Inferring Cooperativity From Pooled Measurements

2026-07-03

AI Summary

This study addresses the challenge of uncovering latent synergistic interactions among components in multivariate stochastic systems when only aggregate observations are available. The authors propose a sum-dependent Markov chain model and introduce a synergy index capable of distinguishing positive synergy, negative synergy, and independence. They develop a consistent estimator for this index and design a stepwise hypothesis testing procedure with asymptotic control of Type I error and guaranteed statistical power. The theoretical framework leverages continuous-time multivariate Markov processes, hidden Markov modeling, and asymptotic statistical inference to establish consistency and asymptotic normality of the parameter estimators. Numerical experiments on both simulated data and real electrophysiological recordings demonstrate the method’s effectiveness and reliability in detecting synergy and accurately recovering underlying parameters.

Abstract

In many modern experiments, latent interactions drive multicomponent stochastic systems, yet the data are available only as pooled measurements that obscure these dependencies. Whether such interactions can be identified and inferred from aggregate signals remains largely unexplored. Motivated by multi-channel electrophysiological recordings, we address this problem by introducing sum-dependent Markov chains, a class of finite-state continuous-time multivariate Markov processes whose transition rates encode interactions through the aggregate state. Under natural structural conditions, we establish identifiability of the latent dynamic parameters from the aggregate process. We define a cooperativity index that distinguishes positive cooperativity, negative cooperativity and independence, and construct its consistent estimators. For discretely and noisily observed pooled data, we develop likelihood-based inference through a hidden Markov model, address the associated embedding problem, and prove consistency and asymptotic normality. We further propose a stepdown test for cooperativity with asymptotic size control and power guarantees. Simulations and real-data analyses, demonstrate the scope and effectiveness of the methodology.

Problem

• cooperativity
• pooled measurements
• latent interactions
• aggregate data
• multicomponent stochastic systems

Innovation

• sum-dependent Markov chains
• cooperativity inference
• aggregate data identifiability
• hidden Markov model
• asymptotic consistency