# Inference from disorder

October 19, 2016 — June 2, 2024

compsci

dynamical systems

networks

physics

probability

pseudorandomness

statistics

statmech

stochastic processes

Placeholder.

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 talk about inferring an arrow of time, or, relatedly, of 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 infromation, statistical mechanics of statistics…

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]*.