Multi-resolution modeling of a discrete stochastic process identifies causes of cancer

Adam Uri Yaari, Maxwell Sherman, Oliver Clarke Priebe, Po-Ru Loh, Boris Katz, Andrei Barbu, Bonnie Berger

Keywords: Computational Biology, non-stationary stochastic processes, cancer research, deep learning, probabelistic models, graphical models

Abstract: Detection of cancer-causing mutations within the vast and mostly unexplored human genome is a major challenge. Doing so requires modeling the background mutation rate, a highly non-stationary stochastic process, across regions of interest varying in size from one to millions of positions. Here, we present the split-Poisson-Gamma (SPG) distribution, an extension of the classical Poisson-Gamma formulation, to model a discrete stochastic process at multiple resolutions. We demonstrate that the probability model has a closed-form posterior, enabling efficient and accurate linear-time prediction over any length scale after the parameters of the model have been inferred a single time. We apply our framework to model mutation rates in tumors and show that model parameters can be accurately inferred from high-dimensional epigenetic data using a convolutional neural network, Gaussian process, and maximum-likelihood estimation. Our method is both more accurate and more efficient than existing models over a large range of length scales. We demonstrate the usefulness of multi-resolution modeling by detecting genomic elements that drive tumor emergence and are of vastly differing sizes.

One-sentence Summary: We integrate a deep learning framework with a probabilistic model to learn a discrete stochastic process at arbitrary length scales, the method accurately and efficiently model mutations load in a tumor and detect cancer driver mutations genome-wide

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