Generative Particle Variational Inference via Estimation of Functional Gradients
This work addresses a bottleneck in variational inference for researchers and practitioners by enabling flexible generative sampling while maintaining asymptotic performance, though it is incremental in improving existing methods.
The paper tackles the problem of arbitrary sampling from posterior distributions in particle-based variational inference by proposing a neural sampler trained with functional gradients in a reproducing kernel Hilbert space, achieving competitive performance with gold-standard methods like Hamiltonian Monte Carlo.
Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.