Telling Cause from Effect using MDL-based Local and Global Regression

Abstract

We consider the fundamental problem of inferring the causal direction between two univariate numeric random variables $X$ and $Y$ from observational data. The two-variable case is especially difficult to solve since it is not possible to use standard conditional independence tests between the variables. To tackle this problem, we follow an information theoretic approach based on Kolmogorov complexity and use the Minimum Description Length (MDL) principle to provide a practical solution. In particular, we propose a compression scheme to encode local and global functional relations using MDL-based regression. We infer $X$ causes $Y$ in case it is shorter to describe $Y$ as a function of $X$ than the inverse direction. In addition, we introduce Slope, an efficient linear-time algorithm that through thorough empirical evaluation on both synthetic and real world data we show outperforms the state of the art by a wide margin.

10 pages, To appear in ICDM17

References in corpus (6)

• Big Data of Materials Science - Critical Role of the Descriptor
• Distinguishing cause from effect using observational data: methods and benchmarks
• On the Identifiability of the Post-Nonlinear Causal Model
• Uncovering structure-property relationships of materials by subgroup discovery
• Discovering Reliable Approximate Functional Dependencies
• Causal Inference on Discrete Data via Estimating Distance Correlations

Cited by in corpus (6)

• Analysis of cause-effect inference by comparing regression errors
• Distinguishing Cause from Effect Using Quantiles: Bivariate Quantile Causal Discovery
• A Critical View of the Structural Causal Model
• Formally Justifying MDL-based Inference of Cause and Effect
• Causal Inference via Conditional Kolmogorov Complexity using MDL Binning
• Merging joint distributions via causal model classes with low VC dimension