First, we develop a measure-preserving and discrete (MAD) invertible map that leaves the discrete target invariant, and then create a mixed variational flow (MAD Mix) based on that map.
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information.
no code implementations • 17 Jun 2022 • Berend Zwartsenberg, Adam Ścibior, Matthew Niedoba, Vasileios Lioutas, Yunpeng Liu, Justice Sefas, Setareh Dabiri, Jonathan Wilder Lavington, Trevor Campbell, Frank Wood
We present a novel, conditional generative probabilistic model of set-valued data with a tractable log density.
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution.
A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during Bayesian inference, with the goal of reducing computational cost.
Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and scalable stochastic optimization algorithms.
Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve mixing in the target.
We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave.
Increasingly, though, data science papers suggest potential alternatives beyond vanilla FMMs, such as power posteriors, coarsening, and related methods.
In this paper, we add rigor to data-analysis folk wisdom by proving that under even the slightest model misspecification, the FMM component-count posterior diverges: the posterior probability of any particular finite number of components converges to 0 in the limit of infinite data.
Completely random measures provide a principled approach to creating flexible unsupervised models, where the number of latent features is infinite and the number of features that influence the data grows with the size of the data set.
Finally, we demonstrate the utility of our proposed workflow and error bounds on a robust regression problem and on a real-data example with a widely used multilevel hierarchical model.
But the automation of past coreset methods is limited because they depend on the availability of a reasonable coarse posterior approximation, which is difficult to specify in practice.
We show that for any target density and any mixture component family, the output of UBVI converges to the best possible approximation in the mixture family, even when the mixture family is misspecified.
Specifically, we extend the framework of the classical Dirichlet diffusion tree to simultaneously infer branch topology and latent cell states along continuous trajectories over the full tree.
Random feature maps (RFMs) and the Nystrom method both consider low-rank approximations to the kernel matrix as a potential solution.
Bayesian inference typically requires the computation of an approximation to the posterior distribution.
We develop an approach to scalable approximate GP regression with finite-data guarantees on the accuracy of pointwise posterior mean and variance estimates.
We begin with an intuitive reformulation of Bayesian coreset construction as sparse vector sum approximation, and demonstrate that its automation and performance-based shortcomings arise from the use of the supremum norm.
Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data.
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices.
Based on the small-variance limit of Bayesian nonparametric von-Mises-Fisher (vMF) mixture distributions, we propose two new flexible and efficient k-means-like clustering algorithms for directional data such as surface normals.
We demonstrate the efficacy of our approach on a number of synthetic and real-world datasets, and find that, in practice, the size of the coreset is independent of the original dataset size.
Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction.
This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models.
The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines its set of received local posteriors.
This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters.