Postdoctoral Fellow Day

Join us on November 14 for Postdoc Day, a special event dedicated to showcasing the work of our postdoctoral researchers! This is a fantastic opportunity to learn about the diverse projects being undertaken in the department. Postdoc Day also provides a valuable platform for networking. We look forward to seeing you there and hearing more about the exciting work happening within our community.

Schedule

Coffee & Pastry starting at 9:45

10:00-10:30 | Archer Gong Zhang: A Semiparametric Approach to Data-Integrated Causal Inference

10:30-11:00 | Samuel Perreault: Fitting seasonally varying distributions with misspecified GAMLSS

10 minute in break

11:10-11:40 | Thibault Randrianarisoa: Semiparametric privacy-constrained inference

11:40-12:10 | Austin Brown: Upper and lower bounds on the convergence of adaptive MCMC

12:10-12:40 |  Yaoming Zhen: Consistent community detection in multi-layer networks with heterogeneous differential privacy.

Lunch & hang out

Archer Gong Zhang: A Semiparametric Approach to Data-Integrated Causal Inference

In causal inference, data may come from multiple sources such as experimental and observational studies. Experimental studies are often limited in size and lack external validity due to the restrictions of their design. Observational studies are typically large and broad but may lack internal validity because of unmeasured confounding. Recently, there has been increasing interest in integrating these types of data to enhance causal inference. In this talk, we present a semiparametric approach based on the density ratio model (DRM) to utilize the complementary features of these data sources. The DRM is well-suited to address shared latent structures among interconnected populations. When related studies include common measurements for the same causal inference problem, the collected datasets are naturally expected to originate from connected populations, which makes the DRM especially effective. Furthermore, the DRM provides a platform for studying causal relationships from a distribution perspective, offering greater insight compared to some existing causal inference methods that focus solely on mean estimation.

Samuel Perreault: Fitting seasonally varying distributions with misspecified GAMLSS

The analysis of environmental time series—such as air pollution concentrations, temperature, and river flows—has long played a crucial role in statistics, and this importance has only grown with today’s pressing environmental challenges. Accurately modeling these data, and in particular quantifying the seasonal variations in their distributions, is essential for monitoring and understanding natural processes. In some cases, emphasis is placed on "time-specific" distributions rather than on capturing temporal dependencies; these distributions may be of intrinsic interest or serve as key inputs for downstream analyses. This motivates the use of composite likelihoods comprised only of univariate distributions to circumvent the complexity involved in modeling temporal relationships. In this work, we investigate the use of (misspecified) Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to fit seasonally varying distributions. We demonstrate our method through an application to Canadian river flow data.

Thibault Randrianarisoa: Semiparametric privacy-constrained inference

We study the problem of non-parametric density estimation for densities in Sobolev spaces, under the additional constraint that only privatized data are allowed to be published and available for inference. More precisely, we focus on the estimation of a functional of the density via plug-in estimators. For this purpose, we adapt recent results from the minimax theory under the framework of local α-differential privacy. We first build a nonparametric projection estimator based on spline wavelets and add suitably scaled Laplace noise to empirical wavelet coefficients to fulfill the privacy requirement. Under some regularity assumptions of the functional, we derive convergence rates in expectation for the corresponding plug-in estimators and show that these are optimal up to a logarithmic factor. We observe different regimes in the rate, depending on the size of α and the regularity of the functional. We also provide a Lepski-type estimator that adapts to the Sobolev regularity of the density.

Austin Brown: Upper and lower bounds on the convergence of adaptive MCMC

Adaptive MCMC often exhibits empirical performance superseding the performance of standard MCMC even though much of the theoretical understanding is lacking. I will discuss some new lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo under arbitrary adaptation strategies. If the adaptation diminishes sufficiently fast, I will also discuss some new explicit upper bounds on the subgeometric convergence that are comparable to the lower bounds. These results provide insight into the optimal design of adaptation strategies and limitations on the convergence behavior of adaptive MCMC in practice. This is joint work with Jeffrey Rosenthal.

Yaoming Zhen: Consistent community detection in multi-layer networks with heterogeneous differential privacy.

As network data becomes increasingly prevalent, significant attention has been devoted to addressing privacy issues in publishing such data. One of the critical challenges for data publishers is to preserve the topological structures of the original network while protecting sensitive information. In this paper, we investigate the utility of community detection in multi-layer networks under a personalized edge-flipping mechanism. This mechanism enables data publishers to protect edge information based on each node's privacy preferences. Within this framework, the community structure under the multi-layer degree-corrected stochastic block model remains invariant after appropriate debiasing, making consistent community detection in privatized multi-layer networks achievable. Theoretically, we establish the consistency of community detection in the privatized multi-layer network, demonstrating the fundamental privacy-utility trade-offs in differentially private community detection in multi-layer networks under the proposed mechanism. Moreover, we support our findings with results from various synthetic networks and a real-life multi-layer network.