Trust-Region Variational Inference with Gaussian Mixture Models
This addresses the challenge of efficient and accurate inference in machine learning for domains with complex, multimodal distributions, though it is an incremental improvement over existing variational methods.
The paper tackles the problem of approximating intractable probability distributions by proposing a trust-region variational inference method using Gaussian mixture models, achieving sample quality comparable to state-of-the-art MCMC samplers with up to three orders of magnitude less computational resources.
Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by using information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. Our use of the lower bound ensures convergence to a stationary point of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multimodal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-the-art MCMC samplers while requiring up to three orders of magnitude less computational resources.