Abstract
Probabilistic programming languages can simplify the development of machine
learning techniques, but only if inference is sufficiently scalable.
Unfortunately, Bayesian parameter estimation for highly coupled models such as
regressions and state-space models still scales badly. This paper describes a
sublinear-time algorithm for making Metropolis-Hastings updates to latent
variables in probabilistic programs. This approach generalizes recently
introduced approximate MH techniques: instead of subsampling data items assumed
to be independent, it subsamples edges in a dynamically constructed graphical
model. It thus applies to a broader class of problems and interoperates with
general-purpose inference techniques. Empirical results are presented for
Bayesian logistic regression, nonlinear classification via joint Dirichlet
process mixtures, and parameter estimation for stochastic volatility models
(with state estimation via particle MCMC). All three applications use the same
implementation, and each requires under 20 lines of probabilistic code.
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