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Methods for computational causal discovery in biomedicine

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Abstract

With the development of high throughput technology in the past twenty years, it has become easier and cheaper to simultaneously measure tens of thousands of molecules in biological systems. One of the major challenges is how to extract knowledge from these high dimensional datasets and infer the underlying mechanisms of the system. In this review, we discuss several topics related to causal discovery from biomedical data, including causal structural learning from observational and experimental data, estimation of causal effects, and using causal information for predictive modeling.

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Notes

  1. Here we assume all variables in the system are observed, see Definition 6), and we consider the smallest \(\varvec{Pa_i}\) possible.

  2. Let \(a_{|V|}\) denote the number of all possible DAGs over |V| vertices. \(a_{|V|}\) could be obtained through the following recursion: \(a_{|V|}=\sum _{k=1}^{|V|}{(-1)}^{k+1}{{|V|}\atopwithdelims (){k}}2^{k(|V|-k)}a_{|V|-k}\)(Robinson 1978).

  3. Such link can also be established through the Markov condition, but the d-separation is more intuitive and useful, as pointed out in chapter 3 of Spirtes et al. (2000).

  4. Here we are talking about the general case. It is easy to recognize that certain manipulations, i.e. the manipulations that do not affect P(T|predictors), would not change the predictive performance of the model. More detailed discussion on this can be found in Tillman and Spirtes (2008).

  5. There still could be unoriented edges in the local causal neighborhood, since certain causal structure cannot be discovered from observational data. By “completely” we mean the orientation of local neighborhood by PCD-by-PCD is the same as that obtained from a global causal discovery algorithm.

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The authors are grateful to Roshan Tourani for helpful comments on the manuscript.

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  1. University of Minnesota, Minneapolis, USA

    Sisi Ma

  2. New York University School of Medicine, New York, USA

    Alexander Statnikov

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Communicated by Shohei Shimizu.

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Ma, S., Statnikov, A. Methods for computational causal discovery in biomedicine. Behaviormetrika 44, 165–191 (2017). https://doi.org/10.1007/s41237-016-0013-5

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