NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters

• URL: http://arxiv.org/abs/2111.01104v1
• Date: Mon, 1 Nov 2021 17:17:34 GMT
• Title: NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters
• Authors: Ben Lengerich, Caleb Ellington, Bryon Aragam, Eric P. Xing, Manolis Kellis
• Abstract summary: We present NOTMAD, which learns to mix archetypal networks according to sample context. We demonstrate the utility of NOTMAD and sample-specific network inference through analysis and experiments, including patient-specific gene expression networks.
• Score: 70.55488722439239
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Context-specific Bayesian networks (i.e. directed acyclic graphs, DAGs) identify context-dependent relationships between variables, but the non-convexity induced by the acyclicity requirement makes it difficult to share information between context-specific estimators (e.g. with graph generator functions). For this reason, existing methods for inferring context-specific Bayesian networks have favored breaking datasets into subsamples, limiting statistical power and resolution, and preventing the use of multidimensional and latent contexts. To overcome this challenge, we propose NOTEARS-optimized Mixtures of Archetypal DAGs (NOTMAD). NOTMAD models context-specific Bayesian networks as the output of a function which learns to mix archetypal networks according to sample context. The archetypal networks are estimated jointly with the context-specific networks and do not require any prior knowledge. We encode the acyclicity constraint as a smooth regularization loss which is back-propagated to the mixing function; in this way, NOTMAD shares information between context-specific acyclic graphs, enabling the estimation of Bayesian network structures and parameters at even single-sample resolution. We demonstrate the utility of NOTMAD and sample-specific network inference through analysis and experiments, including patient-specific gene expression networks which correspond to morphological variation in cancer.

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