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Predicting epistasis from mathematical models.

R B Heckendorn1, D Whitley

  • 1Department of Computer Science, Colorado State University, Fort Collins, CO 80523, USA. heckendo@cs.colostate.edu

Evolutionary Computation
|April 13, 1999
PubMed
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This study introduces new theorems to bound epistasis in mathematical expressions, offering computational savings and insights into problem difficulty. It also presents novel epistasis measures and demonstrates how "parity" can reduce function nonlinearity.

Area of Science:

  • Computational complexity
  • Mathematical optimization
  • Bioinformatics

Background:

  • Epistasis is traditionally computed exactly using Walsh coefficients or estimated via sampling.
  • Exact computation is often theoretically focused due to exponential complexity.
  • Sampling methods for epistasis estimation lack insight into origins and are susceptible to errors.

Purpose of the Study:

  • To present theorems for bounding epistasis in mathematical expressions.
  • To provide computational savings for assessing problem difficulty.
  • To offer mathematical insights into epistasis origins and reduction strategies.

Main Methods:

  • Developed theorems to establish bounds for epistasis in mathematical expressions.
  • Introduced novel measures for quantifying epistasis.

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  • Conducted empirical analysis with examples to validate theorems.

    • Main Results:

    • Established theorems that provide substantial computational savings for bounding problem difficulty.
    • Gained mathematical insight into the origins of epistasis.
    • Demonstrated a "parity" property in some functions, enabling nonlinearity reduction through specific representations.

    Conclusions:

    • The presented theorems offer an efficient method for bounding epistasis.
    • Mathematical analysis provides deeper understanding and strategies for epistasis reduction.
    • The concept of "parity" offers a novel approach to simplifying complex functions.