Causal discovery and inference: concepts and recent methodological advances

Peter Spirtes,Kun Zhang

doi:10.1186/s40535-016-0018-x

Peter Spirtes, Kun Zhang

Open Access

https://doi.org/10.1186/s40535-016-0018-x

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Abstract

This paper aims to give a broad coverage of central concepts and principles involved in automated causal inference and emerging approaches to causal discovery from i.i.d data and from time series. After reviewing concepts including manipulations, causal models, sample predictive modeling, causal predictive modeling, and structural equation models, we present the constraint-based approach to causal discovery, which relies on the conditional independence relationships in the data, and discuss the assumptions underlying its validity. We then focus on causal discovery based on structural equations models, in which a key issue is the identifiability of the causal structure implied by appropriately defined structural equation models: in the two-variable case, under what conditions (and why) is the causal direction between the two variables identifiable? We show that the independence between the error term and causes, together with appropriate structural constraints on the structural equation, makes it possible. Next, we report some recent advances in causal discovery from time series. Assuming that the causal relations are linear with nonGaussian noise, we mention two problems which are traditionally difficult to solve, namely causal discovery from subsampled data and that in the presence of confounding time series. Finally, we list a number of open questions in the field of causal discovery and inference.

Highlights

IntroductionThe goal of many sciences is to understand the mechanisms by which variables came to take on the values they have (i.e., to find a generative model), and to predict what the values of those variables would be if the naturally occurring mechanisms in a population were subject to outside manipulations
The goal of many sciences is to understand the mechanisms by which variables came to take on the values they have, and to predict what the values of those variables would be if the naturally occurring mechanisms in a population1 were subject to outside manipulations
In "Causal discovery from time series" section, after reviewing linear Granger causality with instantaneous effects, we focus on two problems which are traditionally difficult to solve

Summary

Introduction

The goal of many sciences is to understand the mechanisms by which variables came to take on the values they have (i.e., to find a generative model), and to predict what the values of those variables would be if the naturally occurring mechanisms in a population were subject to outside manipulations. A randomized experiment is one kind of manipulation, which substitutes the outcome of a randomizing device to set the value of a variable, such as whether or not a particular diet is used, instead of the naturally occurring mechanism that determines diet. If only observational (nonexperimental) data are available, predicting the effects of manipulations typically involves drawing samples from one density (of the unmanipulated population) and making inferences about the values of a variable in a population that has a different density (of the manipulation population). There are some superficial similarities between traditional supervised machine learning problems and causal inference (e.g., both employ model search and feature selection, the kinds of models employed overlap, and some model scores can be used for both purposes), these similarities can mask some very important differences between the two kinds of problems

Objectives

Conclusion