Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood
  Estimation for Latent Gaussian Models
Alexander Lin Bahareh Tolooshams Yves Atchadé Demba Ba
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.