Inference from disorder

October 19, 2016 — February 26, 2025

causal
compsci
dynamical systems
networks
physics
probability
pseudorandomness
statistics
statmech
stochastic processes

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Figure 1

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I don’t know if this is a real category, but through 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, in the world.

Janzing and Peters talk about inferring an arrow of time or, relatedly, causal ordering.

I believe another way of framing inference from disorder is detecting when the conditions for noise outsourcing are not fulfilled.

Connection: algorithmic statistics, independence, entropy vs information, statistical mechanics of statistics, causal inference…

TBC.

1 References

Azadkia, and Chatterjee. 2019. “A Simple Measure of Conditional Dependence.” arXiv:1910.12327 [Cs, Math, Stat].
Chatterjee. 2020. “A New Coefficient of Correlation.” arXiv:1909.10140 [Math, Stat].
Delaigle, and Hall. 2015. “Methodology for Non-Parametric Deconvolution When the Error Distribution Is Unknown.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Gnecco, Meinshausen, Peters, et al. 2021. “Causal Discovery in Heavy-Tailed Models.” The Annals of Statistics.
Hoyer, Janzing, Mooij, et al. 2009. “Nonlinear Causal Discovery with Additive Noise Models.” In Advances in Neural Information Processing Systems 21.
Janzing. 2007. “On Causally Asymmetric Versions of Occam’s Razor and Their Relation to Thermodynamics.” arXiv:0708.3411 [Cond-Mat, Physics:quant-Ph].
Janzing, Mooij, Zhang, et al. 2012. “Information-Geometric Approach to Inferring Causal Directions.” Artificial Intelligence.
Janzing, and Schölkopf. 2010. “Causal Inference Using the Algorithmic Markov Condition.” IEEE Transactions on Information Theory.
Janzing, Sun, and Schoelkopf. 2009. “Distinguishing Cause and Effect via Second Order Exponential Models.” arXiv:0910.5561 [Stat].
Mooij, Peters, Janzing, et al. 2016. “Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks.” Journal of Machine Learning Research.
Peters, Janzing, Gretton, et al. 2009. “Detecting the Direction of Causal Time Series.” In Proceedings of the 26th Annual International Conference on Machine Learning. ICML ’09.
Peters, Mooij, Janzing, et al. 2014. “Causal Discovery with Continuous Additive Noise Models.” The Journal of Machine Learning Research.
Reiersol. 1950. “Identifiability of a Linear Relation Between Variables Which Are Subject to Error.” Econometrica.
Schölkopf, Janzing, Peters, et al. 2012. “On Causal and Anticausal Learning.” In ICML 2012.
Zhang, Zhang, and Schölkopf. 2015. “Distinguishing Cause from Effect Based on Exogeneity.” arXiv:1504.05651 [Cs, Stat].