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

Petti, Samantha, Martí-Gómez, Carlos, Kinney, Justin B, Zhou, Juannan, McCandlish, David M (July 2025) On learning functions over biological sequence space: relating Gaussian process priors, regularization, and gauge fixing. ArXiv. ISSN 2331-8422

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Abstract

Mappings from biological sequences (DNA, RNA, protein) to quantitative measures of sequence functionality play an important role in contemporary biology. We are interested in the related tasks of (i) inferring predictive sequence-to-function maps and (ii) decomposing sequence-function maps to elucidate the contributions of individual subsequences. Because each sequence-function map can be written as a weighted sum over subsequences in multiple ways, meaningfully interpreting these weights requires "gauge-fixing," i.e., defining a unique representation for each map. Recent work has established that most existing gauge-fixed representations arise as the unique solutions to L 2 -regularized regression in an overparameterized "weight space" where the choice of regularizer defines the gauge. Here, we establish the relationship between regularized regression in overparameterized weight space and Gaussian process approaches that operate in "function space," i.e. the space of all real-valued functions on a finite set of sequences. We disentangle how weight space regularizers both impose an implicit prior on the learned function and restrict the optimal weights to a particular gauge. We also show how to construct regularizers that correspond to arbitrary explicit Gaussian process priors combined with a wide variety of gauges. Next, we derive the distribution of gauge-fixed weights implied by the Gaussian process posterior and demonstrate that even for long sequences this distribution can be efficiently computed for product-kernel priors using a kernel trick. Finally, we characterize the implicit function space priors associated with the most common weight space regularizers. Overall, our framework unifies and extends our ability to infer and interpret sequence-function relationships.

Item Type:	Paper
Subjects:	bioinformatics bioinformatics > genomics and proteomics bioinformatics > quantitative biology bioinformatics > computational biology > algorithms bioinformatics > computational biology
CSHL Authors:	Kinney, Justin B. McCandlish, David Marti Gomez Aldaravi Carlos
Communities:	CSHL labs > Kinney lab CSHL labs > McCandlish lab
SWORD Depositor:	CSHL Elements
Depositing User:	CSHL Elements
Date:	11 July 2025
Date Deposited:	07 Aug 2025 12:16
Last Modified:	07 Aug 2025 12:16
PMCID:	PMC12265488
URI:	https://repository.cshl.edu/id/eprint/41929

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