Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation
This incremental improvement addresses the computational bottleneck of marginal likelihood estimation for Bayesian model selection and online applications, benefiting researchers and practitioners in machine learning and statistics.
The paper tackles the problem of efficiently estimating marginal likelihood in i.i.d. data settings by proposing stochastic gradient annealed importance sampling (SGAIS), which uses mini-batches and an adaptive annealing schedule to achieve faster computation with no noticeable loss in accuracy compared to traditional methods like nested sampling.
We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination.