A swarm intelligence approach to density function reconstruction from moments using entropy optimization
Parthapratim Biswas1,2, Stephen R Elliott1,3,4
1Trinity College, University of Cambridge, Cambridge CB2 1TQ, United Kingdom.
Summary
This study introduces a bioinspired optimization method for entropy optimization problems, efficiently reconstructing probability densities from distribution moments. The approach uses swarm intelligence for robust and accurate solutions in various scientific fields.
Area of Science:
- Computational Physics
- Applied Mathematics
- Data Science
Background:
- Inverse problems are crucial in science and engineering.
- Entropy optimization (EOP) is a key technique for reconstructing distributions from moments.
- Existing methods face challenges with high-dimensional data and accuracy.
Purpose of the Study:
- To present a novel bioinspired optimization approach for entropy optimization problems.
- To reconstruct probability density distributions from a sequence of moments.
- To demonstrate the method's efficacy on diverse datasets.
Main Methods:
- Utilized a bioinspired optimization approach based on swarm intelligence.
- Addressed the Hausdorff moment problem by inverting moment sequences.
- Incorporated information from up to a thousand moments for enhanced accuracy.
Main Results:
- Successfully reconstructed invariant density functions for the logistics map.
- Determined spectral densities for large real-symmetric random matrices.
- Analyzed financial time series, including mutual fund price fluctuations.
- Achieved robust and accurate solutions using collective intelligence.
Conclusions:
- The bioinspired optimization approach offers an efficient and effective solution for entropy optimization inverse problems.
- The method demonstrates broad applicability across physics, mathematics, and finance.
- The technique provides accurate reconstructions of probability densities from moments.
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