Gaussian Approximation of Collective Graphical Models
This work addresses the computational bottleneck in CGMs for applications like population modeling, offering a more efficient inference method, though it is incremental as it builds on existing approximation techniques.
The paper tackles the intractability of exact inference in Collective Graphical Models (CGMs) by proposing a Gaussian approximation (GCGM) that converges to a multivariate Gaussian as population size increases, enabling efficient closed-form inference for certain noise models and showing competitive accuracy with faster computation compared to MAP methods in simulations.
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous work has explored Markov Chain Monte Carlo (MCMC) and MAP approximations for learning and inference. This paper studies Gaussian approximations to the CGM. As the population grows large, we show that the CGM distribution converges to a multivariate Gaussian distribution (GCGM) that maintains the conditional independence properties of the original CGM. If the observations are exact marginals of the CGM or marginals that are corrupted by Gaussian noise, inference in the GCGM approximation can be computed efficiently in closed form. If the observations follow a different noise model (e.g., Poisson), then expectation propagation provides efficient and accurate approximate inference. The accuracy and speed of GCGM inference is compared to the MCMC and MAP methods on a simulated bird migration problem. The GCGM matches or exceeds the accuracy of the MAP method while being significantly faster.