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Updated: Feb 26, 2026
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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
Published on: August 16, 2017
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Information trimming: Sufficient statistics, mutual information, and predictability from effective channel states
Ryan G James1, John R Mahoney1, James P Crutchfield1
1Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Physical Review. E
|July 16, 2017
Summary
We show that high-dimensional random variables can be simultaneously replaced by their minimal sufficient statistics, preserving mutual information. This "information trimming" simplifies complex relationships, aiding analysis in fields like stochastic processes.
Area of Science:
- Information Theory
- Statistical Mechanics
- Machine Learning
Background:
- Mutual information quantifies relationships between random variables.
- High dimensionality complicates analytical and empirical calculation of mutual information.
- Minimal sufficient statistics can preserve mutual information for a single variable replacement.
Purpose of the Study:
- To demonstrate that both random variables can be simultaneously replaced by their minimal sufficient statistics.
- To introduce and validate the 'information trimming' procedure.
- To explore implications for stochastic processes and computational mechanics.
Main Methods:
- Theoretical demonstration of simultaneous minimal sufficient statistic replacement.
- Information-theoretic analysis of mutual information preservation.
- Application of results to causal states in computational mechanics.
Main Results:
- Proven that both X and Y can be replaced by their minimal sufficient statistics simultaneously.
- Established that the information preserved about Y by X's statistic equals that preserved about X by Y's statistic.
- Showcased a connection between information trimming and forward/reverse-time causal states.
Conclusions:
- Information trimming is a valid method for reducing dimensionality while preserving essential relational information.
- The findings offer a new perspective on channel capacity and prediction in stochastic processes.
- The study opens avenues for multivariate extensions of minimal sufficient statistics applications.
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