Blackwell-Rosenbluth Award

We present an innovative regression framework featuring a scalar outcome and a multiplex graph as the predictor, where each layer of the graph captures interactions among a shared set of nodes. Popular regression methods utilizing multiplex graph predictors often face limitations in effectively harnessing information within and across network layers, leading to compromised inference and predictive accuracy, especially in scenarios with limited sample sizes. To overcome these challenges, our method models an edge coefficient in each layer as a bilinear interaction between the latent effects associated with the two connected nodes. Additionally, it employs a variable selection framework on node-specific latent effects from all layers to identify influential nodes linked to the outcome. Crucially, the proposed framework is computationally efficient and provides uncertainty in node identification, regression coefficient estimation, and binary outcome prediction. Simulation studies demonstrate the superior inferential and predictive performance of the proposed approach. 

Data science is at a defining crossroad for modern scientific discovery. On one hand, with remarkable breakthroughs in scientific modeling and experimental technology, reliable data can now be generated for complex systems that were previously unobtainable. On the other hand, the generation of such high-fidelity data requires costly experiments, which greatly limits the amount of available data. This presents a critical bottleneck for modern scientific discovery. My research aims to bridge this gap by developing Bayesian methods (supported by theory & algorithms) that embed scientific knowledge as prior information. This fusing of "data" and "science" within a Bayesian framework allows for principled integration of scientific prior knowledge, thus enabling more accurate and precise scientific findings given a limited experimental cost budget. In this talk, I will present a suite of recent Bayesian methods developed by our group that tackle this integration, motivated by ongoing collaborations in high-energy physics, aerospace engineering and bioengineering. 

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in numerous situations, evaluating even the unnormalized distribution proves to be costly or infeasible. This issue arises in scenarios such as sampling from the Bayesian posterior for large datasets and the 'doubly intractable' distributions. Our work introduces a unified framework that includes various MCMC algorithms, including several minibatch MCMC algorithms and the exchange algorithm. This framework not only simplifies the theoretical analysis of existing algorithms but also paves the way for the development of new, more efficient algorithms. 

Piecewise-deterministic Markov process (PDMP) samplers constitute a state of the art Markov chain Monte Carlo (MCMC) paradigm in Bayesian computation, with examples including the zig-zag and bouncy particle sampler (BPS). Recent work on the zig-zag has indicated its connection to Hamiltonian Monte Carlo, a version of the Metropolis algorithm that exploits Hamiltonian dynamics. Here we establish that, in fact, the connection between the paradigms extends far beyond the specific instance. The key lies in (1) the fact that any time-reversible deterministic dynamics provides a valid Metropolis proposal and (2) how PDMPs' characteristic velocity changes constitute an alternative to the usual acceptance-rejection. We turn this observation into a rigorous framework for constructing rejection-free Metropolis proposals based on bouncy Hamiltonian dynamics which simultaneously possess Hamiltonian-like properties and generate discontinuous trajectories similar in appearance to PDMPs. When combined with periodic refreshment of the inertia, the dynamics converge strongly to PDMP equivalents in the limit of increasingly frequent refreshment. We demonstrate the practical implications of this new paradigm, with a sampler based on a bouncy Hamiltonian dynamics closely related to the BPS. The resulting sampler exhibits competitive performance on challenging real-data posteriors involving tens of thousands of parameters.