BDHS Seminar presented by Abhirup Datta
Department of Biostatistics
Johns Hopkins Bloomberg School of Public Health

In many scientific applications, estimates from an earlier (upstream) analysis are used as inputs for subsequent (downstream) analysis, and uncertainty in these estimates (often available as posterior samples) needs to be propagated into the downstream analysis without reverse feedback. Cutting feedback methods, also termed as cut-Bayes, achieve this by constructing a cut posterior distribution that restricts downstream to upstream information flow. As sampling from the cut posterior is generally computationally challenging, recently variational inference (VI) methods have been developed to approximate the cut posterior. However, they need two variational approximations, cannot directly use samples from the upstream analysis, and often rely on parametric variational families whose approximation quality in finite samples can be poor. We propose, NeVI-Cut, a provably accurate neural network-based variational inference method for cutting feedback. We directly utilize posterior samples available from the first analysis, reducing approximation errors due to a variational approximation for these parameters and circumventing the need to access the data and model used for the first analysis. Conditioning on each MCMC sample, we then use normalizing flows (neural network based generative models) to specify the conditional variational family for the downstream parameters. We estimate the conditional cut posterior by optimizing the Monte Carlo average of the Kullback-Leibler loss over all the MCMC samples. Leveraging the universal expressiveness of neural networks, we provide theoretical guarantees on the ability of NeVI-Cut to approximate any cut posterior. In the process, we provide a general result on uniform approximation of conditional distributions by flows. A triply stochastic scalable algorithm is devised to implement the method. Simulation studies and two real-world analyses illustrate how NeVI-Cut achieves significant computational and performance gains over traditional cutting feedback methods.

A seminar tea will be held at 2:45 p.m. in University Office Plaza, Room 240. All are Welcome.