Inference of the kinetic Ising model with heterogeneous missing data.

Area of Science:

• Statistical Physics
• Machine Learning
• Time Series Analysis

Background:

• Inferring causality from time series data is challenging, especially with missing observations.
• The kinetic Ising model is a framework for analyzing interacting systems over time.
• Existing methods struggle with severe data sparsity.

Purpose of the Study:

• To develop a robust method for inferring causality structure from binary time series with missing data.
• To adapt mean-field methods for models with hidden states to handle data sparsity.
• To estimate the couplings matrix and impute missing observations efficiently.

Main Methods:

• Developed a pseudo-expectation-maximization algorithm inspired by mean-field methods.
• Utilized the Martin-Siggia-Rose path integral with a second-order saddle-point approximation.
• Proposed a recursive algorithm incorporating maximum-likelihood estimates for missing values.
• Integrated the method with sparsification techniques like lasso regularization and decimation.

Main Results:

• The algorithm successfully infers causality and estimates missing data under severe sparsity.
• The method approximates the log-likelihood in polynomial time.
• Performance analysis on synthetic data revealed dependencies on observation frequency heterogeneity.
• Investigated the impact of violated assumptions (small couplings, independence) on the saddle-point approximation.

Conclusions:

• The proposed pseudo-expectation-maximization algorithm offers a powerful tool for causal inference in sparse time series data.
• The recursive approach enhances applicability with standard regularization techniques.
• The study provides insights into the limitations and performance characteristics of the method under various conditions.