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Nearly maximally predictive features and their dimensions.

Sarah E Marzen^1,2, James P Crutchfield³

¹Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review. E

|June 17, 2017

Summary

This summary is machine-generated.

Predicting stochastic processes requires identifying key features. This study bounds the number and cost of "nearly maximally predictive features," showing mixed-state features outperform traditional Markov models.

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Area of Science:

Data analysis and machine learning
Stochastic processes and time series analysis
Information theory and fractal geometry

Background:

Scientific explanation relies on identifying predictive features from data.
Finding the minimal set of maximally predictive features for stochastic processes is often mathematically intractable.
Compromises are made by seeking nearly maximally predictive features.

Purpose of the Study:

To derive upper bounds on the scaling rates of nearly maximally predictive features.
To connect these rates to the fractal dimensions of a process' mixed-state distribution.
To evaluate the predictive capabilities of mixed-state features against traditional finite-order Markov models.

Main Methods:

Derivation of theoretical upper bounds on feature scaling.
Analysis of the relationship between feature rates and fractal dimensions.
Comparative analysis of predictive performance.

Main Results:

The number and coding cost of nearly maximally predictive features scale with desired predictive power at rates determined by fractal dimensions.
Upper bounds on these scaling rates were mathematically derived.
Mixed-state predictive features demonstrate potential for significant improvement over traditional models.

Conclusions:

Fractal dimensions of mixed-state distributions govern the efficiency of feature selection in stochastic processes.
Widely used finite-order Markov models may be inadequate predictors due to limitations in capturing mixed-state dynamics.
Mixed-state predictive features offer a more robust and potentially superior approach for scientific explanation and prediction.