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Non-parametric Bayesian density estimation for biological sequence space with applications to pre-mRNA splicing and the karyotypic diversity of human cancer

Wei-Chia Chen, Juannan Zhou, Jason M Sheltzer, View ORCID ProfileJustin B Kinney, David M McCandlish
doi: https://doi.org/10.1101/2020.11.25.399253
Wei-Chia Chen
aSimons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724
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Juannan Zhou
aSimons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724
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Jason M Sheltzer
bCold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724
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Justin B Kinney
aSimons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724
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  • ORCID record for Justin B Kinney
David M McCandlish
aSimons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724
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  • For correspondence: mccandlish@cshl.edu
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Abstract

Density estimation in sequence space is a fundamental problem in machine learning that is of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy, i.e. calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates. Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data is plentiful while still maintaining a conservative maximum entropy char-acter in regions of sequence space where data is sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyper-parameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand the accumulation of chromosomal abnormalities during cancer progression.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted December 10, 2020.
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Non-parametric Bayesian density estimation for biological sequence space with applications to pre-mRNA splicing and the karyotypic diversity of human cancer
Wei-Chia Chen, Juannan Zhou, Jason M Sheltzer, Justin B Kinney, David M McCandlish
bioRxiv 2020.11.25.399253; doi: https://doi.org/10.1101/2020.11.25.399253
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Non-parametric Bayesian density estimation for biological sequence space with applications to pre-mRNA splicing and the karyotypic diversity of human cancer
Wei-Chia Chen, Juannan Zhou, Jason M Sheltzer, Justin B Kinney, David M McCandlish
bioRxiv 2020.11.25.399253; doi: https://doi.org/10.1101/2020.11.25.399253

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