Graduate Works

Dr. Karen Kafadar is the Chair & Commonwealth Professor of Statistics at the University of Virginia. She earned both her BS and MS in Statistics from Stanford University in 1975 and her PhD in Statistics from Princeton University in 1979, for which her advisor was the esteemed mathematical statistician, Dr. John Tukey. Her dedication to research in statistics motivated her position as a co-PI on the National Institute of Standards and Technology (NIST) Funded Center of Statistical Applications in Forensic Science. Dr. Kafadar has an incredibly diverse work background in industry, government, and academia, holding previous positions at several prestigious institutions. Likewise, her data analysis has contributed to a wide array of fields ranging from chemistry (chemometrics), biology (genomics), medicine (clinical trials), and agriculture (crop yields). Dr. Kafadar stands out as an excellent mathematical statistician because of her strong stewardship to both the mathematical statistics community and beyond. Authoring over 100 journal articles and book chapters and advising numerous MS and PhD students, she has also served as a past Editor of some highly reputable statistical journals such as JASA Reviews, Technometrics, and Annals of Applied Statistics, as well as a past President of the American Statistical Association (2019) and President of the International Association for Statistical Computing (2011-2013). Through her rigorous research in robust mathematical statistics, her outreach of statistics education to historically excluded groups, and her immense service to the profession, Dr. Kafadar has brought justice into the world of statistics, transforming her field as a thought leader. Most importantly, Dr. Kafadar is a strong role model for anyone who seeks to utilize statistics to bring about justice. 

My colleague and I elaborate more on the life of Dr. Karen Kafadar during our presentation, which was given for the Spring 2023 Student Statistics Research Conference (SSRC). Click here to view the slides. It was a full circle moment to create this presentation, as Dr. Kafadar gave a distinguished talk at UTRGV during my first semester as a PhD student! 

This work motivates the consideration of ethics during the design of deep learning architecture by illustrating the consequence of mode collapse in a generative adversarial network (GAN) model. As generative models approach a decade of use and development in the artificial intelligence community, there are barriers to their wide-scale implementation. Mode collapse, causing low output diversity in GAN models, is problematic. In this work, I present mode collapse in the MNIST digits dataset implemented with a standard GAN and implement a deep convolutional generative adversarial network (DCGAN) utilizing the Anime Face dataset to explore the presence of mode collapse for the facial generation problem. After presenting those results, I qualitatively examine the phenomenon and conclude with some remarks on novel generative models that may contribute to more ethical deep learning architectures. Click to read the paper. 

Effective battery management systems (BMS) are critical for optimizing the performance, safety, and lifespan of lithium-ion (Li-ion) batteries in applications such as electric vehicles and energy storage systems. Traditional approaches to passive balancing, which use shunt resistors to dissipate excess energy, are simple but inefficient and often fail to account for critical factors such as temperature dynamics and multi-objective optimization. This research investigates the use of reinforcement learning (RL), especially a deep Q-Network (DQN), to address these limitations and enhance passive balancing strategies. 

A custom simulation environment, BatteryEnv, was created utilizing the Gymnasium library to model a five-cell Li-ion battery system. The environment integrates states-of-charge (SOC), temperature dynamics, and switching operations into a multi-objective reward function. The DQN agent optimizes balancing decisions by minimizing SOC variance, stabilizing temperature, and reducing switching frequency. Stability and scalability were ensured by training 10,000 episodes with replay buffers and target networks. As a result, this research demonstrated that an RL agent significantly reduces SOC variance, maintains thermal stability, minimizes switching operations, and outperforms traditional passive balancing methods. The included temperature dynamics further enhance the model’s safety and applications to real-world systems. This research aims to advance the field by introducing a scalable and generalizable RL-based framework for passive balancing, offering solutions to address key challenges in modern BMS design. Click to read the paper. 

With recent advances in technology, particularly with the widespread use of Internet Of Things (IoT) devices, the cybersecurity field is the fastest growing fields in the STEM job market. Mathematical models, like stochastic branching processes, can be applied to describe phenomenon in the cybersecurity field, such as the spread of self-propagating code, also known as worms. This paper offers a mathematical review of the iconic paper published in an IEEE proceedings on Dependable and Secure Computing, Modeling And Automated Containment of Worms (Sellke, 2008). The research questions, associated branching processes, and main contributions of the paper will be discussed and presented as a high-level summary. Click here to read the paper, or if you prefer, check out the presentation slides. 

Since 1970, breast cancer has been the second most deadly form of cancer in the United States, and it is the leading cause of death for Hispanic women. In spite of this frequency, much progress has been made regarding the diagnosing and preventative care of breast cancer, as deaths have decreased 43% overall from the 1990s to 2020s. The fact that deaths from breast cancer have decreased steadily since 1989 has been contributed to the advancement of treatment efforts and earlier detection via cancer screening methods, made particularly possible through statistical learning models. 

In this report, we employed Random Forest, Support Vector Machine, and Neural Networks methods in order to create an accurate model to observe which features are most helpful in predicting malignant or benign cancer.

Towards the end of the semester, we were tasked to take all the concepts we learned, and piece them together like a mind map - it was a lot of fun! This was the moment I realized that I learned a lot more in the course than I had previously thought. Plus, it was nice to use my stickers :) you can check out my poster here, which received top accolodes out of the class. The medium was posterboard with glued origami paper and calligraphy markers. Some of the characters featured include Gon and Killua from Hunter x Hunter, bootleg Clefairy ordered from Wish.com, Ash, Pikachu, and Meowth, that's right! 

I also give a virtual presentation of the poster here.