Towards a Learning Theory of Cause-Effect Inference

Abstract

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i){\}}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i\times Y_i$, and $l_i$ is a binary label indicating whether "$X_i\to Y_i$" or "$X_i\leftarrow Y_i$". Given these data, we build a causal inference rule in two steps. First, we featurize each $S_i$ using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.

References in corpus (4)

• Distinguishing cause from effect using observational data: methods and benchmarks
• On Causal and Anticausal Learning
• Learning from Distributions via Support Measure Machines
• Consistency of Causal Inference under the Additive Noise Model

Cited by in corpus (14)

• Detecting crosstalk errors in quantum information processors
• Causality for Machine Learning
• Optimal Rates for Random Fourier Features
• A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings
• Causal Discovery Using Proxy Variables
• Identifying Spurious Correlations for Robust Text Classification
• Causal Analysis of Customer Churn Using Deep Learning
• Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots
• A Critical View of the Structural Causal Model
• Leveraging directed causal discovery to detect latent common causes
• Model Reuse with Reduced Kernel Mean Embedding Specification
• Supervised Whole DAG Causal Discovery
• Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations
• Lipschitz Learning for Signal Recovery