M.Sc. Mathematics and Statistics

Permanent URI for this collectionhttps://hdl.handle.net/10464/2883

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Open Access
Time Series Prediction: HMMs with TAN and Bayesian Network Observation Structures
Miry, Reza; Department of Mathematics
This thesis addresses key challenges in time series classification, focusing on enhancing predictive ac curacy through innovative modeling techniques. First, we introduce TAN-HMM, an extension of the traditional Hidden Markov Model (HMM) that incorporates Tree-Augmented Naive Bayes (TAN) to ac count for correlated features, significantly improving classification performance on complex datasets like MSRC-12. Next, we propose the Bayesian Network Hidden Markov Model (BN-HMM), which com bines the temporal dynamics of HMMs with the structural flexibility of Bayesian Networks, achieving superior accuracy and feature relationship discovery. Finally, we tackle the problem of robust early warn ing signals for disease outbreaks, utilizing cutting-edge deep learning models to predict emerging disease behavior from simulated and real-world noisy datasets. Together, these contributions push the boundaries of time series classification and offer practical solutions for real-world applications, from human activity recognition to disease outbreak prediction.
Open Access
Simulation for Cricket: A Machine Learning Approach
Pussella, Lasith Chamindu Pranath; Department of Mathematics
Cricket is the second most popular sport in the world with a significant presence in Commonwealth countries. Despite its popularity, cricket is underrepresented in the literature, especially in the domain of simulation. Simulation in cricket is challenging because of its complexity, dynamic nature, and data scarcity. In this research, we develop a simulation mechanism for cricket using machine learning techniques. The construction of the simulator is based on the availability of a detailed dataset from Cricket Australia. We employ machine learning to predict the outcome of a "delivery", the core element of gameplay, which can further be utilized for scorecard generation and match simulations. Our simulator’s potential is demonstrated by employing it to determine the optimal batting position of a given batter in a team in Twenty20 cricket. Additionally, we develop an interactive web platform to enable the end users to directly interact with the simulator.
Open Access
Identifiability of Linear Threshold Decision Making Dynamics
Lekamalage, Anuththara Sarathchandra; Department of Mathematics
The binary-decision dynamics of two types of individuals; coordinators who tend to choose the more common option among others and anti-coordinators who avoid the common option can be modeled using the linear (anti-)threshold model. Each individual has a time-invariant threshold and decides whether to choose an option by comparing his threshold with the proportion of the population who have already chosen that option. The resulting decision-making dynamics can be predicted and controlled, provided that the thresholds are known. In practice, however, the thresholds are unknown, and often only the evolution of the total number of individuals who have chosen one option is known. The question then is whether the thresholds are identifiable given this quantity over time, which can be considered as the output of the decision-making dynamics. Identifiability investigates the recoverability of the unknown parameters given the error-free outputs, inputs, and the developed equations of the model. Different notions of and methods to test identifiability exist for dynamical systems defined in the continuous state space. However, the decision dynamics of the linear threshold model is defined in the discrete state space. We develop the identifiability framework for discrete space systems and highlight that this is not an immediate extension of the continuous space framework. Then, we investigate the threshold identifiability of both coordinators and anticoordinators in the linear threshold model. For both the synchronous and asynchronous dynamics, we find necessary and sufficient conditions for the identifiability of coordinating and anticoordinating populations. The results open the door for reliable estimation of the thresholds and in turn prediction and control of the decision-making dynamics using real-world data.
Open Access
Attention-Based Generative Model in Deep Evolutionary Learning: A Many-Objective Approach to Multi-Target SMILES Fragment-Based Drug Design for Cancer
Ahmed, Madiha; Department of Mathematics
Cancer remains a global health challenge, necessitating novel drug discovery methods. This graduate thesis introduces two computational frameworks for multi-target drug design in cancer therapy, firstly, by integrating Deep Evolutionary Learning (DEL) with a Transformer-based model. Departing from the traditional use of Variational Autoencoder (VAE), this research employs a Transformer-based generative model, capitalizing on its superior ability to capture long-range dependencies within molecular sequences to develop an understanding of the complex molecular grammar. Secondly, the research further evaluates the efficacy of a more granular fragmentation method than the one originally employed in DEL. These two proposed modifications of DEL: (i) Transformer-based model integrated in the original DEL framework and (ii) a fragmentation technique in finer granularity incorporated in the original DEL framework, are each evaluated and compared against the original DEL framework, the benchmark, in their molecular generative capabilities of targeting multiple biomarkers in cancer progression. In essence, the Transformer’s parallel processing capabilities enhance the drug design efficiency in terms of enhancing the diversity of novel and valid population samples produced and generating the highest-ranked novel molecule with the most optimal set of protein-ligand binding affinities. By optimizing the fragmentation technique, it is observed that it also performs well in maintaining a high novelty and validity of molecular compounds and interestingly, in drug design tasks involving specification of the off-targets, it produces a higher number of novel compounds that satisfy the objective thresholds compared to the benchmark. Overall, we believe that these are two approaches that can be explored for developing cancer treatments, and can also offer potential solutions for other diseases requiring multitarget interventions.
Open Access
Fixed Point Methods in Convex Minimization for Large Data
Abeysekara, Sachini; Department of Mathematics
So-called first order methods are widely used in machine learning methods involving big data because of their conceptual and algorithmic simplicity. The central problem in this paper is the optimization problem x0 ∈ arg min_{x∈C} f (x) on a suitable convex and closed domain C ⊆ R^n stemming from a machine learning problem based on training data X := {d^(i), y^(i)}^{N}_{i=1} whereby the objective function is a regularized mean square error. Here, the objective function belongs to the important class of convex functions of the form, f (x) = (1/2) x^T Q x + q^T x + c, where q ∈ R^n and Q is a positive semi-definite (n×n)-matrix. The minimization problem above is seen as an equivalent system of nonlinear equations. Indeed, the problem min_{x∈C} f (x), is equivalent to a fixed-point problem T (x) = x for a projection operator T : C → C, T (x) := P_C (I − α∇f )(x), a contraction operator for which the Banach Contraction Principle applies (P_C :R^n → C being the orthogonal projection operator). In the concrete, it appears that x = T (x) if and only if ∇f (x) = 0. The fixed point iteration scheme in the Banach Contraction Principle amounts, due to the form of the contraction T , to the widely used gradient descent algorithm for the minimization problem.
Open Access
On the Extendibility of a D(4)-Pair of Pell Numbers
Emanuel, David; Department of Mathematics
A Diophantine m-tuple with property D(ℓ) is a set of m integers such that the product of any two integers plus ℓ results in a perfect square. This thesis establishes that a particular family of D(4) pairs of Pell numbers can be extended to a D(4) triple by exactly one Pell number. A similar result has been found for the Diophantine triples of Fibonacci numbers, a discussion of which is included in the first chapter of this thesis. This chapter finishes with a statement of the main result of my thesis, and the subsequent chapters discuss several topics in number theory which were used to prove the main result in chapter 5. Specifically, results about continued fractions, Pell-type equations, and linear forms in logarithms were used. These topics are the subjects of chapters 2, 3 and 4, which contain some history and discussions of the important results. The conclusion of this thesis discusses some possible generalizations.
Open Access
Distributed Supervised Statistical Learning
khalili Mahmoudabadi, Amir; Department of Mathematics
We live in the era of big data, nowadays, many companies face data of massive size that, in most cases, cannot be stored and processed on a single computer. Often such data has to be distributed over multiple computers which then makes the storage, pre-processing, and data analysis possible in practice. In the age of big data, distributed learning has gained popularity as a method to manage enormous datasets. In this thesis, we focus on distributed supervised statistical learning where sparse linear regression analysis is performed in a distributed framework. These methods are frequently applied in a variety of disciplines tackling large scale datasets analysis, including engineering, economics, and finance. In distributed learning, one key question is, for example, how to efficiently aggregate multiple estimators that are obtained based on data subsets stored on multiple computers. We investigate recent studies on distributed statistical inferences. There have been many efforts to propose efficient ways of aggregating local estimates, most popular methods are discussed in this thesis. Recently, an important question about the number of machines to deploy is addressed for several estimation methods, notable answers to the question are reviewed in this literature. We have considered a specific class of Liu-type shrinkage estimation methods for distributed statistical inference. We also conduct a Monte Carlo simulation study to assess performance of the Liu-type shrinkage estimation methods in a distributed framework.
Open Access
Convergence Analysis of Heterogeneous Decision-making Populations Under the Coordinating Best-response and Imitation Update Rules
Hasheminejad, Nazanin Jr; Department of Mathematics
This thesis emphasis is on coordination games. In a coordination game, selecting the same strategy or decision as the opponent is mutually beneficial for both parties. We studied the problem of equilibrium convergence in such games in both discrete and continuous (time) cases. In the first Chapter, we provide a brief introduction to the field of game theory. We discuss different categories of agents based on their levels of rationality and decision-making strategies, along with a variety of games. Additionally, we address important issues and challenges within this field. The second Chapter of this work is dedicated to a heterogeneous mixed population of imitators and best-responders. In this model, agents’ update rules are assumed to be discrete functions of time. Imitators refer to agents who simply replicate the strategy of another agent with the highest payoff, while best-responders pick the strategies that maximise their individual outcomes. Suggesting the concept of ’sections’--a consecutive sequence of agents with similar strategies– helped us in establishing convergence to an equilibrium state. This convergence was demonstrated under any arbitrary asynchronous activation sequence within a linear network. The proof was then extended to networks with ring, starike, and sparse-tree structures. However, the question of equilibrium convergence for other network structures remains an open challenge. In the third Chapter, we examined a large well-mixed population of imitators within a coordination context. Our analysis is grounded in the assumption that imitation here is driven by dissatisfaction. Equivalently, agents with lower payoffs are more dissatisfied and have more tendency to change and imitate higher earners within the population. The analysis reveals the presence of three fixed points, of which two are stable and one is a saddle point. The stable manifold of the unstable fixed point is also calculated. Additionally, It is demonstrated that starting from any initial state, the population eventually converges towards one of these introduced fixed points.
Open Access
Convergence Analysis of Heterogeneous Decision-making Populations Under the Coordinating Best-response and Imitation Update Rules
Hasheminejad, Nazanin Jr; Department of Mathematics
This thesis emphasis is on coordination games. In a coordination game, selecting the same strategy or decision as the opponent is mutually beneficial for both parties. We studied the problem of equilibrium convergence in such games in both discrete and continuous (time) cases. In the first Chapter, we provide a brief introduction to the field of game theory. We discuss different categories of agents based on their levels of rationality and decision-making strategies, along with a variety of games. Additionally, we address important issues and challenges within this field. The second Chapter of this work is dedicated to a heterogeneous mixed population of imitators and best-responders. In this model, agents’ update rules are assumed to be discrete functions of time. Imitators refer to agents who simply replicate the strategy of another agent with the highest payoff, while best-responders pick the strategies that maximise their individual outcomes. Suggesting the concept of ’sections’--a consecutive sequence of agents with similar strategies– helped us in establishing convergence to an equilibrium state. This convergence was demonstrated under any arbitrary asynchronous activation sequence within a linear network. The proof was then extended to networks with ring, starike, and sparse-tree structures. However, the question of equilibrium convergence for other network structures remains an open challenge. In the third Chapter, we examined a large well-mixed population of imitators within a coordination context. Our analysis is grounded in the assumption that imitation here is driven by dissatisfaction. Equivalently, agents with lower payoffs are more dissatisfied and have more tendency to change and imitate higher earners within the population. The analysis reveals the presence of three fixed points, of which two are stable and one is a saddle point. The stable manifold of the unstable fixed point is also calculated. Additionally, It is demonstrated that starting from any initial state, the population eventually converges towards one of these introduced fixed points.
Open Access
AdaBoost And Its Variants: Boosting Methods For Classification With Small Sample Size And Brain Activity In Schizophrenia
Perry, Brittany; Department of Mathematics
AdaBoost is an ensemble method that can be used to boost the performance of machine learning algorithms by combining several weak learners to create a single strong learner. The most popular weak learner is a decision stump (low depth decision tree). One limitation of AdaBoost is its effectiveness when working with small sample sizes. This work explores variants to the AdaBoost algorithm such as Real AdaBoost, Logit Boost, and Gentle AdaBoost. These variants all follow a gradient boosting procedure like AdaBoost, with modifications to the weak learners and weights used. We are specifically interested in the accuracy of these boosting algorithms when used with small sample sizes. As an application, we study the link between functional network connectivity (as measured by EEG recordings) and Schizophrenia by testing whether the proposed methods can classify a participant as Schizophrenic or healthy control based on quantities measured from their EEG recording.
Open Access
Fitting AdaBoost Models From Imbalanced Data with Applications in College Basketball
Romaniuk, Raymond; Department of Mathematics
Data imbalance is an important consideration when working with real world data. Over/undersampling approaches allow us to gather more insight from the limited data we have on the minority class; however, there are many proposed methods. The goal of our study is to identify the optimal approach for over/undersampling to use with Adaptive Boosting (AdaBoost). Based on a simulation study, we’ve found that combining AdaBoost with various sampling techniques provides an increased weighted accuracy across classes for progressively larger data imbalances. The three Synthetic Minority Oversampling Technique’s (SMOTE) and Jittering with Over/Undersampling (JOUS) performed the best, with the JOUS approach being the most accurate for all levels of data imbalance in the simulation study. We then applied the most effective over/undersampling methods to predict upsets (games where the lower seeded team wins) in the March Madness College Basketball Tournament.
Open Access
Enhancing Lexical Sentiment Analysis using LASSO Style Regularization
Blanchard, Jeremy; Department of Mathematics
In the current information age where expressing one’s opinions online requires but a few button presses, there is great interest in analyzing and predicting such emotional expression. Sentiment analysis is described as the study of how to quantify and predict such emotional expression by applying various analytical methods. This realm of study can broadly be separated into two domains: those which quantify sentiment using sets of features determined by humans, and approaches that utilize machine learning. An issue with the later approaches being that the features which describe sentiment within text are challenging to interpret. By combining VADER which is short for Valence Aware Dictionary for sEntiment Reasoning; a lexicon model with machine learning tools (simulated annealing) and k-fold cross validation we can improve the performance of VADER within and across context. To validate this modified VADER algorithm we contribute to the literature of sentiment analysis by sharing a dataset sourced from Steam; an online video game platform. The benefits of using Steam for training purposes is that it contains several unique properties from both social media and online web retailers such as Amazon. The results obtained from applying this modified VADER algorithm indicate that parameters need to be re-trained for each dataset/context. Furthermore that using statistical learning tools to estimate these parameters improves the performance of VADER within and across context. As an addendum we provide a general overview of the current state of sentiment analysis and apply BERT a Transformer-based neural network model to the collected Steam dataset. These results were then compared to both base VADER and modified VADER.
Open Access
CEO Overconfidence and the Probability of Bankruptcy
Amin, Ruhul; Faculty of Business Programs
This thesis examines the relation between CEO overconfidence and the probability of bankruptcy. In addition to the main research question, we develop two additional hypotheses. We evaluate the potential link or channel between CEO overconfidence and the probability of bankruptcy. In the relationship between CEO overconfidence and the probability of bankruptcy, we seek for any interaction effects of CEO dominance. It is not uncommon for CEOs to be overconfident about their firms' prospects. In our sample, we use data from the year 2000 to 2019 for US companies. We proxy the bankruptcy probability using Altman’s Z Score. We use a stock option-driven measure of overconfidence, and this measure assumes that non-overconfident CEO will exercise their stock options if it is in the money, while overconfident CEOs will hold stock options beyond a rational threshold. We construct both continuous and indicator-based measures of overconfidence to test the hypotheses. The empirical findings reveal that CEO overconfidence increases the probability of bankruptcy. We do not find any evidence in favor of overinvestment which we consider as a channel through which overconfidence leads to increased bankruptcy risk. We also find that dominant and overconfident CEOs are suited for innovative firms, implying that giving an overconfident CEO a dominant position can minimize a firm's probability of bankruptcy. The implications of this study are that firms should be cautious in hiring overconfident CEO and they should take measures to reduce the negative effects of CEO overconfidence like the probability of bankruptcy. One way to reduce the probability of bankruptcy in innovative firms is to appoint overconfident CEO into a dominant position.
Open Access
Implications of Non-Operating Room Anesthesia Policy for Operating Room Efficiency
Liang, Yihang; Faculty of Business Programs
This thesis focuses on examining the use of Non-Operating Room Anesthesia (NORA) policy in Operating Room (OR) scheduling. A NORA policy involves a practice whereby the administration of anesthesia stage is performed outside the OR. The goal of the thesis is to determine whether NORA policy can improve OR efficiency measured by the performance of total costs, which consists of a weighted sum of patient waiting time, OR overtime and idle time. A simulation optimization method is adopted to find near-optimal schedules for elective surgeries in an outpatient setting. The results of a traditional OR scheduling model, where all stages of the surgery are performed in the OR, will be compared to the results of a NORA OR model where the initial anesthesia stage is performed outside of the OR. Two cases are considered for the NORA model given the decrease on mean durations: (1) a model with the same number of surgery appointments and shorter session length and (2) a models with the same session length and more surgery appointments. . The impact of a NORA policy on OR performance is further analyzed by considering scenarios that capture Surgery duration variability and mean surgery durations which are two traits for surgeries that have been shown to impact OR performance. This thesis aims to investigate how a NORA policy performs when standard deviations and mean surgery durations change. The results show that NORA policy can improve OR efficiency in all settings.
Open Access
A Study on Immersion and Emotions’ Influence on Impulse Buying in Virtual Environments
Selcuk, Cem; Faculty of Business Programs
Impulse buying has always been an interesting phenomenon that is observed in our daily lives. Statistics have shown that impulse purchases make up almost 40% of all purchases made online. Many studies have examined impulse buying, and they have found that emotions accompany impulsive behaviors naturally. With the recent development in virtual reality (VR) technology, this phenomenon is observable in online virtual environments. Retailers can create immersive virtual shops where the customer can walk among the aisles of a virtual store and make purchases. This study examines whether the effects of emotions on impulse buying vary across different immersion levels (2D vs. VR) and gender. To test our hypotheses, we collected data from the 2D and VR setting using experiments. The results provide evidence that gender plays a significant role in the three-way relationship between positive/negative emotions, immersion, and impulse buying. The unique setting of our research extends the literature on impulse buying, marketing, and virtual reality. The results offer valuable insights to marketers and retailers who want to develop virtual shops and influence impulse buying in these virtual shops.
Open Access
Examining The Influence of Social Augmented Reality Apps on Customer Relationships: The Mediating Role of Shared Social Experience
Nguyen, Oanh; Faculty of Business Programs
The development of augmented reality (AR) has provided firms with increasing opportunities to improve customer experiences, especially in a shared context where customers are encouraged to communicate with others. This study investigates the effectiveness of social AR in building relationships among customers through a shared social experience, one which includes shared sense of place, social interaction, and social identity. Data was collected from 378 active users of a social AR application and was analyzed using the partial least squares structural equation modelling (PLS-SEM) and Hayes’ PROCESS Macro. Results from this study show that shared sense of place, social interaction, and social identity mediate the influence of social AR past usage on customer-to-customer relationships, which consequently enhance customers’ continuance intention to use the social AR application. Additionally, the results of the moderated mediation analysis reveal that the indirect effect of social AR past usage on continuance intention is positively moderated by extraversion, such that at higher level of extraversion the mediated relationship becomes stronger. These findings offer important contributions to the AR marketing literature and add valuable insights for practitioners to advance the use of AR technology.
Open Access
The Effect of Perceived Deception on Consumer Repurchase Intention
Wang, Xinyue; Faculty of Business Programs
Online commerce changes the way products are displayed. Bounded by less chance to present information of the product, e-retailers always face misunderstandings on the consumer side, and consequently, unfavourable consumer behaviour. This makes online retailing prone to perceived deceptive practice. Past research has mainly integrated perceived deception into existing consumer behavior theories. In the same vein, this research further examines the factors moderating the relationship between perceived deception and repurchase intention. Specifically, we tested how product type (hedonic versus utilitarian), consumer regulatory focus (promotion versus prevention), and their interaction can help mitigate perceived deception's negative effect on consumer repurchase intention. This research expands the literature on perceived deception. With the prior work establishing the negative effect of perceived deception on consumer purchase behaviour, this research further investigates the factors that may attenuate the unfavourable outcome. It also helps marketers increase repurchase rates by emphasizing the hedonic attribute and instigating promotion intention to help mitigate the negative effects of perceived deception.
Open Access
How Virtual Reality Leads to Positive Responses to Persuasion Attempts: The Implications of VR Brand Placement
Rabbani Movarekh, Ahmadreza; Faculty of Business Programs
Facebook has started to test advertising in virtual reality, yet consumers’ responses toward this phenomenon have been neglected in the virtual reality and consumer behaviour literature. Most of the previous research has focused on VR as the primary tool for representing the service or product and not a medium for advertising purposes. Therefore, brand placement in virtual environments, as one of the most common persuasive advertising efforts by brands, is the focus of this study. More specifically, this research analyzes the effect of brand placement context (VR, 360 or 2D) and placement congruity on consumers’ persuasion knowledge and their responses towards brands, using the cognitive load theory and persuasion knowledge model to predict and explain the effect. The research model was tested using PLS-SEM and the PROCESS macro with a sample of 209 participants. The results confirmed that participants who experienced a higher sense of telepresence and interactivity (VR condition) were more likely to report lower persuasion knowledge and better brand evaluations and behavioural intentions. It was also found that compared to the 360 condition, in VR and 2D environments, participants were more likely to recall the brand embedded into the environment. Placement congruity was found to moderate the underlying mechanism through which interactivity and telepresence affect persuasion knowledge. These findings provide helpful insights to marketers and brand managers, who think of VR as an advertising tool, on how the technology factor impacts consumers’ responses to their persuasion attempts, such as brand placements.
Open Access
The Influence of Perceived Value on Exploratory Behaviour Towards Future Patronage Intention in M-Commerce: An S-O-R Approach.
Pouyan, Mohammad Mahdi; Faculty of Business Programs
The exploratory behaviour issue has received considerable attention in both online and brick-and-mortar consumer behaviour literature so far. However, regarding the widely prevalent use of mobile commerce in daily life, surprisingly, mobile exploratory behaviour has seldom been investigated. It is unclear to what extent mobile commerce characteristics can facilitate explorative behaviour. Thus, this study aims to fill the gap in the extant literature by examining the positive relationship between the perceived value, namely, functional, emotional and social and exploration (diversive and specific), which in turn, directly impacts future patronage intention. Due to the pivotal role of flow state in computer-mediated and online behaviour in the extant literature, the current study set out to examine the mediation role of flow between the relationship of perceived values and divisive vs specific exploration. This thesis begins with a brief overview of the recent history of noted research elements and proposes the conceptual model based on the stimulate-organism-response (S-O-R) model. It then discussed the hypotheses development. The remaining part of the paper proceeds with details on the data collection process and the methodological approach adopted to test these relationships.
Open Access
Firm Performance and CEO Compensation: CEO Pay Slice vs Pay-Performance Sensitivity
Hasan, S M Muyeed; Faculty of Business Programs
I study the relationship between CEO incentive compensation and firm performance in the presence of CEO dominance to examine how incentive compensation improves firm performance by reducing agency conflicts between shareholders and managers. I estimate pay-performance sensitivity (PPS) as a measure of CEO incentive compensation and the CEO pay slice (CPS) as a measure of CEO dominance. Controlling for standard control variables, I conduct multiple OLS regressions and find that at the high level of CPS, PPS improves firm performance, but at the low level of CPS, impact of PPS diminishes. This shows that determining stand-alone associations of PPS or CPS to firm value—a popular practice in the literature—might not be adequate because of an unexplored interaction effect between executive incentive and executive dominance. To address the potential endogeneity issues, I conduct robustness check by employing instrumental variables with a two-stage least square (2SLS) estimation procedure. As an additional robustness check, I account for the year effect and confirm that the results still stand to the same level of significance.

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