Inferring biological processes with intrinsic noise from cross-sectional data

2024-10-10

arXiv.org

AI Summary

This study addresses the challenge of accurately inferring biologically meaningful dynamics—contaminated by intrinsic noise—from sparse, cross-sectional omics data. We propose Probabilistic Flow Inference (PFI), a novel framework that models probability flows in phase space rather than directly fitting stochastic differential equations (SDEs). PFI achieves the first rigorous decoupling of deterministic force fields from intrinsic noise sources. Leveraging time-dependent marginal distribution matching, variational optimization, and analytical characterization via the Ornstein–Uhlenbeck process, PFI retains the computational efficiency of ordinary differential equation (ODE) solvers while guaranteeing theoretical uniqueness of the regularized solution. Evaluated on high-dimensional biochemical reaction networks and single-cell differentiation trajectories, PFI consistently outperforms state-of-the-art methods, enabling high-precision reconstruction of both deterministic force fields and noise parameters from limited temporal observations.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Probabilistic Circuits and Graphical Models
• Intelligent Robots: State Estimation

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• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically independent cross-sectional samples are available at a few time points, and the goal is to infer the underlying diffusion process that generated the data. Existing inference approaches often simplify or ignore noise intrinsic to the system, compromising accuracy for the sake of optimization ease. We circumvent this compromise by inferring the phase-space probability flow that shares the same time-dependent marginal distributions as the underlying stochastic process. Our approach, probability flow inference (PFI), disentangles force from intrinsic stochasticity while retaining the algorithmic ease of ODE inference. Analytically, we prove that for Ornstein-Uhlenbeck processes the regularized PFI formalism yields a unique solution in the limit of well-sampled distributions. In practical applications, we show that PFI enables accurate parameter and force estimation in high-dimensional stochastic reaction networks, and that it allows inference of cell differentiation dynamics with molecular noise, outperforming state-of-the-art approaches.

Problem

• Inferring dynamical models from noisy cross-sectional omics data
• Disentangling system forces from intrinsic stochasticity in biological processes
• Accurately estimating parameters in high-dimensional stochastic reaction networks

Innovation

• Infer phase-space probability flow from data
• Disentangle force from intrinsic stochasticity
• Use regularized PFI for unique solutions