achieves a better PI estimation than benchmark methods by ignoring uninformative sequences while improving explainability by identifying the informative sequences. We also provide an implementation of the CBPI algorithm on a real dataset of large banks’ stock prices in the U.S. In the last part of this paper, we show how the CBPI algorithm is related to the well-known information bottleneck in its deterministic version.

Neural Joint Entropy Estimation

“…The first approach considers every variable in every timestamp as a separate variable, and uses any MI or CMI estimator to estimate the TE [34]- [36]. The second approach applies a sequential model that considers the time dependencies among different time lags to extract an estimator for the TE and its related measures [37], [38].…”