Learning in Integer Latent Variable Models with Nested Automatic Differentiation
This provides a more efficient solution for researchers and practitioners working with complex probabilistic models involving integer latent variables, though it is incremental as it builds on prior work.
The paper tackles the computational challenge of exact inference and learning in integer latent variable models by developing faster and more stable nested automatic differentiation algorithms, achieving polynomial-time complexity in nesting levels and significantly improving speed and accuracy.
We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many levels of nested high-order derivatives. We contribute faster and more stable AD algorithms for this challenging problem and a novel algorithm to compute exact gradients for learning. These contributions lead to significantly faster and more accurate learning algorithms, and are the first AD algorithms whose running time is polynomial in the number of levels of nesting.