SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models
This provides an unbiased estimator for latent variable models, addressing a fundamental limitation in training and enabling applications like minimizing reverse KL divergences, which is significant for researchers in probabilistic modeling.
The paper tackles the problem of biased estimates from variational lower bounds in latent variable models by introducing an unbiased estimator of log marginal likelihood based on randomized truncation of infinite series. The result shows that models trained with this estimator achieve better test-set likelihoods than standard importance-sampling approaches at the same computational cost.
Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost. This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.