ÉîÒ¹¸£ÀûÕ¾

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248

Title: Statistical Learning Methods for Challenges Arising from Self-Reported Data, with Applications to Chronic Pain Studies

Abstract: 

This thesis focuses on developing advanced clustering methods and analyzing data arised from chronic pain (CP) studies, with a particular emphasis on the unique challenges posed by self-reported (SR) data. Latent class analysis (LCA) is explored in the early stages of this work to cluster patients, and the clusters are compared to find features that are significantly different among clusters. While LCA is effective for categorical variables, it fails to address the mixed data types and subjective biases inherent in SR data. To overcome these limitations, we propose a novel distance metric tailored specifically for SR questionnaire data. This distance incorporates the correlation distance with other elementary distances for clustering data of mixed type, which outperforms existing metrics in handling mixed data when SR variables are present. Additionally, interpretable clustering techniques are utilized to generate simple, actionable rules that can be applied in clinical practice.

To integrate the domain knowledge of CP experts into the clustering process, a semi-supervised clustering algorithm is introduced, allowing the distance metric to be adjusted using pairwise constraints provided by CP experts. We develop a two-step active learning query strategy to identify and query the most informative patient cases, enhancing query efficiency and minimizing the number of interactions required between experts and the algorithm.

In addition to clustering, we analyze data arised from CP studies and explore predictive modeling. Canonical correlation analysis (CCA) is applied to investigate relationships among CP measurements, revealing important connections between pain characteristics and psychological factors. Furthermore, multiple classification models are used to predict nociplastic pain, and the best cut of each predictor is investigated using the prediction model.

Overall, we made significant contributions to the field of CP studies by introducing novel methods for clustering CP patients and analyzing complex data relationships. The proposed approaches emphasize clinical applicability, interpretability, and the integration of domain knowledge, offering practical solutions for real-world challenges in CP management. These advancements provide a foundation for further exploration of personalized treatment strategies and an improved understanding of chronic pain mechanisms.

Time: April 8th, 2025, 2:30 PM - 3:30 PM
Location: ÉîÒ¹¸£ÀûÕ¾ Interdisciplinary Research Building 1170
Speaker: Prof. Patrick Brown - Department of Statistical Sciences, The University of Toronto

Dr. Patrick Brown's research focuses on models and inference methodologies for spatio-temporal data, motivated by problems in spatial epidemiology and the environmental sciences. Current statistical methods research involves Bayesian inference for non-Gaussian spatial data, and non-parameteric methods for spatially aggregated and censored locations.

Title: Daily air pollution and mortality: putting it all together

Supervisors: Dr. Shu Li
Time: April 3rd, 2025, 9:30 AM - 10:10 AM
Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 187

Title: The structure of the number of claims until first passage times

Abstract: This thesis focuses on the first-passage problem in insurance risk models, and mainly we extend the traditional ruin theory and two-sided exit problem by examining the corresponding discrete features and their applications. We study the structural characteristics of three critical discrete random variables of interest in the risk process. For instance, under the compound Poisson risk model, we prove that the distribution of the number of claims until first up-crossing time is of a compound Poisson structure, where the primary parameter and secondary distribution are identified explicitly. We illustrate the computational advantage of the identified structures using numerical examples. We subsequently conduct a parallel analysis in a discrete-time model. Our study shows how such a discrete setting offers valuable insights while preserving theoretical connections to the continuous-time framework, particularly regarding the distributional structures of the number of claims. The discrete-time model provides not only theoretical elegance but also computational advantages for practical implementation. By generalizing to a discrete-time Sparre Anderson risk model, we further enhance the applicability of our results. Based on these foundational structures, our research moves towards the practical applications by introducing a novel two-sided risk measure. By expanding beyond traditional ruin-based risk measures, our methodology provides a deeper understanding on risk assessment and risk management.

The talks are given in the alphabetic order of the speakers' last names.

Location: (Waiting room activated. No passcode. After the public lecture, except the examination committee, all other participants are asked to leave the room so that the examination can start)

Title: Statistical Learning Methods for Challenges Arised from Self-Reported Data, with Applications to Chronic Pain Studies

Abstract: This thesis focuses on developing advanced clustering methods and analyzing data arised from chronic pain (CP) studies, with a particular emphasis on the unique challenges posed by self-reported (SR) data. Latent class analysis (LCA) is explored in the early stages of this work to cluster patients, and the clusters are compared to find features that are significantly different among clusters. While LCA is effective for categorical variables, it fails to address the mixed data types and subjective biases inherent in SR data. To overcome these limitations, we propose a novel distance metric tailored specifically for SR questionnaire data. This distance incorporates the correlation distance with other elementary distances for clustering data of mixed type, which outperforms existing metrics in handling mixed data when SR variables are present. Additionally, interpretable clustering techniques are utilized to generate simple, actionable rules that can be applied in clinical practice. To integrate the domain knowledge of CP experts into the clustering process, a semi-supervised clustering algorithm is introduced, allowing the distance metric to be adjusted using pairwise constraints provided by CP experts. We develop a two-step active learning query strategy to identify and query the most informative patient cases, enhancing query efficiency and minimizing the number of interactions required between experts and the algorithm.In addition to clustering, we analyze data arised from CP studies and explore predictive modeling. Canonical correlation analysis (CCA) is applied to investigate relationships among CP measurements, revealing important connections between pain characteristics and psychological factors. Furthermore, multiple classification models are used to predict nociplastic pain, and the best cut of each predictor is investigated using the prediction model. Overall, we made significant contributions to the field of CP studies by introducing novel methods for clustering CP patients and analyzing complex data relationships. The proposed approaches emphasize clinical applicability, interpretability, and the integration of domain knowledge, offering practical solutions for real-world challenges in CP management. These advancements provide a foundation for further exploration of personalized treatment strategies and an improved understanding of chronic pain mechanisms.

Time: March 7th, 2025, 11:00 AM - 12:00 PM
Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248
Speaker: Dr. Florian Bourgey - Bloomberg

Dr. Florian Bourgey is a researcher in the Quantitative Research team in the Office of the CTO at Bloomberg in New York. His research focuses on Monte Carlo simulations, stochastic approximations, climate risk, volatility modeling, and machine learning. He holds a Ph.D. in applied mathematics from Ecole Polytechnique, France.

Title: Smile Dynamics and Rough Volatility

Time: March 4th, 2025, 1:30 PM - 2:30 PM
Location: ÉîÒ¹¸£ÀûÕ¾ Interdisciplinary Research Building 1170
Speaker: Prof. Silvana Pesenti - Department of Statistical Sciences, The University of Toronto

Dr. Silvana Pesenti is an Assistant Professor in Insurance Risk Management at the Department of Statistical Sciences at the University of Toronto. She was named the 2022 Rising Star in Quant Finance by Risk.net. She received the 2020 Peter Clark Best Paper Prize from the Institute and Faculty of Actuaries (IFoA). In 2019, she was awarded the  Dorothy Shoichet Women Faculty Science Award of Excellence. She is an Associate Editor of Computational and Applied Mathematics (since 2022) an Associate Editor of Annals of Actuarial Science (since 2023), and on the Editorial Board of Applied Mathematical Finance (since 2023) and of ASTIN Bulletin (since 2023).

Title: Risk budgeting allocation for dynamic risk measures

Time: February 7th, 2025, 11:00 AM - 12:00 PM
Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248
Speaker: Dr. Junhe Chen, Associate Director, Risk Modelling at RBC

Dr. Junhe Chen completed the PhD in Financial Modeling at ÉîÒ¹¸£ÀûÕ¾ Universtiy in 2021. His research areas are differential games in energy finance and portfolio optimization. After his graduation, he worked at CIBC, BMO as two contractors, and is mainly working on counterparty credit risks (CCR) and fundamental review of the trading books (FRTB) — default risk capital (DRC) at RBC. 

Title: CCR Simulation and Exposure Generation

Location: (Waiting room activated. No passcode. After the public lecture, except the examination committee, all other participants are asked to leave the room so that the examination can start)

Title: Artificial Intelligence in Banking and Insurance: Optimizing Credit Limit Adjustments with Reinforcement Learning, Multi-Treatment Selection via Causal Inference, and Negotiation Pricing Analysis with a Fairness Approach

Abstract:  In this thesis, I develop a series of methodologies to improve financial management in the lending and insurance industry. I first examine innovative methodologies for addressing whether to increase or maintain a customer’s credit line and by what factor if an increase is granted. These decisions impact both customers and the company’s capital for covering expected losses. To automate an optimal policy for credit limit adjustments, I formulated this as an optimization problem that maximizes expected profit while balancing risk. Using historical data from a Latin American super-app, I trained a reinforcement learning (RL) agent through offline simulations. The results indicate that a Double Q-learning agent with optimized hyperparameters can outperform other strategies and establish a robust decision-making framework based on data-driven methods. I also explore alternative data for balance prediction, finding that such data does not always improve accuracy.

My second work, using now a diverse dataset, I framed the credit limit increase decision as a treatment selection problem, where treatments represent the increase factor and controls maintain the current limit. I included causal effect estimation to compare potential outcomes under different treatments, addressing the inadequacy of relying solely on individual treatment effects. By incorporating uncertainty measured by conditional value-at-risk and prioritizing treatments that lead to favorable post-treatment outcomes, I propose a comprehensive methodology for multitreatment selection. This approach ensures the overlap assumption is satisfied by training propensity score models before employing traditional causal models, significantly enhancing policy performance.

In the last part of the thesis, I aim to explore disparities in healthcare service pricing in light of recent regulations aimed at increasing transparency. The Transparency in Coverage (TiC) Rule and the Hospital Price Transparency Rule require health insurers and hospitals to disclose in-network negotiated rates and out-of-network allowed amounts, creating an opportunity to investigate whether these prices vary across demographic factors such as income, location, and education. By integrating healthcare pricing data, the General Social Survey (GSS), and social network analysis, I propose to determine whether significant differences exist in the cost of medical services across different regions and income levels.

In summary, this thesis delves into how modern AI and ML enhance financial service management, specifically by making tasks like credit limit adjustment more data-driven. It develops a multi-treatment selection methodology applicable to this problem. directly applicable to credit limit modifications. Finally, through multimodal analysis, it examines the nature of current healthcare negotiation pricing in the U.S.

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 256

Title: Predicting Rare Events from Large Spatiotemporal Data: Application to Wildland Fires and Species Occupancy

Abstract: 

Subsampling of large data is commonly employed in statistical modelling with the goal of efficiency. When the event being modelled is rare, the data is imbalanced and thus sampling methods focus on preferentially subsampling the observations which represent those rare event occurrences. This thesis extends methodology for the subsampling of large data when modelling rare events, motivated by applications in environmetrics and ecology.

The first two projects present extensions to response-based sampling. The response-based sampling approach takes independent samples of event occurrence and non-occurrence, often sampling all occurrences and a small proportion of the non-occurrences. I propose a stratified sampling approach, which defines strata based on a key variable. Independent samples of occurrences and non-occurrences are then sampled from each stratum. The bias induced by this sampling must be accounted for in the logistic regression model. The first project employs sampling weights in the logistic to account for the bias induced by this sampling design. The second project instead uses stratum-specific offsets to the same end, which now allows for the model to include multiple predictors. These approaches are validated using simulation, where they are compared to existing approaches for sampling imbalanced data. I apply these methods to fine-scale human-caused fire occurrence prediction in a region of Ontario, Canada where stratifying on a measure of fire weather and sampling more extreme observations leads to more locally precise estimates of fire occurrence.

The third project presents a novel method for subsampling species detection data to fit occupancy models. When a species is rarely detected, the number of detections will be far outnumbered by the non-detections. I propose a response-based sampling method for species detection data, which allows preferential sampling of the rarer detection observations. I present a method for estimating occupancy and detection probabilities of the subsampled data, as the assumptions of traditional occupancy models no longer hold. I apply this method to detection data of Canada Warbler (Cardellina canadensis) from the Breeding Bird Survey, where we can accurately estimate the occupancy and detection parameters using just 10% of the original dataset, including estimating the effects of a habitat-related covariate.

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 256

Title: Deep Learning Methodologies for Complex Network-Driven Credit Risk Assessment

Abstract: In the past few years, the field of risk management has increasingly turned its attention towards enhancing the efficacy of credit scoring models. This shift has been characterized by a growing emphasis on integrating advanced machine learning methodologies and tapping into non-traditional data sources. Building on this momentum, this study is dedicated to exploring the optimal utilization of network data to bolster the benefits of credit scoring practices. The primary aim of this study is to broaden the existing body of knowledge concerning the development of sophisticated credit scoring models. Specifically, it seeks to investigate the incorporation of network data into these models through the application of machine learning techniques and social network analysis. The first project introduces an innovative model for assessing credit risk in the context of behavioral scoring. This model combines Graph Neural Networks (GNNs) and Recurrent Neural Networks (RNNs) to account for borrower connections and their evolution over time, offering a dynamic perspective on creditworthiness. The second project presents a novel method for estimating credit risk among Small and Medium-sized Enterprises (SMEs) within the framework of application scoring. This multimodal model, leveraging both unstructured multilayer network data and traditional structured data, provides a holistic approach to understanding SME credit risk. Finally, the third project, which is ongoing, unveils a new approach to model explainability in credit risk modeling using Large Language Models (LLMs).

Location: ÉîÒ¹¸£ÀûÕ¾ Interdisciplinary Research Building 1170

Title: Estimating Variants of Concern Without Knowledge of Variants of Concern: Statistical Modelling and Clustering of COVID-19 Wastewater Data

The talks are given in the alphabetic order of the speakers' last names.

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248

Title: Anomaly detection and model construction with the focus on natural language processing in consumer complaint textual analysis

Abstract: Detecting anomalies, which could be good, bad and ugly, plays an important role in business decision-making. The detection relies on the information received, and it comes in numerical and textual forms. Much has been done in quantitative analysis of claim amounts and frequencies, but claim texts and related textual (qualitative) data are also of paramount importance. Sometimes, it is the only available source of information. In this project we concentrate on machine learning (ML) tools to detect anomalies and utilize the acquired information for the betterment of business decision-making. We also discuss the necessary for our research tools, with references to earlier studies and uses on ML in insurance and related fields.

Based on this foundation, we provide detailed analyses of textual data using complaint narratives from the Consumer Complaint Database of the Consumer Financial Protection Bureau (CFPB). A procedure is developed for detecting systematic non-meritorious consumer complaints, simply called systematic anomalies, among complaint narratives. Based on this procedure, we convert complaint narratives into quantitative data, which are then analyzed using indices to detect systematic anomalies. The research further explores involving expert opinions on classification errors to improve the performance of predicting classification errors. Finally, this research examines how diverse evaluation metrics could influence the performance of predicting classification errors.

This seminar is organized by CANSSI Ontario in partnership with the Department of Statistical and Actuarial Sciences at ÉîÒ¹¸£ÀûÕ¾. 

Nathaniel Lewis Phelps, our PhD student, is the moderator. 

The event is online via zoom. Faculty and students can watch the seminar together in ÉîÒ¹¸£ÀûÕ¾ Science Centre 248 on November 18th, 2024, 3:30-4:30 PM.

To join online, please .

Ryan is Founder and CEO at Riskfuel, a capital markets focused AI startup. Previously, Ryan was Managing Director and Head of Securitization, Credit Derivatives and XVA at Scotiabank. Prior roles have included credit correlation trading and managing the equity derivatives trading desk. Ryan began his career with positions in risk management and financial engineering. Ryan has a PhD in Physics from Imperial College, and a BASc and MASc in Electrical Engineering from the University of Waterloo.

Title: Riskfuel: Accelerating valuation and risk sensitivity calculations in the capital markets - Replacing slow numerical solvers with fast neural network inferencing

Location: North Campus Building 240B

Title: The financial consequences of social capital in the boardroom

The study begins by examining trends in gender and ethnic diversity on corporate boards from 2007 to 2021. Using a bootstrapping methodology, the analysis reveals significant improvements in diversity over time but also highlights a disconnect between workforce diversity and boardroom representation. This suggests that industry-specific factors significantly shape board composition, with workforce diversity not directly translating to board diversity.

Building on this, the dissertation investigates the economic implications of diverse boards, particularly their impact on bond issuance costs. The findings indicate that firms with boards reflecting the demographic diversity of their workforce tend to incur lower underwriting fees. However, increasing female or ethnic-minority representation beyond a certain threshold does not significantly affect borrowing costs, emphasizing the complexity of the relationship between board diversity and financial outcomes.

The research further explores the role of professional networks in board appointments, focusing on gender disparities. Using social network analysis combined with deep learning models, the study reveals that women face substantial challenges in achieving board positions, needing to build broader and more influential networks than their male counterparts. The findings underscore the importance of female-to-female networks in promoting gender diversity, suggesting a pathway to overcoming existing barriers.

Finally, the dissertation examines how boardroom networks influence corporate credit ratings. By integrating multi-layer board network data with traditional financial metrics, the research demonstrates that the structure and strength of director networks can significantly impact a firm’s credit rating. This highlights the critical role of social capital in financial decision-making and corporate governance.

Overall, this dissertation provides a comprehensive analysis of how diversity and networking dynamics affect corporate boards and their associated financial outcomes. It offers valuable insights for policymakers, corporate leaders, and stakeholders aiming to enhance board diversity and improve corporate governance practices.

Location: Middlesex College 204

Title: Bayesian methods for clustering change-point data and functional data analysis

Time: October 8th, 2024, 1:30 PM - 2:30 PM
Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248
Speaker: Dr. Sebastian Ferrando - Professor, Department of Mathematics, Toronto Metropolitan University.

Title: Agent-Based Models for Two Stocks with Superhedging

Abstract: An agent-based modelling methodology for the joint price evolution of two stocks is introduced. The method models future multidimensional price trajectories reflecting how a class of agents rebalance their portfolios in an operational way by reacting to how stocks’ charts unfold. Prices are expressed in units of a third stock that acts as numeraire. The methodology is robust, in particular, it does not depend on any prior probability or analytical assumptions and it is based on constructing scenarios/trajectories. A main ingredient is a superhedging interpretation that provides relative superhedging prices between the two modelled stocks. The operational nature of the methodology gives objective conditions for the validity of the model and so implies realistic risk-rewards profiles for the agent’s operations. Superhedging computations are performed with a dynamic programming algorithm deployed on a graph data structure. The superhedging algorithm handles null sets in a rigorous and intuitive way.

Title: Introduction to Counterparty Credit Risk Modelling

Location: (Waiting room activated. No passcode. After the public lecture, except the examination committee, all other participants are asked to leave the room so that the examination can start.)

Title: Variational Bayesian inference for functional data clustering and survival data analysis

Abstract: Variational Bayesian inference is a method to approximate the posterior distribution under a Bayesian model analytically. As an alternative to Markov Chain Monte Carlo (MCMC) methods, variational inference (VI) produces an analytical solution to an approximation of the posterior but have a lower computational cost compared to MCMC methods. The main challenge of applying VI comes from deriving the equations used to update the approximated posterior parameters iteratively, especially when dealing with complex data. In this thesis, we apply the VI to the context of functional data clustering and survival data analysis. The main objective is to develop novel VI algorithms and investigate their performance under these complex statistical models.

In functional data analysis, clustering aims to identify underlying groups of curves without prior group membership information. The first project in this thesis presents a novel variational Bayes (VB) algorithm for simultaneous clustering and smoothing of functional data using a B-spline regression mixture model with random intercepts. The deviance information criterion is employed to select the optimal number of clusters.

The second project shifts focus to survival data analysis, proposing a novel mean-field VB algorithm to infer parameters of the log-logistic accelerated failure time (AFT) model. To address intractable calculations, we propose and incorporate a piecewise approximation technique into the VB algorithm, achieving Bayesian conjugacy.

The third project is motivated by invasive mechanical ventilation data from intensive care units (ICUs) in Ontario, Canada, which form multiple clusters. We assume that patients within the same ICU cluster are correlated. Extending the second project's methodology, a shared frailty log-logistic AFT model is introduced to account for intra-cluster correlation through a cluster-specific random intercept. A novel and fast VB algorithm for model parameter inference is presented.

Extensive simulation studies assess the performance of the proposed VB algorithms, comparing them with other methods, including MCMC algorithms. Applications to real data, such as ICU ventilation data from Ontario, illustrate the methodologies' practical use. The proposed VB algorithms demonstrate excellent performance in clustering functional data and analyzing survival data, while significantly reducing computational cost compared to MCMC methods.

Location: (Waiting room activated. No passcode. After the public lecture, except the examination committee, all other participants are asked to leave the room so that the examination can start.)

Title: Conditional Dependence Learning of Noisy Data under Graphical Models

Abstract: Graphical models are useful tools for characterizing the conditional dependence among variables with complex structures. While many methods have been developed under graphical models, their validity is vulnerable to the quality of data. A fundamental assumption associated with most available methods is that the variables need to be precisely measured. This assumption is, however, commonly violated in reality. In addition, the frequent occurrence of missingness in data exacerbates the difficulties of estimation within the context of graphical models. Ignoring either mismeasurement or missingness effects in estimation procedures can yield biased results, and it is imperative to accommodate these effects when conducting inferences under graphical models. In this thesis, we address challenges arising from noisy data with measurement error or missing observations within the framework of graphical models for conditional dependence learning.

The first project addresses mixed graphical models applied to data involving mismeasurement in discrete and continuous variables. We propose a mixed latent Gaussian copula graphical measurement error model to describe error-contaminated data with mixed continuous and discrete variables. To estimate the model parameters, we develop a simulation-based expectation-maximization method that incorporates the measurement error effects. Furthermore, we devise a computationally efficient procedure to implement the proposed method. The asymptotic properties of the proposed estimator are established, and the finite sample performance of the proposed method is evaluated by numerical studies.

In contrast to analyzing error-prone variables in the first project, we further examine variables that are susceptible to not only mismeasurement but also missingness. In the second project, we examine noisy data that are subject to both error-contamination and incompleteness, in which we focus on the Ising model designed for learning the conditional dependence structure among binary variables. We extend the conventional Ising model using additional layers of modeling to describe data with both misclassification and missingness. To estimate the model parameters with the misclassification and missingness effects accommodated simultaneously, we develop a new inferential procedure by utilizing the strength of the insertion correction strategy and the inverse probability weighted method. To facilitate the sparsity of the graphical model, we further employ the regularization technique, and accommodate for a class of penalty functions, including widely-used penalty functions such as Lasso, SCAD, MCP, and HT penalties. To broaden the applicability scope, we investigate settings with both fixed and diverging dimensions of the variables, and moreover, we rigorously establish the asymptotic properties of the proposed estimators, with associated regularity conditions identified.

The third project deepens the second one by accommodating mixed variables subject to both mismeasurement and missingness. Unlike the first two projects that focus on a single dataset, we consider the availability of auxiliary datasets from related studies, along with the target study dataset, where data are subjected to missingness. From the measurement error perspective, the target and auxiliary datasets can be regarded as accurate and error-contaminated measurements for the variables of interest, respectively. To describe the conditional dependence relationships among variables, we explore mixed graphical models characterized by the exponential family distributions. Moreover, leveraging the transfer learning strategy, we propose an inferential procedure that accommodates missingness effects to enhance the estimation of the model parameters pertinent to the target study using the information from auxiliary datasets. We rigorously establish theoretical properties for the proposed estimators and evaluate the finite sample performance of the proposed methods through numerical studies.

This thesis contributes new methodologies to address challenges arising from the presence of noisy data with mismeasurement or missing values. The proposed methods broaden the application of graphical models for learning complex conditional dependency among variables of various nature.

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 187

Title: Enhancing portfolio investment strategies through CEV-related frameworks

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248

Title: Statistical Learning of Noisy Data: Classification and Causal Inference with Measurement Error and Missingness

The first project addresses causal inference about longitudinal studies with bivariate responses, focusing on data with missingness and censoring. We decompose the overall treatment effect into two separable effects, each mediated through different causal pathways. Furthermore, we establish identification conditions for estimating these separable treatment effects using observed data. Subsequently, we employ the likelihood method to estimate these effects and derive hypothesis testing procedures for their comparison.

In the second project, we tackle the problem of detecting cause-effect relationships between two sets of variables, formed as two vectors. Although this problem can be framed as a binary classification task, it is prone to mislabeling of causal relationships for paired vectors under the study - an inherent challenge in causation studies. We quantify the effects of mislabeled outputs on training results and introduce metrics to characterize these effects. Furthermore, we develop valid learning methods that account for mislabeling effects and provide theoretical justification for their validity. Our contributions present reliable learning methods designed to handle real-world data, which commonly involve label noise.

The third project extends the research in the second project by exploring binary classification with noisy data in the general framework. To scrutinize the impact of different types of label noise, we introduce a sensible way to categorize noisy labels into three types: instance-dependent, semi-instance-independent, and instance-independent noisy labels. We theoretically assess the impact of each noise type on learning. In particular, we quantify an upper bound of bias when ignoring the effects of instance-dependent noisy labels and identify conditions under which ignoring semi-instance-independent noisy labels is acceptable. Moreover, we propose correction methods for each type of noisy label.

Contrasting with the third project that focuses on classification with label noise, the fourth project examines binary classification with mismeasured inputs. We begin by theoretically analyzing the bias induced by ignoring measurement error effects and identify a scenario where such an ignorance is acceptable. We then propose three correction methods to address the mismeasured input effects, including methods leveraging validation data and modifications to the loss function using regression calibration and conditional expectation. Finally, we establish theoretical results for each proposed method.

In summary, this thesis explores several interesting problems in causal inference and statistical learning concerning noisy data. We contribute new findings and methods to enhance our understanding of the complexities induced by noisy data and provide solutions to address them.

Location: ÉîÒ¹¸£ÀûÕ¾ Science Centre 248

Title: Disease analytic models with applications to estimating undetected COVID-19 cases

Title: Drawdown-dependent surplus analysis and applications

Title: Statistical inference and learning with incomplete data

Incomplete data commonly arise in applications, and research on this topic has received extensive attention over the past few decades. Numerous inference methods have been developed to address various issues related to incomplete data, such as different types of missing observations and distinct missing data mechanisms, which are often classified as missing completely at random, missing at random, and missing not at random. However, research gaps still remain.

Assessing a plausible missing data mechanism is typically difficult due to the lack of validation data, and the presence of spurious variables in covariates further complicates the challenge. Prediction in the presence of incomplete data is another area worth exploring. By utilizing newly emerging techniques, we explore new avenues in the analysis of incomplete data. This thesis aims to contribute fresh insights into statistical inference within the context of incomplete data and provide valid methods to address a few existing research gaps.

Focusing on missingness in the response variable, the first project proposes a unified framework to address the effects of missing data. By leveraging the generalized linear model to facilitate the dependence of the response on associated covariates, we develop concurrent estimation and variable selection procedures using regularized likelihood. We rigorously establish the asymptotic properties of the resultant estimators. The proposed methods offer flexibility and generality, eliminating the need to assume a specific missing data mechanism -- a requirement in most available methods. Empirical studies demonstrate the satisfactory performance of the proposed methods in finite sample settings. Furthermore, the project outlines extensions to accommodate missingness in both the response and covariates.

The second problem of interest approaches missing data from a different perspective by placing it within the framework of statistical machine learning, with a specific emphasis on exploring boosting techniques; two projects are generated accordingly. Despite the increasing attention gained by boosting, many advancements in this area have primarily focused on numerical implementation procedures, with relatively limited theoretical work. Moreover, existing boosting approaches are predominantly designed to handle datasets with complete observations, and their validity is hampered by the presence of missing data. In this thesis, we employ semiparametric estimation approaches to develop unbiased boosting estimation methods for data with missing responses. We investigate several strategies to account for the missingness effects. The proposed methods are implemented using the functional gradient descent algorithm and are justified by the establishment of theoretical properties, including convergence and consistency of the proposed estimators. Numerical studies confirm the satisfactory performance of the proposed methods in finite sample settings.

The third topic further explores different boosting procedures in the context of interval censored data, where the exact observed value for the response variable is unavailable but only known to fall within an interval. Such data commonly arise in survival analysis and fields involving time-to-events, and they present a unique challenge in data analysis. In this project, we develop boosting methods for both regression and classification problems with interval censored data. We address the censoring effects by adjusting the loss functions or imputing transformed responses. The proposed methods are implemented using a functional gradient descent algorithm, and we rigorously establish their theoretical properties, including mean squared error tradeoffs and the optimality of the proposed estimators. Numerical studies are conducted to assess the performance of the proposed methods in finite sample settings.

Title: Iterated Data Sharpening for Local Polynomial Regression

Abstract: Data sharpening in kernel regression has been shown to be an effective method of reducing
 bias while having minimal effects on variance. Earlier efforts to iterate the data sharpening 
procedure have been less effective, due to the employment of an inappropriate sharpening
 transformation. In the present talk, an iterated data sharpening algorithm is described which
 reduces the asymptotic bias at each iteration, while having modest effects on the variance. The efficacy of the iterative approach is demonstrated
 theoretically and via a simulation study. Boundary effects persist and the affected region successively
 grows when the iteration is applied to local 
 constant regression. By contrast, boundary bias successively decreases for each iteration step when applied to local linear regression. After iteration, the resulting estimates
 are less sensitive to bandwidth choice, and a further simulation study demonstrates that iterated
 data sharpening with data-driven
 bandwidth selection via cross-validation can lead to more accurate regression function estimation. 
 Examples with real data are used to illustrate the scope of change made possible
 by using iterated data sharpening and to also identify its limitations.

(Based on joint work with Hanxiao Chen of Boston University and Xiaoping Shi of UBC)

Title: On Robust Inference In Some Mean-Reverting Processes With Change-Points