Sketching for Latent Dirichlet-Categorical Models
This work addresses memory efficiency in Bayesian inference for large-scale models, but it is incremental as it applies known sketching techniques to a specific model class.
The paper tackles the problem of scaling Bayesian inference for large parameter models by proposing compact sketching representations, specifically using count-min sketch and approximate counters for latent Dirichlet-Categorical models, and proves that sketched MCMC converges to the exact chain as sketch error is reduced.
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in memory, and propose more compact representations of parameter values that can be used during inference. We focus on a class of graphical models that we refer to as latent Dirichlet-Categorical models, and show how a combination of two sketching algorithms known as count-min sketch and approximate counters provide an efficient representation for them. We show that this sketch combination -- which, despite having been used before in NLP applications, has not been previously analyzed -- enjoys desirable properties. We prove that for this class of models, when the sketches are used during Markov Chain Monte Carlo inference, the equilibrium of sketched MCMC converges to that of the exact chain as sketch parameters are tuned to reduce the error rate.