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

Presentation 1

Time: 11:00am – 11:30am

Speaker: William Laplante, UBC Statistics MSc student

Title: Improving Uncertainty Quantification of Epidemiological Models with Probabilistic Numerics

Abstract: Recent work in Probabilistic Numerics (PN) – a subfield of machine learning that aims to quantify uncertainty arising from intractable numerical computation – has developed a new class of numerical algorithms to solve ordinary differential equations (ODEs) with a latent force. These solvers pose the problem of numerically computing the solution of ODEs as one of statistical inference: each step of numerical integration is a task of prediction with uncertainty. By formulating a state-space model (SSM) with two likelihoods – one to fit the data, and one to ensure state alignment – and by using Kalman filters and smoothers to estimate the states of the SSM, the estimates (with uncertainty) of an ODE's solution and its latent force are obtained in a single, linear complexity pass. In this work, we demonstrate the practicality of these PN methods in epidemiology by fitting data from the COVID-19 pandemic with a compartmental model – a type of epidemiological model that divides a population in compartments and is expressed as ODEs. To facilitate the fitting process, we propose a "fix-all-vary-one" approach to calibrate the model's hyperparameters, and implement the EM algorithm to estimate the likelihood's covariance. From estimates of the compartmental model's states, we retrieve (1) the model's time-varying contact rate (the latent force), (2) an estimate of the time-varying instantaneous reproductive number, and (3) a prediction for daily and cumulative case counts. Overall, we show that the key feature of PN methods, "uncertainty-awareness", can greatly benefit quantitative epidemiologists that make extensive use of differential equations to describe epidemics.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Elvis (Zhenglun) Cai, UBC Statistics MSc student

Title: Modeling and Estimating the Effective Reproduction Number

Abstract: The effective Reproduction Number (Rt) of an infectious disease is a latent variable that measures the total number of secondary infections generated by an individual on average. It informs policymakers on the virulence of infectious diseases so that they can decide on the type of non-medical intervention that should be implemented. In this project, we model Rt with penalized Poisson regression using the Renewal Equation and provide a framework that can handle various smoothness assumptions of Rt. The penalty terms that are determined by smoothness assumptions yield a convex, separable, but non-differentiable objective function that is solved with the linearized Alternating Direction Method of Multiplier (ADMM). The corresponding algorithm is implemented in our R package, “RtEstim”, with cross validation. We compare the RMSE/RMAE of the estimated Rt and its corresponding case counts between “RtEstim” and “EpiEstim” – one of the most widely used Rt estimation packages in R – using various synthetic datasets. We find that “RtEstim” has a smaller prediction error than “EpiEstim” on most synthetic datasets.

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Title: Statistical Imaging of Black Holes using the Event Horizon Telescope

Abstract: In 2019 and 2021, the Event Horizon Telescope produced the first-ever images of the black holes M87* and Sgr A*, respectively. However, the Event Horizon Telescope is not a regular camera. It does not directly measure the on-sky image, and the high computational cost is converting the estimated sparse data to an actual image. As a result, imaging requires high-performance computing and statistical modeling. In this presentation, I will present the different statistical techniques used by the EHT to analyze the data. The focus will be on recent advances in applying computational Bayesian inference to the imaging problem. I will introduce the statistical model we use, which requires modeling the instrument and the image using non-linear and often weakly non-identifiable models. To sample from this posterior required using novel statistical inference techniques, such as the recently developed non-reversible optimal parallel tempering algorithm developed at UBC. These results demonstrate the potential collaboration between computational statistics and radio imaging and how it can benefit both communities. This collaboration will become more critical shortly with the advent of more powerful telescopes, such as the next-generation Event Horizon telescope, that will increase the data volume and model complexity by 2-3 orders of magnitude.

Abstract: Consider a large random structure – a random graph, a stochastic process on the line, a random field on the grid – and a function that depends only on a small part of the structure. Now use a family of transformations to ‘move’ the domain of the function over the structure, collect each function value, and average. Under suitable conditions, the law of large numbers generalizes to such averages; that is one of the deep insights of modern ergodic theory. My own recent work with Morgane Austern (Harvard) shows that central limit theorems and other higher-order properties also hold. Loosely speaking, if the i.i.d. assumption of classical statistics is substituted by suitable properties formulated in terms of groups, the fundamental theorems of inference still hold.

Registration & talk details

Date: Thursday, April 20, 2023

Time: 5:00 PM - 9:00 PM (Pacific Time)

Schedule:

5:00 - 5:45 PM : Meet-The-Speaker *

5:45 - 6:00 PM : Break

6:00 - 6:05 PM : Seminar begins / Announcements

6:05 - 6:25 PM : Presentation by Trainee Speaker

6:25 - 7:20 PM : Presentation by Featured Speaker

7:20 - 9:00 PM : Seminar ends / Networking + light refreshments

* Pending on the number of RSVPs

Please fill out RSVP form if you are interested in attending this seminar in-person (or the meet-the-speaker session before the seminar at 5PM).

Talk Title: Learning deep biology with shallow statistical models

Abstract: As deep learning approaches gained much popularity, typical statistical learning methods were replaced by deep generative models and black-box classification algorithms in many types of biological data analysis, including genetic variant calling, regulatory genomics, high-dimensional data embedding, missing value imputations, and risk predictions. Despite being readily accessible with general-purpose libraries, so-called deep methods demand long hours of training, specialized hardware resources, and a large amount of data; yet, we are often startled at seeing only marginally improved classification performance, model overfitting, or lack of generalizability. Not undermining important advancements made possible by deep models, this talk will seek to showcase that we can deepen our understanding of biological systems with shallow statistical models.

First, I will discuss our scalable algorithm for probabilistic topic modelling in single-cell genomics data. Based on probabilistic topic assignments in each cell, we identify the latent representation of cellular states and heterogeneity, and the latent topic vectors often yield much-improved clustering results than other types of dimensionality reduction methods. We were initially inspired by several empirical observations: (1) Data sets compressed by repeatedly applying random projection operations highlight cell type-specific signature genes. (2) We also noted that rare cell types are better characterized with lowly-expressed genes (in total data) that are typically removed in quality control steps, thus, not included in embedding model estimations. (3) Bulk sequencing data sets are generally less prone to zero inflation or measurement errors. Based on these key findings, we designed a statistical framework termed ASAP--short for Annotating Single-cell data matrix by Approximate Pseudo-bulk projection) to identify cell topics. ASAP seeks to reduce sample size by interactively collapsing cell-level expression vectors into pseudo-bulk vectors in order to accurately perform non-negative matrix factorization to learn topic-specific gene frequency patterns.

Another example will be a sparse regression model with a causal inference flavour that can effectively handle putative confounding issues in a genetic fine-mapping problem. Our idea is rooted in Rubin's causal inference framework (Rubin and Rosenbaum, 1983), with which non-genetic and indirect genetic effects can be cancelled out in implicit adjustment steps. In order to handle the non-binary nature of exposure variables (genetic dosage), our method first matches individuals with one another based on a covariate similarity matrix. If paired individuals share non-genetic factors, then any gene expression changes between them will be removed so that genetic dosage will become a causal factor in the expression divergence. We implemented the algorithm in the SuSiE framework (Wang et al. 2020).

Overall, this talk will reassure us that it is okay to work on a shallow model. In fact, if our scientific goal is straightforward enough to be coded in a simple model armed with intuitive algorithms, such a modelling approach can help uncover deeper layers of biological mechanisms underneath high-dimensional genomics data.

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

Presentation 1

Time: 11:00am – 11:30am

Speaker: Yuwei Yang, UBC Statistics MSc student

Title: Statistical Consulting and Process

Abstract: Improvement in Surgical Research Projects The use of statistical analysis and data-driven approaches in healthcare is crucial for improving patient outcomes and optimizing resource allocation. During my co-op at UBC Province Wide Division of General Surgery at Vancouver General Hospital, I contributed to over 15 surgical research projects around the province, focusing on study design, data analysis, and statistical consulting. My work involved managing missing data, validating data integrity, collaborating on grant applications and abstracts, conduct statistical analysis, and supporting quality improvement initiatives through metrics monitoring and assessment. Through this co-op experience, I have gained valuable insights into the application of statistical methods in healthcare and the importance of data-driven decision-making in surgical research and quality improvement.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Marc Wettengel, UBC Statistics MSc student

Title: Analysis of the associations between environmental conditions and norovirus outbreaks in shellfish harvest zones on Vancouver Island

Abstract: Norovirus is a common cause of gastroenteritis with infection characterized by diarrhea, vomiting, and stomach pain. Bivalve molluscan shellfish (oysters, muscles, scallops, etc.) are common sources of community norovirus outbreaks in the Lower Mainland. This project uses longitudinal and time series methods to analyze the relationship between environmental conditions and norovirus outbreaks in shellfish harvesting zones on Vancouver Island. Weekly measurements on rainfall, ocean salinity, sea surface temperature and other environmental conditions were compiled from 2003 through 2019. Community norovirus case counts were also included as norovirus is not naturally present environment. This covariate is used as a proxy to determine if norovirus could potentially be present in the inter tidal zones which shellfish harvesting occurs. These covariates were compared to outbreak periods in shellfish harvesting zones during the same time period. Generalized linear mixed effect models, generalized estimating equations, and distributed lag non-linear models were fitted and compared with each other to determine the associations between environmental conditions and norovirus outbreaks in shellfish.

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

Presentation 1

Time: 11:00am – 11:30am

Speaker: Jiayang Yin, UBC Statistics MSc student

Title: On the Improvement of Density Ratio Estimation – Theoretical Study and Its Applications

Abstract: Density ratio estimation is an effective tool in the world of machine learning and data science, especially in transfer learning and contrastive learning. By contrastive learning, it is also linked to intractable likelihood and un-normalized model inference. Our work mainly focuses on a type of density ratio estimation based on a probabilistic classification from the perspective of statistical inference. We study how such a density ratio estimation relates to a probabilistic classifier such as Logistic regression. We analyze the potential cause for its inefficiency and inaccuracy when the two distributions are much different from each other. Opposite to the target of a probabilistic classification, a density ratio estimation task with a more efficient estimator indicates the corresponding classification task is harder, which means it is more difficult to separate the two samples by a probabilistic classifier. We provide a theoretical explanation for this phenomenon from a mathematical and statistical standpoint. For the basic density ratio estimation by a probabilistic classification, we give a necessary and sufficient condition for its existence under a sample level. We analyze the probability with such conditions held asymptotically. Besides, we explore the asymptotic properties of a recent proposed approach to improving density ratio estimation by a probabilistic classification – Telescoping Density Ratio Estimation TDRE by Rhodes, et al. Numerically, we compare the asymptotic variance of basic density ratio estimation and TDRE. We also explore some generalization on TDRE with unbalanced data and under some model misspecification by both theoretical discussion and empirical analysis. Based on our work, some suggestions for future work on un-normalized model inference are also provided.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Jintong Yan, UBC Statistics MSc student

Title: Biostatistical Analysis of Biomarker Discovery in Two Chronic Diseases

Abstract: Exploring biomarkers, such as DNA sequencing, RNA sequencing, and protein data, that may be correlated with a specific disease can help guide its treatment and diagnosis. During my co-op at PROOF Centre, I worked on multiple projects with a focus on two: using Somalogic protein profiling to explore early diagnosis of acute rheumatic fever from plasma, and developing biomarkers to guide immunosuppression strategies during cytomegalovirus (CMV) infection in heart transplant patients. The main objective of this presentation is to demonstrate how statistics can be used in these two projects to help identify biomarkers that can be used for diagnosing or treating diseases.

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

Title: AI-Driven Experimental Design for Accelerating Science and Engineering

Abstract: AI-driven experimental design methods have the potential to accelerate costly discovery and optimization tasks throughout science and engineering—from materials design and drug discovery to computer systems tuning and instrument control. These methods are promising as they provide the intelligent decision making needed for use in complex real-world problems where experiments are time-consuming or expensive, and efficiency is paramount. In the first part of my talk, I will discuss challenges that I encountered while applying these methods to new types of scientific optimization problems being pursued at national labs. I will then introduce an information-based framework for flexible experimental design, which overcomes these challenges by enabling easy customization to new problem settings. This framework is theoretically principled, and has been used by scientists for efficient materials synthesis and optimization in large scientific instruments. Along the way, I will discuss my vision for reliable systems that expand the scope of AI-driven experimental design and make it easier to use, so that it can be put in the hands of scientists, engineers, and other practitioners everywhere.

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

Title: Optimal methods for reinforcement learning: Efficient algorithms with instance-dependent guarantees

Abstract: Reinforcement learning (RL) is a pillar for modern artificial intelligence and data-driven decision making. Compared to classical statistical learning, several new statistical phenomena arise from RL problems, leading to different trade-offs in the choice of the estimators, tuning of their parameters, and the design of computational algorithms. In many settings, asymptotic and/or worst-case theory fails to provide the relevant guidance.

In this talk, I present recent advances in optimal algorithms for reinforcement learning. The bulk of this talk focuses on function approximation methods for policy evaluation. I establish a novel class of optimal and instance-dependent oracle inequalities for projected Bellman equations, as well as efficient computational algorithms achieving them under different settings. Among other results, I will highlight how the instance-dependent guarantees guide the selection of tuning parameters in temporal different methods. Drawing on this perspective, I will also discuss a novel class of stochastic approximation methods, yielding optimal statistical guarantees for solving the Bellman optimality equation. At the end of this talk, I will discuss additional works on optimal and instance-dependent guarantees for functional estimation with off-policy data.

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Abstract: Inferring the causal relationship between a treatment and a response is complicated in non-randomized studies owing to the effects of potentially confounding variables. Extensive work has been conducted to account for the effects of such variables in statistical analyses. However, previous works have demonstrated that misspecifying the set of potential confounders can have significant consequences for causal effect estimation. Bayesian Adjustment for Confounders (BAC) is a Bayesian approach to variable selection, whereby a mixture of posteriors is used to combine the causal effect estimates from each model corresponding to a combination of the potential confounders. Our work uses Monte Carlo simulation techniques in order to estimate the inflation in the average mean squared error due to prior misspecification in the BAC methodology over repeated experiments in a saturated probability model case study. Our findings shed light on future areas for research, and provide users of the BAC methodology with advice on selecting an appropriate prior model for their studies.

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Title: Statistically efficient offline reinforcement learning

Abstract: Despite the empirical success of reinforcement learning (RL) in gaming, such as for AlphaGo and OpenAI Five, we have not seen this level of successful application of RL in many scientific domains. This is because running experiments involving human interaction is often costly and risky. Thus, statistically efficient offline RL (i.e., sequential decision-making in a sample-efficient manner using offline data) is key to solving this limitation. In this talk, I will showcase my research on statistically efficient offline RL. Mostly, I will explain our unified “double minimax RL framework” for offline policy evaluation, which satisfies several desiderata such as (1) it can integrate any rich function approximation such as deep neural networks, (2) it is statistically efficient (i.e., attaining the semiparametric efficiency bound). For the remainder of the time, I will discuss model-based offline RL with general function approximation. I present a new algorithm named constrained pessimistic policy optimization (CPPO) to address the most challenging problem in offline RL known as “distributional shift,” which occurs when the offline data coverage is not sufficient. Our CPPO algorithm is able to learn high-quality policies even if the coverage of offline data is not sufficient.