Justifying Additive Noise Model-Based Causal Discovery via Algorithmic Information Theory

Janzing, Dominik; Steudel, Bastian

doi:10.1142/s1230161210000126

Cited by 23 publications

(27 citation statements)

References 16 publications

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“…Janzing & Steudel (2009) give further theoretical support for this principle using the concept of Kolmogorov complexity and Peters et al (2009) use this way of reasoning for detecting the arrow of time.…”

Section: Additive Noise Models For Discrete Variablesmentioning

confidence: 94%

Causal Inference on Discrete Data Using Additive Noise Models

Peters

Janzing

Schölkopf

2011

IEEE Trans. Pattern Anal. Mach. Intell.

155

158

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Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. We prove that whenever the joint distribution P (X,Y ) admits such a model in one direction, e.g. Y = f (X) + N, N ⊥ ⊥ X, it does not admit the reversed model X = g(Y )+Ñ ,Ñ ⊥ ⊥ Y as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. In an extensive experimental study we show that this algorithm works both on synthetic and real data sets.

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Section: Additive Noise Models For Discrete Variablesmentioning

confidence: 94%

Causal Inference on Discrete Data Using Additive Noise Models

Peters

Janzing

Schölkopf

2011

IEEE Trans. Pattern Anal. Mach. Intell.

155

158

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“…The second definition of γ, on the other hand, gets a particularly simple meaning when (11) in Postulate 1 holds. Then…”

Section: Strength Of Confoundingmentioning

confidence: 99%

Detecting Confounding in Multivariate Linear Models via Spectral Analysis

Janzing

Schoelkopf

2017

Journal of Causal Inference

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We study a model where one target variable Y is correlated with a vector X := (X1, . . . , X d ) of predictor variables being potential causes of Y . We describe a method that infers to what extent the statistical dependences between X and Y are due to the influence of X on Y and to what extent due to a hidden common cause (confounder) of X and Y . The method relies on concentration of measure results for large dimensions d and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of each X on Y typically has 'generic orientation' relative to the eigenspaces of the covariance matrix of X. For the special case of a scalar confounder we show that confounding typically spoils this generic orientation in a characteristic way that can be used to quantitatively estimate the amount of confounding.

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“…We store the best split per attribute (lines 10-12). Then we greedily select the overall best split and iterate until no further split can be found that can save any bits (lines [13][14][15][16]. We refer the interested reader to the original paper [36] for more details on Pack.…”

Section: Algorithm 1: Greedypackmentioning

confidence: 99%

“…The algorithmic information theoretic viewpoint of causality is more general in the sense that any physical process can be simulated by a Turing machine. Janzing and Steudel [13] use it to justify the ANM-based causal discovery.…”

Section: Related Workmentioning

confidence: 99%

Origo: causal inference by compression

Budhathoki

Vreeken

2017

Knowl Inf Syst

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Causal inference from observational data is one of the most fundamental problems in science. In general, the task is to tell whether it is more likely that X caused Y , or vice versa, given only data over their joint distribution. In this paper we propose a general inference framework based on Kolmogorov complexity, as well as a practical and computable instantiation based on the Minimum Description Length principle. Simply put, we propose causal inference by compression. That is, we infer that X is a likely cause of Y if we can better compress the data by first encoding X , and then encoding Y given X , than in the other direction. To show this works in practice, we propose Origo, an efficient method for inferring the causal direction from binary data. Origo employs the lossless Pack compressor and searches for that set of decision trees that encodes the data most succinctly. Importantly, it works directly on the data and does not require assumptions about neither distributions nor the type of causal relations. To evaluate Origo in practice, we provide extensive experiments on synthetic, benchmark, and real-world data, including three case studies. Altogether, the experiments show that Origo reliably infers the correct causal direction on a wide range of settings.

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Justifying Additive Noise Model-Based Causal Discovery via Algorithmic Information Theory

Cited by 23 publications

References 16 publications

Causal Inference on Discrete Data Using Additive Noise Models

Causal Inference on Discrete Data Using Additive Noise Models

Detecting Confounding in Multivariate Linear Models via Spectral Analysis

Origo: causal inference by compression

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