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Presentation 1

Time: 11:00 am - 11:30 am

Speaker: Zefan (Steve) Liu, UBC Statistics MSc student

Title: Modelling peaks over thresholds in panel data: a grouped panel generalized Pareto regression model

Abstract: Extreme Value Theory (EVT) provides probabilistic tools to understand the behaviour of extreme events, making it widely applicable across various fields. When modelling the marginal distributions of the extremes in panel data, one may wish to balance the flexibility to capture the heterogeneity among margins and the efficiency of estimation through a combination of regression technique and assuming a latent group structure among subjects. This group structure facilitating information pooling may not be known a priori and needs to be estimated from data, which may then lead to potential physical interpretations. One existing approach addressing this modelling idea builds on the Block Maxima (BM) method in EVT, which can result in a loss of valuable information. Moreover, similar to the classic k-means clustering method, the current algorithm for estimating group structure is prone to converging to locally optimal solutions. We extend the current approach to a new framework called the grouped panel generalized Pareto regression model, which utilizes the Peaks Over Threshold (POT) method to model excesses over high thresholds, thereby leveraging extreme event information more exhaustively. To account for the conditional dependence structure within clusters of excesses, we introduce a dependence-window-based sandwich estimator for standard error estimation. Taking advantage of the POT method, we develop a new grouping algorithm inspired by hierarchical clustering, which relies on a pre-determined linkage and stopping rule. This algorithm estimates the latent number of groups, the group structure and associated parameters simultaneously, and it demonstrates improved performance in identifying the globally optimal structure and balancing the goodness of fit across subjects under reasonable conditions. The finite-sample performance of our methodology is carefully evaluated through simulation studies, and an application to the river flow data from 31 hydrological stations in Upper Danube river basin is used to illustrate the real-world applicability of our modelling strategy, where the estimation efficiency is notably improved and physically interpretable group structures are identified.

Presentation 2

Time: 11:30 am – 12:00 pm

Speaker: Tom Tang, UBC Statistics MSc student

Title: The challenges of non-identifiability and a penalized maximum likelihood estimator for the beta mixture model

Abstract: This thesis explores statistical inference for the finite mixture models, with a particular focus on beta mixture models, which are widely used in biostatistics, bioinformatics, and computer science. It addresses significant issues such as unbounded likelihood and non-identifiability, which can complicate parameter estimation. To overcome the obstacle caused by the unbounded likelihood, we propose a penalized maximum likelihood estimation approach by adding a penalty term to the log-likelihood function, leading to stable parameter estimation. Additionally, we derive a closed-form expression for testing non-identifiability in beta mixture models. The effectiveness of our penalized approach is evaluated through simulation studies and compared with alternative approaches, such as the method of moments. Practical applicability is demonstrated through applications to DNA methylation analysis and local false discovery rate estimation. Finally, we suggest several directions for future research.

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Abstract: With skyrocketing improvements in the computational performance of modern computing machines, the area of Bayesian inference applications is outstandingly improved, and Bayesian statistical analysis is used more frequently. In Bayesian inference, most computational resources are applied to running Markov chain Monte Carlo (MCMC) algorithms to obtain samples from posterior distributions. The MCMC algorithm is the main route to implement Bayesian inference. It allows for high-dimensional and flexible sampling. However, at the same time, researchers can undergo poorer computational performance when Bayesian statistical inference is performed using some specific families of models, namely partially identified models. This is because the good computational performance of the MCMC algorithm is not guaranteed. The parameters of the partially identified model are not uniquely identified, which makes the off-she-shelf MCMC algorithm hard to sample from posterior distributions. Importance sampling with transparent reparameterization (ISTP) is a good computational remedy for posterior inference with partially identified models. With the ISTP algorithm, researchers could obtain better and more stable computational performance while having samples in their original parameterization. In this talk, we first traverse scenarios of worsening computational performance with partially identified models and compare the results of ISTP with an off-the-shelf MCMC algorithm. Then, we discuss the general usability of ISTP and develop the diagnostic method for models suspected to have partial or weak identification. Along with ISTP, we introduce an R package for the Bayesian inference with the partially identified model.  Lastly, we discuss what was completed, its limitations, and possible future improvements.

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Abstract: The current and projected growth of the space industry has brought risk assessment for near-space encounters into sharper focus.  The dominant paradigm is the computation of a so-called collision probability, but this has a number of drawbacks, including a `dilution paradox'. I shall describe an alternative statistically-based approach to the problem that seems to have numerous advantages over existing procedures, though it brings some issues of its own.  The work is joint with Soumaya Elkantassi, Russell Carpenter and Matt Hejduk.

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Abstract: Markov-switching models are powerful tools that allow capturing complex patterns from time series data driven by latent states. Recent work has highlighted the benefits of estimating components of these models nonparametrically, enhancing their flexibility and reducing biases, which in turn can improve state decoding, forecasting, and overall inference. Formulating such models using penalised splines is straightforward, but practically feasible methods for a data-driven smoothness selection in these models are still lacking. Traditional techniques, such as cross-validation and information criteria-based selection suffer from major drawbacks, most importantly their reliance on computationally expensive grid search methods, hampering practical usability for Markov-switching models. Michelot (2022) suggested treating spline coefficients as random effects with a multivariate normal distribution and using the R package TMB (Kristensen et al., 2015) for marginal likelihood maximisation. While this method avoids grid search and typically results in adequate smoothness selection, it entails a nested optimisation problem, thus being computationally demanding. We propose to exploit the simple structure of penalised splines treated as random effects, thereby greatly reducing the computational burden while potentially improving fixed effects parameter estimation accuracy. The proposed method offers a reliable and efficient mechanism for smoothness selection, rendering the estimation of Markov-switching models involving penalised splines feasible for complex data structures.

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Abstract: Bayesian nonparametric (BNP) models provide a flexible and powerful framework for statistical modeling by allowing the number of features or subgroups within a population to grow with the data volume. However, posterior inference in BNP models is challenging due to the infinite parameters involved, and the lack of general and efficient inference procedures impedes their practical application. Exact posterior inference methods either analytically marginalize out the infinitely many parameters, or introduce auxiliary variables to adaptively adjust the model size during inference. The former approach relies on conjugacy relationships between priors and likelihoods and suffers from high computational costs. Similarly, the latter approach is also computationally demanding, as it requires numerical integration during sampling for nonconjugate models.

An alternative common practice in fitting BNP models involves approximating the nonparametric model with a parametric one, and subsequently applying a standard inference algorithm. While this is practical, parametric truncation can lead to significant unknown posterior approximation errors, particularly for BNP models with heavy tails that support the power-law behavior of the population. Previous work on truncated inference in BNP models has determined the truncation level via analysis of the forward generative model, which does not accurately reflect the error of approximation of the target posterior distribution. This thesis aims to develop approximate inference algorithms that can be directly used for posterior inference for general BNP models. We propose truncated inference methods and provide estimates of the posterior truncation error. Rather than setting the truncation level based on prior approximation error, we establish a desired posterior truncation error level, allowing the algorithm to adapt the truncation level until the desired truncation error is reached. The proposed algorithms are general in that they can be applied to a wide range of BNP models with completely random measure (CRM) priors. We have applied these algorithms to edge-exchangeable network models, where feature assignment variables are observed, and to latent feature models with latent feature assignment variables.

Zoom Registration

https://ubc.zoom.us/meeting/register/Z_eCE0H9QqGknxiuC66eBg  

Title

From Diffusion Models to Schrödinger Bridges - When Generative Modeling meets Optimal Transport

Abstract

Denoising Diffusion models have revolutionized generative modeling. Conceptually, these methods define a transport mechanism from a noise distribution to a data distribution. Recent advancements have extended this framework to define transport maps between arbitrary distributions, significantly expanding the potential for unpaired data translation. However, existing methods often fail to approximate optimal transport maps, which are theoretically known to possess advantageous properties. In this talk, we will show how one can modify current methodologies to compute Schrödinger bridges—an entropy-regularized variant of dynamic optimal transport. We will demonstrate this methodology on a variety of unpaired data translation tasks.

van Eeden speakers

Dr. Arnaud Doucet has been invited to be this year's van Eeden speaker by the graduate students in the Department of Statistics at the University of British Columbia. A van Eeden speaker is a prominent statistician who is chosen each year to give a lecture, supported by the UBC Constance van Eeden Fund (https://www.stat.ubc.ca/constance-van-eeden-fund). The 2025 seminar is additionally sponsored by the Canadian Statistical Sciences Institute (CANSSI), the Pacific Institute for the Mathematical Sciences (PIMS), and the Walter H. Gage Memorial Fund.

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Abstract: Experiments where treatment assignment varies over time, such as micro-randomized trials and switchback experiments, are essential for guiding dynamic decisions. These experiments often exhibit nonstationarity due to factors like hidden states or unstable environments, posing substantial challenges for accurate policy evaluation.

In this talk, I will discuss how Partially Observed Markov Decision Processes (POMDPs) with explicit mixing assumptions provide a natural framework for modeling dynamic experiments and can guide both the design and analysis of these experiments. In the first part of the talk, I will discuss properties of switchback experiments in finite-population, nonstationary dynamic systems. We find that, in this setting, standard switchback designs suffer considerably from carryover bias, but judicious use of burn-in periods can considerably improve the situation and enable errors that decay nearly at the parametric rate. In the second part of the talk, I will discuss policy evaluation in micro-randomized experiments and provide further theoretical grounding on mixing-based policy evaluation methodologies. Under a sequential ignorability assumption, we provide rate-matching upper and lower bounds that sharply characterize the hardness of off-policy evaluation in POMDPs. These findings demonstrate the promise of using stochastic modeling techniques to enhance tools for causal inference. Our formal results are mirrored in empirical evaluations using ride-sharing and mobile health simulators.

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Dear STAT news subscribers:

Please be advised that this seminar has been cancelled. We sincerely apologize for any inconvenience.

Best wishes,

UBC Statistics Department

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Abstract: The advent of deep learning has completely revolutionized how we perceive data to obtain super-human performance across all fields of modern science. However, despite the remarkable empirical successes of deep learners, the theoretical guarantees for their statistical accuracy remain rather pessimistic. In particular, the data distributions on which deep learners are generally applied, such as natural images, are often hypothesized to have an intrinsic low-dimensional structure in a typically high-dimensional feature space. However, this is often not reflected in the derived rates in the state-of-the-art analyses. This talk aims to bridge the gap between the theory and practice of deep learning from a statistical perspective. We demonstrate that deep learners exhibit a convergence rate determined solely by the intrinsic dimensionality of the data, rather than its nominal high-dimensional feature representation. Our work not only provides practical guidelines for selecting suitable network architectures but also connects the theoretical analyses of these models to established convergence rates in optimal transport and non-parametric statistics literature. In particular, we derive the sharpest convergence rates for various learning scenarios, including Generative Adversarial Networks (GANs), Wasserstein Autoencoders (WAEs), federated learning, Bi-directional GANs, and general deep supervised learners. Furthermore, we introduce a novel measure, called the entropic dimension, to characterize the intrinsic dimension of probability measures and achieve the sharpest known approximation results for neural networks employing Rectified Linear Unit (ReLU) activation, improving upon classical benchmarks.

Bio: Saptarshi Chakraborty is a fifth-year Ph.D. student in Statistics at the University of California, Berkeley, advised by Prof. Peter Bartlett. Prior to joining Berkeley, he earned his M.Stat and B. Stat (Hons.) degrees in Statistics from the Indian Statistical Institute (ISI), Kolkata, India. Saptarshi is the recipient of the Two-sigma PhD fellowship, 2023-24. He is primarily interested in the theoretical and methodological foundations of machine learning, especially, deep learning theory, unsupervised learning, dimensionality reduction, optimal transport, and optimization.

***

Dear STAT news subscribers:

Please be advised that this seminar has been cancelled. We sincerely apologize for any inconvenience.

Best wishes,

UBC Statistics Department

To join this seminar virtually: Please request Zoom connection details from ea@stat.ubc.ca

Abstract: Earth System Models (ESMs) are state-of-the-art mathematical formulations used to describe the Earth’s climate system. Supported by supercomputing resources, ESMs can generate large-ensemble, high-resolution global climate simulations, which supplement real-world observations and enhance our understanding of climate changes and their associated variabilities. However, the substantial computational and storage demands of these simulations often limit their broader utility. We propose an efficient statistical emulator—referred to as a stochastic generator (SG)—to address these challenges. By applying the spherical harmonic transformation (SHT), the SG converts climate simulations into a lower-dimensional spectral domain, significantly reducing computational and storage requirements. As a practical complement to ESMs, the SG can rapidly generate multiple emulations of climate simulations. We demonstrate this approach by developing an SG for surface temperature simulations from the newly published CESM2-LENS2 data. To capture non-stationary spatial dependencies, our model incorporates axial symmetry and applies distinct ranks for land and ocean regions. To handle non-Gaussianity in high-temporal-resolution data, we use a modified Tukey g-and-h transformation. The SG successfully emulates CESM2-LENS2 surface temperature simulations across multiple scales, marking the first attempt at reproducing daily data. With the support of supercomputers, we further validate the SG's scalability by emulating ultra-high-resolution climate simulations—an achievement that contributed to winning the prestigious 2024 Gordon Bell Prize for Climate Modelling. Finally, we extend the SG's capabilities to near real-time regional climate simulations by leveraging Slepian concentration on the sphere and an online updating technique. These developments offer a promising complementary pathway for efficient climate modeling and analysis, overcoming critical computational and storage barriers.

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Please note that this seminar will now be held virtually only, and will not take place in person.

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Abstract: Knowledge transfer, a core human ability, has inspired numerous data integration methods in machine learning and statistics. However, data integration faces significant challenges: (1) unknown similarity between data sources; (2) data contamination; (3) high-dimensionality; and (4) privacy constraints. This talk addresses these challenges in three parts across different contexts, presenting both innovative statistical methodologies and theoretical insights.

In Part I, I will introduce a transfer learning framework for high-dimensional generalized linear models that combines a pre-trained Lasso with a fine-tuning step. We provide theoretical guarantees for both estimation and inference, and apply the methods to predict county-level outcomes of the 2020 U.S. presidential election, uncovering valuable insights.

In Part II, I will explore an unsupervised learning setting where task-specific data is generated from a mixture model with heterogeneous mixture proportions. This complements the supervised learning setting discussed in Part I, addressing scenarios where labeled data is unavailable. We propose a federated gradient EM algorithm that is communication-efficient and privacy-preserving, providing estimation error bounds for the mixture model parameters.

In Part III, I will introduce a representation-based multi-task learning framework that generalizes the distance-based similarity notion discussed in Parts I and II. This framework is closely related to modern applications of fine-tuning in image classification and natural language processing. I will discuss how this study enhances our understanding of the effectiveness of fine-tuning and the influence of data contamination on representation multi-task learning.

Finally, I will summarize the talk and briefly introduce my broader research interests. The three main sections of this talk are based on a series of papers [TF23, TWXF22, TWF24, TGF23] and a short course I co-taught at NESS 2024 [STL24]. More about me and my research can be found at https://yet123.com.  

[TF23] Tian, Y., & Feng, Y. (2023). Transfer Learning under High-dimensional Generalized Linear Models. Journal of the American Statistical Association, 118(544), 2684-2697. [Link]

[TWXF22] Tian, Y., Weng, H., Xia, L., & Feng, Y. (2022). Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models. arXiv preprint arXiv:2209.15224. [Link]

[TWF24] Tian, Y., Weng, H., & Feng, Y. (2024). Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithms. ICML 2024. [Link]

[TGF23] Tian, Y., Gu, Y., & Feng, Y. (2023). Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness. arXiv preprint arXiv:2303.17765. [Link]

[STL24] A (Selective) Introduction to the Statistics Foundations of Transfer Learning. (2024). [Link]