Elements of information theory
Elements of information theory
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Computer Generation of Random Variables Using the Ratio of Uniform Deviates
ACM Transactions on Mathematical Software (TOMS)
Kernel Methods for Measuring Independence
The Journal of Machine Learning Research
A Linear Non-Gaussian Acyclic Model for Causal Discovery
The Journal of Machine Learning Research
On the identifiability of the post-nonlinear causal model
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Causal inference using the algorithmic Markov condition
IEEE Transactions on Information Theory
Gaussian Processes for Machine Learning (GPML) Toolbox
The Journal of Machine Learning Research
Causal Inference on Discrete Data Using Additive Noise Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Information geometry on hierarchy of probability distributions
IEEE Transactions on Information Theory
Information theoretic inequalities
IEEE Transactions on Information Theory
Replacing Causal Faithfulness with Algorithmic Independence of Conditionals
Minds and Machines
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While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis ''X causes Y'' imposes that the marginal distribution P"X and the conditional distribution P"Y"|"X represent independent mechanisms of nature. Recently it has been postulated that the shortest description of the joint distribution P"X","Y should therefore be given by separate descriptions of P"X and P"Y"|"X. Since description length in the sense of Kolmogorov complexity is uncomputable, practical implementations rely on other notions of independence. Here we define independence via orthogonality in information space. This way, we can explicitly describe the kind of dependence that occurs between P"Y and P"X"|"Y making the causal hypothesis ''Y causes X'' implausible. Remarkably, this asymmetry between cause and effect becomes particularly simple if X and Y are deterministically related. We present an inference method that works in this case. We also discuss some theoretical results for the non-deterministic case although it is not clear how to employ them for a more general inference method.