Modeling confounding by half-sibling regression

Abstract

We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as "half-sibling regression," is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the potential of the method in a challenging astronomy application.machine learning | causal inference | astronomy | exoplanet detection | systematic error modeling W e assay a method for removing the effect of confounding noise, based on a hypothetical underlying causal structure. The method does not infer causal structures; rather, it is influenced by a recent thrust to try to understand how causal structures facilitate machine learning tasks (1).Causal graphical models as pioneered by (2, 3) are joint probability distributions over a set of variables X 1 , . . . , X n , along with directed graphs (usually, acyclicity is assumed) with vertices X i , and arrows indicating direct causal influences. By the causal Markov assumption, each vertex X i is independent of its nondescendants, given its parents.There is an alternative view of causal models, which does not start from a joint distribution. Instead, it assumes a set of jointly independent noise variables, one for each vertex, and a "structural equation" for each variable that describes how the latter is computed by evaluating a deterministic function of its noise variable and its parents (2, 4, 5). This view, referred to as a functional causal model (or nonlinear structural equation model), leads to the same class of joint distributions over all variables (2, 6), and we may thus choose either representation.The functional point of view is useful in that it often makes it easier to come up with assumptions on the causal mechanisms that are at work, i.e., on the functions associated with the variables. For instance, it was recently shown (7) that assuming nonlinear functions with additive noise renders the two-variable case identifiable (i.e., a case where conditional independence tests do not provide any information, and it was thus previously believed that it is impossible to infer the structure of the graph based on observational data).In this work we start from the functional point of view and assume the underlying causal graph shown in Fig. 1. In the present paper, N, Q, X, Y are random variables (RVs) defined on the same underlying probability space. We do not require the ranges of the RVs to be R, and, in particular, they may be vectorial; we use n, q, x, y as placeholders for the values these variables can take. All equalities regarding RVs should be interpreted to hold with probability one. We further (implicitly) assume the existence of conditional expectations.Note that, although the causal motivation was helpful for our work, one can also view Fig. 1 as a directed acyclic graph (DAG) without causal interpretation, i.e., as a directed graphical model. We need Q and X...

Drawing causal inference from Big Data

“…Finally, Schölkopf et al (13) present "Modeling confounding by half-sibling regression," showing how to remove the effect of confounders in large-scale data, and give an application to astronomy.…”

A causal inference framework for estimating genetic variance and pleiotropy from GWAS summary data

“…Our confounder correction strategy is largely inspired by existing methods in genomics [11,36] and astrophysics [37]. In genomics, the RUV methods (removing unwanted variance) identify "control" genes or samples, which are not affected by case-control labels, and perform principal component analysis (PCA) on the control data to ascertain biases introduced by technical covariates.…”

“…The half-sibling regression [37] also adopts a similar idea, but without PCA, measurements of control variates are directly included in a regression model. Sparse modeling of genetic effects proves to be indispensable in high-dimensional multivariate analysis.…”

“…Our approach is inspired by existing methods, established on individual-level data analysis in genomics [11,36] and astrophysics [37]. We conceived our approach asking, "What could have been done if we had fully observed information?"…”

Assessing causal claims about complex engineered systems with quantitative data: internal, external, and construct validity

“…A general approach to detecting and controlling for confounds remains an open area of research in machine learning (see Refs. and for promising advances in this area). Rather than relying solely on a predictive approach, we contend that domain knowledge can also be used to explain an algorithm's performance, and applied to determine which confounds are plausible, as in the examples below.…”