Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference.
We propose NeRF-VAE, a 3D scene generative model that incorporates geometric structure via NeRF and differentiable volume rendering.
When it comes to meta-learning in Gaussian process models, approaches in this setting have mostly focused on learning the kernel function of the prior, but not on learning its mean function.
The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching.
We explore different techniques for selecting inducing points on discrete domains, including greedy selection, determinantal point processes, and simulated annealing.
We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set.
We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite-dimensional.
In this context, the MMD may be used in two roles: first, as a discriminator, either directly on the samples, or on features of the samples.
Our test statistic is based on an empirical estimate of this divergence, taking the form of a V-statistic in terms of the log gradients of the target density and the kernel.
We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC).
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution.
A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support.
The methodology is reviewed on well-known examples such as the parameters in Ising models, the posterior for Fisher-Bingham distributions on the $d$-Sphere and a large-scale Gaussian Markov Random Field model describing the Ozone Column data.
A means of parameter selection for the two-sample test based on the MMD is proposed.