Causal inference is the process of drawing a conclusion about a causal connection based on the conditions of the occurrence of an effect. The main difference between causal inference and inference of association is that the former analyzes the response of the effect variable when the cause is changed.
In epidemiology, when an association between an exposure (a putative risk factor) and a disease is found, causality is often uncertain. Bradford Hill criteria  are often used to assess causality, although the criteria are not solid exclusive ways to assess causality. A recent trend is to identify evidence for influence of the exposure on molecular pathology within diseased tissue or cells, in the emerging interdisciplinary field of molecular pathological epidemiology (MPE). Linking the exposure to molecular pathologic signatures of the disease can help to assess causality. Considering the inherent nature of heterogeneity of a given disease (the unique disease principle), disease phenotyping and subtyping are surging trends in biomedical and public health sciences, well exemplified as personalized medicine and precision medicine.
In computer science, determination of cause and effect from joint observational data for two time-independent variables, say X and Y, has been tackled using asymmetry between evidence for some model in the directions, X → Y and Y → X. One idea is to incorporate an independent noise term in the model to compare the evidences of the two directions.
Here are some of the noise models for the hypothesis Y → X with the noise E:
- Additive Noise:
- Linear Noise:
- Post Non Linear:
- Heteroskedastic Noise
- Functional Noise:
The common assumption in these models are:
- There are no other causes of Y.
- X and E have no common causes.
- Distribution of cause is independent from causal mechanisms.
On an intuitive level, the idea is that the factorization of the joint distribution P(Cause,Effect) into P(Cause)*P(Effect | Cause) typically yields models of lower total complexity than the factorization into P(Effect)*P(Cause | Effect). Although the notion of “complexity” is intuitively appealing, it is not obvious how it should be precisely defined.
- Bradford Hill criteria
- Correlation does not imply causation
- Epidemiological method
- Granger causality
- Molecular pathology
- Molecular pathological epidemiology
- Multivariate statistics
- Partial least squares regression
- Regression analysis
- Transfer entropy
- NIPS 2013 Workshop on Causality
- Causal inference at the Max-Planck-Institute for Intelligent Systems Tübingen
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