Invariant Causal Prediction with Local Models

TL;DR

The task of identifying the causal parents of a target variable among a set of candidates from observational data is considered and a practical method called L-ICP is introduced, based on a hypothesis test for parent identification using a ratio of minimum and maximum statistics.

Abstract

We consider the task of identifying the causal parents of a target variable among a set of candidates from observational data. Our main assumption is that the candidate variables are observed in different environments which may, under certain assumptions, be regarded as interventions on the observed system. We assume a linear relationship between target and candidates, which can be different in each environment with the only restriction that the causal structure is invariant across environments. Within our proposed setting we provide sufficient conditions for identifiability of the causal parents and introduce a practical method called L-ICP ($\textbf{L}$ocalized $\textbf{I}$nvariant $\textbf{Ca}$usal $\textbf{P}$rediction), which is based on a hypothesis test for parent identification using a ratio of minimum and maximum statistics. We then show in a simplified setting that the statistical power of L-ICP converges exponentially fast in the sample size, and finally we analyze the behavior of L-ICP experimentally in more general settings.

Figures (6)

• Figure 1: The reported graphs from L-ICP (left) and PCMCI (right). Solid blue: Correctly found. Dashed red: Not found (false negative discovery). Dotted yellow: Falsely reported (false positive discovery.)
• Figure 2: The structure of the linear structural equation model (SEM) we use in some experiments, ignoring the noise variables. The corresponding structural equations are given in \ref{['eq:semstart']}-\ref{['eq:semend']}.
• Figure 3: Under Student-t distributed noise, L-ICP achieves not the target calibration and this affects, in particular for larger samples, the performance. A near-optimal performance can be recovered if we adjust $\alpha$.
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Theorems & Definitions (22)

• Lemma 1
• Proposition 1
• Theorem 1
• Proposition 2
• Remark 1
• Theorem 2
• Theorem 3
• proof
• proof
• proof