Tensor product algorithms for inference of contact network from epidemiological data.

Area of Science:

• Epidemiology
• Network Science
• Computational Biology

Background:

• Inferring contact networks is crucial for understanding disease spread.
• Traditional methods struggle with the computational complexity of large networks.
• Estimating likelihoods for epidemiological models is challenging due to rare events.

Purpose of the Study:

• To develop a computationally efficient method for inferring contact networks from epidemiological data.
• To overcome the limitations of stochastic simulation in estimating small probabilities.
• To enable accurate black-box Bayesian inference of network structures.

Main Methods:

• Utilizing a black-box Bayesian optimization framework.
• Replacing stochastic simulations with solving the chemical master equation.
• Applying tensor train approximations to manage the curse of dimensionality.

Main Results:

• Demonstrated efficient and accurate computation of network state probabilities.
• Successfully inferred contact networks even when probabilities are very small.
• Numerical simulations confirmed the effectiveness of the proposed approach.

Conclusions:

• The chemical master equation combined with tensor train approximations offers a powerful solution for network inference.
• This approach significantly enhances the efficiency and accuracy of epidemiological modeling.
• Enables robust inference of contact networks from observed nodal states.