Nonparametric variational inference
This addresses the problem of approximate posterior inference in machine learning for researchers and practitioners, offering a more flexible method for general graphical models, though it is incremental in extending variational techniques.
The paper tackles the limitation of variational inference to conjugate distributions by proposing a nonparametric kernel-based variational family, achieving predictive performance comparable to or better than specialized variational and sampling methods in hierarchical logistic regression and nonlinear matrix factorization.
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. The locations of these kernels and their bandwidth are treated as variational parameters and optimized to improve an approximate lower bound on the marginal likelihood of the data. Using multiple kernels allows the approximation to capture multiple modes of the posterior, unlike most other variational approximations. We demonstrate the efficacy of the nonparametric approximation with a hierarchical logistic regression model and a nonlinear matrix factorization model. We obtain predictive performance as good as or better than more specialized variational methods and sample-based approximations. The method is easy to apply to more general graphical models for which standard variational methods are difficult to derive.