Detecting Changes in Causal Dependence with Kernels and Copulas

TL;DR

This paper introduces a non-parametric kernel-based method to detect changes in causal dependence over time, applicable to real-world scenarios like financial markets, with proven theoretical properties and efficient estimation.

Contribution

It develops a novel kernel mean embedding-based statistic for identifying causal dependence changes, with explicit convergence rates and practical change point detection capabilities.

Findings

High accuracy in synthetic and real-world datasets

Provably zero under no change, positive if change occurs

Near-linear time estimator with explicit convergence rates

Abstract

We propose a framework for determining whether the causal dependence of an outcome $Y$ on a covariate $X$ changes at a given time point, given confounders $\boldsymbol{Z}$. For instance, in financial markets, the effect of a market indicator on asset returns may causally change over time. While many existing measures of association can be used to detect changes in joint and marginal distributions, in the absence of strong assumptions on the data generating process none are suitable for detecting changes in the causal mechanism or in the strength of causal relationship. In this work we approach the problem from a fully non-parametric perspective, and treat the causal mechanism as well as the distribution of the data as unknown. We introduce a quantity based on the integrated difference between kernel mean embeddings of certain conditionals copula, which is provably equal to zero if the causal dependence does not change and strictly positive else. A near-linear time estimator for the quantity is proposed, with rates of convergence explicitly spelled out. Extensive experiments demonstrate that the proposed statistic achieves high accuracy on multiple synthetic and real-world datasets. We additionally show how the proposed statistic can be used for change point detection when the goal is to detect changes in causal dependence occurring at an unknown times.