Detecting Confounding in Multivariate Linear Models via Spectral Analysis

Janzing, Dominik; Schoelkopf, Bernhard

doi:10.1515/jci-2017-0013

Cited by 20 publications

(42 citation statements)

References 35 publications

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“…In particular, we consider performance in telling causal from confounded for both in-model and adversarial se ings on both synthetic and real-world data. We compare to the recent methods by Janzing and Schölkopf [9,10]. We implemented C C in Python using PyMC3 [29] for posterior inference via ADVI [15].…”

Section: Methodsmentioning

confidence: 99%

“…Most relevant to this paper is the recent work by Janzing and Schölkopf on determining the "structural strength of confounding" for a continuous-valued pair X, Y , which they propose to measure using resp. spectral analysis [9] and ICA [10]. Like us, they also focus on linear relationships, but in contrast to us de ne a one-sided signi cance score, rather than a two-sided information theoretic con dence score.…”

Section: Related Workmentioning

confidence: 99%

“…Finally, we consider real world optical data [9]. In these experiments, X is a low-resolution (3×3 2 https://webdav.tuebingen.mpg.de/cause-effect/ 3 e complete list can be found in the online appendix at http://eda.…”

Section: Optical Datamentioning

confidence: 99%

“…Recently, Janzing and Schölkopf [9,10] showed how to measure the "structural strength of confounding" for linear models using resp. spectral analysis [9] and ICA [10]. Rather than implicitly measuring the signi cance, we explicitly model the hidden confounder Z via probabilistic PCA.…”

Section: Introductionmentioning

confidence: 99%

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We Are Not Your Real Parents: Telling Causal from Confounded using MDL

Kaltenpoth¹,

Vreeken²

2019

Proceedings of the 2019 SIAM International Conference on Data Mining

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Given data over variables (X 1 , ..., X m , Y ) we consider the problem of nding out whether X jointly causes Y or whether they are all confounded by an unobserved latent variable Z . To do so, we take an information-theoretic approach based on Kolmogorov complexity. In a nutshell, we follow the postulate that rst encoding the true cause, and then the e ects given that cause, results in a shorter description than any other encoding of the observed variables. e ideal score is not computable, and hence we have to approximate it. We propose to do so using the Minimum Description Length (MDL) principle. We compare the MDL scores under the models where X causes Y and where there exists a latent variables Z confounding both X and Y and show our scores are consistent. To nd potential confounders we propose using latent factor modeling, in particular, probabilistic PCA (PPCA).Empirical evaluation on both synthetic and real-world data shows that our method, C C , performs very well-even when the true generating process of the data is far from the assumptions made by the models we use. Moreover, it is robust as its accuracy goes hand in hand with its con dence.

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Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Optical Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

We Are Not Your Real Parents: Telling Causal from Confounded using MDL

Kaltenpoth¹,

Vreeken²

2019

Proceedings of the 2019 SIAM International Conference on Data Mining

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“…For further analysis, we write a mathematical model, and denote the non-observable confounder as Z. Directly following the paper [6], we assume that the Z is a one dimensional variable, and consider the model…”

Section: Introductionmentioning

confidence: 99%

Confounder Detection in High-Dimensional Linear Models Using First Moments of Spectral Measures

Liu

Chan

2018

Neural Computation

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In this letter, we study the confounder detection problem in the linear model, where the target variable [Formula: see text] is predicted using its [Formula: see text] potential causes [Formula: see text]. Based on an assumption of a rotation-invariant generating process of the model, recent study shows that the spectral measure induced by the regression coefficient vector with respect to the covariance matrix of [Formula: see text] is close to a uniform measure in purely causal cases, but it differs from a uniform measure characteristically in the presence of a scalar confounder. Analyzing spectral measure patterns could help to detect confounding. In this letter, we propose to use the first moment of the spectral measure for confounder detection. We calculate the first moment of the regression vector-induced spectral measure and compare it with the first moment of a uniform spectral measure, both defined with respect to the covariance matrix of [Formula: see text]. The two moments coincide in nonconfounding cases and differ from each other in the presence of confounding. This statistical causal-confounding asymmetry can be used for confounder detection. Without the need to analyze the spectral measure pattern, our method avoids the difficulty of metric choice and multiple parameter optimization. Experiments on synthetic and real data show the performance of this method.

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The Cause-Effect Problem: Motivation, Ideas, and Popular Misconceptions

Janzing

2019

The Springer Series on Challenges in Machine Learning

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Detecting Confounding in Multivariate Linear Models via Spectral Analysis

Cited by 20 publications

References 35 publications

We Are Not Your Real Parents: Telling Causal from Confounded using MDL

We Are Not Your Real Parents: Telling Causal from Confounded using MDL

Confounder Detection in High-Dimensional Linear Models Using First Moments of Spectral Measures

The Cause-Effect Problem: Motivation, Ideas, and Popular Misconceptions

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