Inferring hidden states in Langevin dynamics on large networks: Average case performance

Area of Science:

• Complex Systems
• Statistical Physics
• Computational Biology

Background:

• Dynamical inference problems arise in analyzing large networks like signal transduction and gene regulation.
• Observing partial network dynamics while inferring hidden states is a common challenge.

Purpose of the Study:

• To present average performance results for dynamical inference in large networks with hidden nodes.
• To analyze the inference error as a function of system parameters and the ratio of hidden to observed nodes.

Main Methods:

• Linear stochastic dynamics of continuous variables with random Gaussian couplings.
• Kalman filter recursions to model posterior dynamics.
• Random Matrix Theory and dynamical functionals to characterize posterior variance.

Main Results:

• The posterior dynamics are governed by an effective drift incorporating observational effects.
• Two approaches characterize posterior variance for equilibrium and nonequilibrium dynamics.
• Spectral properties of inference error and relaxation times are revealed by Random Matrix Theory.

Conclusions:

• The study provides a framework for quantifying inference error in complex dynamical systems.
• The developed methods offer insights into network behavior and parameter estimation.
• This work has implications for understanding and predicting biological network functions.