Minimum description length

August 6, 2020 — August 6, 2020

Bayes
information
model selection
statistics
stringology
Figure 1

A formalisation of Occam’s razor of some kind. I see it invoked in model selection.

In the Bayes context, I think this typically means model selection by optimising marginal likelihood

1 References

Arora, and Zhang. 2021. “Rip van Winkle’s Razor: A Simple Estimate of Overfit to Test Data.” arXiv:2102.13189 [Cs, Stat].
Barron, Andrew R. 1991. “Complexity Regularization with Application to Artificial Neural Networks.” In Nonparametric Functional Estimation and Related Topics. NATO ASI Series 335.
Barron, A. R., and Cover. 1991. “Minimum Complexity Density Estimation.” IEEE Transactions on Information Theory.
Barron, A., Rissanen, and Yu. 1998. “The Minimum Description Length Principle in Coding and Modeling.” IEEE Transactions on Information Theory.
Collins, Dasgupta, and Schapire. 2001. “A Generalization of Principal Components Analysis to the Exponential Family.” In Advances in Neural Information Processing Systems.
Grünwald, Peter. 1996. “A Minimum Description Length Approach to Grammar Inference.” In Connectionist, Statistical, and Symbolic Approaches to Learning for Natural Language Processing. Lecture Notes in Computer Science.
Grünwald, Peter D. 2004. “A Tutorial Introduction to the Minimum Description Length Principle.” Advances in Minimum Description Length: Theory and Applications.
———. 2007. The Minimum Description Length Principle.
Hansen, and Yu. 2001. “Model Selection and the Principle of Minimum Description Length.” Journal of the American Statistical Association.
Jun Li, and Dacheng Tao. 2013. “Simple Exponential Family PCA.” IEEE Transactions on Neural Networks and Learning Systems.
Legg. 2006. “Is There an Elegant Universal Theory of Prediction?” In Algorithmic Learning Theory. Lecture Notes in Computer Science 4264.
Mavromatis. 2009. “Minimum Description Length Modelling of Musical Structure.” Journal of Mathematics and Music.
Mohamed, Ghahramani, and Heller. 2008. “Bayesian Exponential Family PCA.” In Advances in Neural Information Processing Systems.
Rissanen. 1984. “Universal Coding, Information, Prediction, and Estimation.” IEEE Transactions on Information Theory.
Roy, Gordon, and Thrun. 2005. “Finding Approximate POMDP Solutions Through Belief Compression.” Journal of Artificial Intelligence Research.
Solomonoff. 1964a. “A Formal Theory of Inductive Inference. Part I.” Information and Control.
———. 1964b. “A Formal Theory of Inductive Inference. Part II.” Information and Control.
Sterkenburg. 2016. “Solomonoff Prediction and Occam’s Razor.” Philosophy of Science.
Ullrich. 2020. “A Coding Perspective on Deep Latent Variable Models.”
Vitányi. 2006. “Meaningful Information.” IEEE Transactions on Information Theory.
Wojtowicz, and DeDeo. 2020. “From Probability to Consilience: How Explanatory Values Implement Bayesian Reasoning.” Trends in Cognitive Sciences.