Bayesian approaches to distribution regression

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images

A Dirichlet process mixture model for survival outcome data: assessing nationwide kidney transplant centers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/110837/1/sim6438.pd

Proceedings of the 35th International Workshop on Statistical Modelling : July 20- 24, 2020 Bilbao, Basque Country, Spain

466 p.The InternationalWorkshop on Statistical Modelling (IWSM) is a reference workshop in promoting statistical modelling, applications of Statistics for researchers, academics and industrialist in a broad sense. Unfortunately, the global COVID-19 pandemic has not allowed holding the 35th edition of the IWSM in Bilbao in July 2020. Despite the situation and following the spirit of the Workshop and the Statistical Modelling Society, we are delighted to bring you the proceedings book of extended abstracts

Distribution Regression: Theory and Application

In this dissertation we discuss the problem of distribution regression. That is, the problem of utilizing distributional covariates in predicting scalar outcomes. We first show an application in neuroimaging that relates functional connectivity measurements viewed as statistical distributions to outcomes. We consider 47 primary progressive aphasia (PPA) patients with various levels of language ability. These patients were randomly assigned to two treatment arms, tDCS (transcranial direct-current stimulation and language therapy) vs sham (language therapy only), in a clinical trial. We analyze the effect of direct stimulation on functional connectivity by treating connectivity measures as samples from individual distributions. As such, we estimate the density of correlations among the regions of interest (ROIs) and study the difference in the density post-intervention between treatment arms. This distributional approach gives the ability to drastically reduces the number of multiple comparisons compared to classic edge-wise analysis. In addition, it allows for the investigation of the impact of functional connectivity on the outcomes where the connectivity is not geometrically localized. We next propose and study the theoretical properties of a related functional expectation model, where we show that optimal information rate bounds can be achieved by a distributional Gaussian process regression, without estimating any individual densities. The model can perform closed form posterior inference via a Gaussian process prior on the regression function. We also propose a low-rank approximation method to accelerate the inference in real applications. In the next chapter, we attached a less related work that reviews state-of-art algorithms to accelerate the convergence of fixed-point iteration problems. Fixed point iteration algorithms have a wide range of applications in statistics and data science. We propose a modified restart Nesterov accelerated gradient algorithm that can also be used for black-box acceleration of general fixed-point iteration problems and show that works well in practice via investigation under six different tasks