Causal Patterns: Extraction of multiple causal relationships by Mixture of Probabilistic Partial Canonical Correlation Analysis

TL;DR

This paper introduces MPPCCA, a novel probabilistic method for extracting multiple causal relationships from multivariate time series, outperforming existing techniques in synthetic and real data scenarios.

Contribution

The paper presents MPPCCA, a new mixture model with an EM algorithm to identify multiple causal patterns without supervision in multivariate time series.

Findings

MPPCCA accurately estimates multiple partial canonical correlations.

The method successfully detects communication patterns in motion-capture data.

MPPCCA is applicable to diverse signals like brain and human communication data.

Abstract

In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of two elements having multiple types of mutually causal relationships, rather than a mixture of simultaneous correlations or the absence of presence of a causal relationship between the elements. In multivariate statistics, partial canonical correlation analysis (PCCA) evaluates the correlation between two multivariates after subtracting the effect of the third multivariate. PCCA can calculate the Granger Causal- ity Index (which tests whether a time-series can be predicted from an- other time-series), but is not applicable to data containing multiple partial canonical correlations. After introducing the MPPCCA, we propose an expectation-maxmization (EM) algorithm that estimates the parameters and latent variables of the MPPCCA. The MPPCCA is expected to ex- tract multiple partial canonical correlations from data series without any supervised signals to split the data as clusters. The method was then eval- uated in synthetic data experiments. In the synthetic dataset, our method estimated the multiple partial canonical correlations more accurately than the existing method. To determine the types of patterns detectable by the method, experiments were also conducted on real datasets. The method estimated the communication patterns In motion-capture data. The MP- PCCA is applicable to various type of signals such as brain signals, human communication and nonlinear complex multibody systems.