Forest-weighted non-linear causal inference for high-dimensional and multimodal time series

Forecasting and causal inference in complex, non-linear dynamical systems pose significant challenges due to high-dimensional and noisy time-series data. Traditional methods, such as Empirical Dynamic Modeling, struggle with the "curse of dimensionality," which distorts distance measurements as dimensions increase. This research introduces Forest-Weighted S-map (FORWS) and Forest-Weighted Causal Inference (FORWC), which employ adaptive forest weights from random forest ensembles, rather than Euclidean metrics.

These novel methods were tested using both simulated and empirical ecological datasets, revealing comparable or improved forecasting skill and greater resilience against dynamic process noise compared to conventional tools. FORWC's key feature is its ability to perform multimodal causal inference, successfully identifying directed interactions between high-dimensional acoustic vectors and scalar temperature data observed in a honeybee hive.

This approach effectively integrates chaotic physics with machine learning to accurately extract the topological structure of intrinsic manifolds, offering a robust framework for uncovering causal networks in complex real-world environments.