Inference from disorder


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I don’t know if this is a real category, but between conversations with Jonas Peters, Aurora Delaigle and Zdravko Botev, I’ve seen a few references to the idea that we can draw inference from the lack of structure, in some sense, of the world.

Janzing and Peters and so forth do this with inferring the arrow of time or causality. Delaigle and Hall do very blind statistical deconvolution. I’m sure other uses could be made of the idea. Perhaps the Chatterjee correlation does this also? Azadkia and Chatterjee (2019); Chatterjee (2020)

Connection: algorithmic statistics, independence.

TBC.

Azadkia, Mona, and Sourav Chatterjee. 2019. “A Simple Measure of Conditional Dependence,” December. http://arxiv.org/abs/1910.12327.

Chatterjee, Sourav. 2020. “A New Coefficient of Correlation,” January. http://arxiv.org/abs/1909.10140.

Delaigle, Aurore, and Peter Hall. 2015. “Methodology for Non-Parametric Deconvolution When the Error Distribution Is Unknown.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), February, n/a–n/a. https://doi.org/10.1111/rssb.12109.

Janzing, Dominik. 2007. “On Causally Asymmetric Versions of Occam’s Razor and Their Relation to Thermodynamics,” August. http://arxiv.org/abs/0708.3411.

Janzing, Dominik, and Bernhard Schölkopf. 2010. “Causal Inference Using the Algorithmic Markov Condition.” IEEE Transactions on Information Theory 56 (10): 5168–94. https://doi.org/10.1109/TIT.2010.2060095.

Janzing, Dominik, Xiaohai Sun, and Bernhard Schoelkopf. 2009. “Distinguishing Cause and Effect via Second Order Exponential Models,” October. http://arxiv.org/abs/0910.5561.

Peters, Jonas, Dominik Janzing, Arthur Gretton, and Bernhard Schölkopf. 2009. “Detecting the Direction of Causal Time Series.” In Proceedings of the 26th Annual International Conference on Machine Learning, 801–8. ICML ’09. New York, NY, USA: ACM. https://doi.org/10.1145/1553374.1553477.