Asymptotically Exact Data Augmentation: Models, Properties, and Algorithms

Asymptotically exact streaming algorithms

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the algorithm is restricted to polylog(n) size. Thus, the output of the algorithm is optimal in the limit. We show positive results in our model for a series of imp...

Asymptotically exact inference in differentiable generative models

Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class of procedurally defined simulator models. We present a method for performing efficient MCMC inference in such models when conditioning on observations of the...

Exact Bayesian inference via data augmentation

Data augmentation is a common tool in Bayesian statistics, especially in the application of MCMC. Data augmentation is used where direct computation of the posterior density, π(θ |x), of the parameters θ , given the observed data x, is not possible. We show that for a range of problems, it is possible to augment the data by y, such that, π(θ |x,y) is known, and π(y|x) can easily be computed. In...

Supplemental to Asymptotically Exact Inference in Conditional Moment Inequality Models

Supplement to “Asymptotically Exact Inference in Conditional Moment Inequality Models”

This supplementary appendix contains auxiliary results and proofs for the main paper. Section A contains a proof of Theorem 3.1 in the case where l = dY = 1, which contains the main technical ideas of the general result, but requires less notation. Section B proposes an alternative way of obtaining critical values using the asymptotic distribution results in this paper. Section C contains proof...