Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models
This addresses a computational bottleneck for researchers and practitioners using latent Gaussian models in applications like factor analysis and time series analysis, though it is an incremental improvement over existing methods.
The paper tackles the scalability issue of expectation-maximization (EM) for latent Gaussian models with high-dimensional latent variables and large datasets, introducing probabilistic unrolling to avoid matrix inversions and achieving up to an order of magnitude faster learning with minimal performance loss.
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models is the expectation-maximization (EM) algorithm. For problems with high-dimensional latent variables and large datasets, EM scales poorly because it needs to invert as many large covariance matrices as the number of data points. We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversion. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.