Consistent diffusion matrix estimation from population time series

TL;DR

This paper introduces a method to accurately estimate the diffusion matrix in complex dynamical systems using population snapshots and velocity data, overcoming challenges of nonidentifiability in single-cell sequencing analyses.

Contribution

It presents a novel, provably consistent estimator that combines population time series with velocity measurements to recover the diffusion matrix.

Findings

Estimator is mathematically proven to be consistent.

Method effectively distinguishes diffusion from measurement noise.

Applicable to large-scale biological datasets.

Abstract

Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing technologies is learning the behavior of individuals from population snapshots. In the absence of individual-level time series, standard stochastic differential equation models are often nonidentifiable because intrinsic diffusion cannot be distinguished from measurement noise. Despite the difficulty, accurately recovering diffusion terms is required to answer even basic questions about the system's behavior. We show how to combine population-level time series with velocity measurements to build a provably consistent estimator of the diffusion matrix.