An Upper Bound for Random Measurement Error in Causal Discovery

Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in erroneous, irreproducible results. In this work we show how to obtain an upper bound for the variance of random measurement error from the covariance matrix of measured variables and how to use this upper bound as a correction for constraint-based causal discovery. We demonstrate a practical application of our approach on both simulated data and real-world protein signaling data.

[1]  J. Wishart.  SAMPLING ERRORS IN THE THEORY OF TWO FACTORS , 1928 .

[2]  S. Sullivant,et al.  Trek separation for Gaussian graphical models , 2008, 0812.1938.

[3]  Y. Rosseel,et al.  Local fit evaluation of structural equation models using graphical criteria. , 2017, Psychological methods.

[4]  Peter Bühlmann,et al.  Predicting causal effects in large-scale systems from observational data , 2010, Nature Methods.

[5]  Bernd Bodenmiller,et al.  Influence of node abundance on signaling network state and dynamics analyzed by mass cytometry , 2017, Nature Biotechnology.

[6]  Matthew R Clutter,et al.  Single‐cell mass cytometry adapted to measurements of the cell cycle , 2012, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[7]  Ingram Olkin,et al.  Moments of minors of Wishart matrices , 2006 .

[8]  Naftali Harris,et al.  PC algorithm for nonparanormal graphical models , 2013, J. Mach. Learn. Res..

[9]  Vincenzo Lagani,et al.  Predicting Causal Relationships from Biological Data: Applying Automated Causal Discovery on Mass Cytometry Data of Human Immune Cells , 2017, Scientific Reports.

[10]  Gregory F. Cooper,et al.  A Simple Constraint-Based Algorithm for Efficiently Mining Observational Databases for Causal Relationships , 1997, Data Mining and Knowledge Discovery.

[11]  Peter Bühlmann,et al.  Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm , 2007, J. Mach. Learn. Res..

[12]  R. P. McDonald,et al.  Structural Equations with Latent Variables , 1989 .

[13]  Richard Scheines,et al.  Measurement Error and Causal Discovery , 2016, CFA@UAI.

[14]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[15]  Richard Scheines,et al.  Learning the Structure of Linear Latent Variable Models , 2006, J. Mach. Learn. Res..

[16]  Mingming Gong,et al.  Causal Discovery in the Presence of Measurement Error: Identifiability Conditions , 2017, ArXiv.

[17]  Judea Pearl,et al.  On Measurement Bias in Causal Inference , 2010, UAI.

[18]  J. Pearl,et al.  Measurement bias and effect restoration in causal inference , 2014 .

[19]  P. Spirtes,et al.  Causation, prediction, and search , 1993 .