Events

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: 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: Western 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: ZOOM (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: Zoom (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: Western Science Centre 187

Title: Enhancing portfolio investment strategies through CEV-related frameworks

Location: Western 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: Western 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