On learning functions over biological sequence space: relating Gaussian process priors, regularization, and gauge...

Area of Science:

• Computational Biology
• Machine Learning
• Genomics

Background:

• Biological sequence-to-function maps are crucial for understanding DNA, RNA, and protein functionality.
• Inferring these maps and decomposing them to understand subsequence contributions are key challenges.
• Interpreting sequence-function maps requires unique representations achieved through "gauge-fixing."

Purpose of the Study:

• To establish the relationship between regularized regression in weight space and Gaussian process approaches in function space for sequence-to-function mapping.
• To disentangle how weight space regularizers influence implicit priors and gauge choices.
• To enable construction of regularizers for arbitrary Gaussian process priors and various gauges.

Main Methods:

• Analyzing regularized regression in overparameterized weight space.
• Connecting weight space regularizers to Gaussian process priors in function space.
• Deriving posterior distributions for sequence-to-function statistics using a kernel trick.

Main Results:

• Demonstrated that weight space regularizers implicitly define function space priors and select specific gauges.
• Showed how to construct regularizers corresponding to explicit Gaussian process priors and desired gauges.
• Derived efficient computation methods for posterior distributions of gauge-fixed weights and epistatic coefficients.

Conclusions:

• The study provides a unified framework linking weight space regression and function space Gaussian processes for sequence-to-function analysis.
• It offers a method to construct specific regularizers for desired prior assumptions and gauge choices.
• The derived computational methods facilitate efficient analysis of complex sequence-function relationships and genetic interactions.