It is difficult to anticipate the myriad challenges that a predictive model will encounter once deployed. Common practice entails a reactive, cyclical approach: model deployment, data mining, and retraining. We instead develop a proactive longtail discovery process by imagining additional data during training. In particular, we develop general model-based longtail signals, including a differentiable, single forward pass formulation of epistemic uncertainty that does not impact model parameters or predictive performance but can flag rare or hard inputs. We leverage these signals as guidance to generate additional training data from a latent diffusion model in a process we call Longtail Guidance (LTG). Crucially, we can perform LTG without retraining the diffusion model or the predictive model, and we do not need to expose the predictive model to intermediate diffusion states. Data generated by LTG exhibit semantically meaningful variation, yield significant generalization improvements on numerous image classification benchmarks, and can be analyzed by a VLM to proactively discover, textually explain, and address conceptual gaps in a deployed predictive model.

Bio

David Hayden leads Perception AI Research at Cruise, where he focuses on generative and world models, foundation model alignment and guidance, longtail robustness, uncertainty quantification, and synthetic data. He has consulted on machine learning and computer vision for diverse industries including pharmaceuticals, retail, and competitive sports. His work has shipped to hundreds of driverless cars, ran live in stadiums of 40,000 people, supported seed and Series A rounds, and is published in top conferences and journals including ICML, CVPR, Neurips, and Nature. He previously founded Essistive Technologies, where he developed and licensed discreet note-taking tech for individuals with limited vision. David received a PhD at MIT working on interpretable machine learning and computer vision, with emphasis on behavior analysis, multi-object tracking, Bayesian nonparametrics for time-series, distributions on manifolds, and uncertainty to guide decision making. 

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Variational inference with stochastic gradients, commonly called black-box variational inference (BBVI) or stochastic gradient variational inference, is the workhorse of probabilistic inference in the large data, large model regime. For a decade, however, the computational properties of VI have largely been unknown. For instance, under what conditions is BBVI guaranteed to converge, and is it provably efficient? In this talk, I will present recent theoretical results on VI in the form of quantitative non-asymptotic convergence guarantees for obtaining a variational posterior. Following this, I will demonstrate the usefulness of the theoretical framework by investigating the theoretical properties of various design choices and algorithmic modifications, such as parametrizations of variational approximation, variance-reduced gradient estimators such as sticking-the-landing, structured variational families, and beyond.

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

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

Abstract: The first passage time (FPT) is a useful tool in stochastic modeling of many biological, physical, social and economic processes evolving with time. It refers to the time when a random process first passes a threshold, e.g., when the population of an endangered species reaches a certain critical level, or when the number of infected individuals with a disease reaches a limit. Other examples include the survival time of a cancer patient, failure time of a mechanical system, and default time of a business, etc.

We study the boundary crossing problem for jump-diffusion processes over a discontinuous boundary and provide a complete characterization on the FPT distributions. We derive new formulas for piecewise linear boundary crossing probabilities and density of Brownian motion with general random jumps. These formulas can be used to approximate the boundary crossing distributions for general nonlinear boundaries. The method can be extended to more general diffusion processes such as geometric Brownian motion and Ornstein-Uhlenbeck processes with jumps. The numerical computation can be done by Monte Carlo integration which is straightforward and easy to implement. Some numerical examples are presented for illustration.

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Presentation 1

Time: 11:00am – 11:30am

Speaker: Xihan (Henry) Qian, UBC Statistics MSc student

Title:  Modeling Diatom Dynamics and Environmental Drivers Using Functional Regression and Rank-Based Model Selection

Abstract: In this project, we analyze the relationship between diatom concentrations and environmental drivers in the Salish Sea using functional data analysis (FDA). Daily measurements of solar radiation, wind speed, air temperature, and diatom levels from 2007 to 2024 are treated as smooth functions over time. To capture the delayed effects of environmental variables on diatom dynamics, we apply a historical functional linear model and estimate a time-varying coefficient surface using finite element basis functions defined over a triangular domain. Smoothness is enforced using directional roughness penalties. Two model selection strategies are compared: one based on the Bayesian Information Criterion (BIC), and another prioritizing predictive performance using mean squared error and rank correlation. We show how the choice of tuning parameters affects predictive accuracy and highlight patterns in the estimated effects of environmental variables on diatom levels.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Joey Hotz, UBC Statistics MSc student

Title: The Rocky Road Toward Effective Vanilla Bayesian Optimization in High-Dimensional Search Spaces

Abstract: Bayesian optimization (BayesOpt) is a well-established statistical methodology for efficiently finding the true optimum value of a black-box function. A common concern with Bayesian optimization is the "Curse of Dimensionality", as these methods often struggle for input spaces with many parameters unless the algorithm is adjusted accordingly. Despite the prevalence of these challenges, a recently published paper empirically demonstrated that under certain specifications for the surrogate model, the sole adjustment required to make Bayesian optimization effective for higher-dimensional problems is to simply scale the prior distribution for the model based on the dimensionality of the search space. In this presentation, we discuss the background, methodology, and findings of the aforementioned paper. Additionally, we significantly broaden the scope of their simulation study to a wider class of statistical models to evaluate the robustness of their stated result.

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Abstract: Statistics education stands at a critical juncture as we navigate the intersection of traditional statistical theory, modern computational approaches, and emerging AI technologies. This talk examines how statisticians can reimagine curricula by embracing computation as foundational elements rather than afterthoughts. While traditional statistics education has prioritized theoretical frameworks and applications, computation has emerged as the backbone of contemporary data analysis—from data acquisition and wrangling to visualization, modeling, and communication. Now, AI tools are further transforming this landscape, creating both opportunities and challenges for statistics and data science educators. The presentation will outline a forward-looking curriculum model for introductory courses that balances statistical thinking, data science methods, and explicit computational instruction

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Presentation 1

Time: 11:00am – 11:30am

Speaker: Sarah Masri, UBC Statistics MSc student

Title: Compartmental models and Hawkes processes: equivalence and computational advantages in epidemiological modelling

Abstract: Epidemiological modelling is crucial for understanding and responding to the spread of infectious diseases, helping public health officials assess the impact of interventions and inform policy decisions. Some prominent models within this field, such as the SIR and SEIR compartmental models, rely on unobserved measurements and can be computationally intensive. This thesis investigates the equivalence between the stochastic SIR and SEIR compartmental models and the Hawkes process, a self-exciting point process, in the epidemiological setting. The research demonstrates that, under specified conditions, the SIR and SEIR models can be interpreted as special cases of the finite population Hawkes process, offering a unified framework for disease modelling that does not rely on latent measurements. This thesis contributes to the growing body of literature on stochastic epidemic models by providing an alternative approach to complement compartmental models, highlighting how inference under the Hawkes process, when fitting the process to data, is consistent with the parameters associated with the SIR and SEIR models. The findings suggest that the Hawkes process can approximate some compartmental models, offering a promising tool for epidemiological modelling.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Christine Chuong, UBC Statistics MSc student

Title: Forecasting Influenza, COVID-19 and Respiratory Syncytial Virus Detections in Canada

Abstract: Respiratory illnesses such as influenza, respiratory syncytial virus, and COVID-19 result in many hospitalizations and deaths per year in Canada. Anticipating the behaviour of viruses can be challenging as behaviour can differ between seasons, so accurate forecasts of future behaviour can help reduce uncertainty. Modelling hubs can be a useful tool in collecting and evaluating multiple forecasts in one place. Hubs run forecasting challenges that invite teams to make weekly probabilistic short-term forecasts for illnesses of interest, but no national challenge predicting respiratory viruses exists in Canada. Using data on respiratory virus detections taken from historic reports and an interactive dashboard maintained by the Public Health Agency of Canada, we established a forecasting hub for the 2024-2025 respiratory illness season. We submitted forecasts for a climatological model using historical data and an ensemble of this climatological model and an autoregressive with exogenous covariate (ARX) model with the predicted climatological medians. Forecasts were evaluated using the absolute error of the predicted median, weighted interval score (WIS) and empirical coverage of prediction intervals.

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Abstract: In complex systems such as financial networks, the failure of a single entity can trigger cascading effects that threaten the stability of the entire system, and this is known as the systemic risk. A common measure for quantifying systemic risk is CoVaR, the Value-at-Risk of the system conditional on the distress of a single component.

In this talk, I will present a new approach to CoVaR based on tail expansions of copulas. Tail expansions of copulas provide a systematic way to characterize the joint tail behavior of multiple dependent random variables. This characterization naturally integrates and extends classical extreme value theory, offering a more flexible and interpretable representation of extremal dependence.

I will highlight the theoretical value of tail expansions in understanding the asymptotic behavior of CoVaR and demonstrate their practical use in developing new extreme value estimation methods. The talk also includes an empirical study that illustrates how the proposed approach can be used to assess the systemic risk in the U.S. financial industry.

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Abstract: We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework. At every time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and latent positions but allow for different connectivity matrices. We propose efficient tensor algorithms under both fixed and random latent position cases to minimize the detection delay while controlling false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimation that is applicable to a wide range of scenarios, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online.

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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.

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

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.