My dream is to use my background in mathematics and software development skills to design sophisticated tools that can improve data-driven health care 🩺 and help facilitate the urgent action needed to combat climate change ♻️.
At the moment, I'm in the second year of my PhD in mathematics at the Technical University of Munich 🇩🇪, where I'm researching topological and geometric deep learning as a member of the AIDOS Lab🍩. I'm also a co-founder of Krv Analytics📊, a startup focused on new-age analytics solutions that target problems aligned with the UN's Sustainable Development Goals🇺🇳.
I'm always looking for new opportunities to collaborate, learn, and exchange ideas, so please feel free to reach out if you find my page interesting 📮.
I've been primarily an academic for for almost a decade... which I actually can't believe. I started as an undergrad in mathematics and physics at UC Berkeley, finishing just before the pandemic went underway. During COVID, I completed a masters in data science and machine learning at Chapman University while living at my childhood home in Orange County. Luckily, I was also was able to pick up some industry experience and hone my development skills, working first as a ML consultant at Madiba, and then part-time as a software and research developer for Encryptek during my Masters. These experiences helped me build towards my position at CHOC as a grant-funded Research Scientist. During this position, I worked with my advisor Louis Ehwerhemuepha to build predictive models for early identification of pediatric sepsis. This applied research invited me into the world of computational topology, an amazing playground straddling the worlds of pure mathematics and machine learning. After that I was hooked! Soon after, I accepted an offer to work with Bastian Rieck, studying topological and geometric deep learning. I've also had the pleasure of working with Stuart Wayland and Sidney Gathrid on various projects for the last few years, eventually culminating in us founding Krv Analytics in 2023. Stay tuned for updates on the journey! 🚀
Krv Analytics CHOC ResearchIdentifying (a) systemic barriers to quality healthcare access and (b) key indicators of care efficacy in the United States remains a significant challenge. To improve our understanding of regional disparities in care delivery, we introduce a novel application of curvature, a geometrical-topological property of networks, to Physician Referral Networks. Our initial findings reveal that Forman-Ricci and Ollivier-Ricci curvature measures, which are known for their expressive power in characterizing network structure, offer promising indicators for detecting variations in healthcare efficacy while capturing a range of significant regional demographic features. We also present `apparent`, an open-source tool that leverages Ricci curvature and other network features to examine correlations between regional Physician Referral Networks structure, local census data, healthcare effectiveness, and patient outcomes.
Echoing recent calls to counter reliability and robustness concerns in machine learning via multiverse analysis, we present PRESTO, a principled framework for mapping the multiverse of machine-learning models that rely on latent representations. Although such models enjoy widespread adoption, the variability in their embeddings remains poorly understood, resulting in unnecessary complexity and untrustworthy representations. Our framework uses persistent homology to characterize the latent spaces arising from different combinations of diverse machine-learning methods, (hyper)parameter configurations, and datasets, allowing us to measure their pairwise (dis)similarity and statistically reason about their distributions. As we demonstrate both theoretically and empirically, our pipeline preserves desirable properties of collections of latent representations, and it can be leveraged to perform sensitivity analysis, detect anomalous embeddings, or efficiently and effectively navigate hyperparameter search spaces.
In response to rising interest for generative model use in drug development, we introduce a new topological and geometric descriptor for graph distributions based on curvature filtrations. As well as favorable stability and expressivity properties, our method affords scalable statistical comparisons and hypothesis testing for sets of graphs, providing an exciting and well-principled method for evaluating Graph Generative Models.
Discrete curvature has recently been used in graph machine learning to improve performance, understand message-passing and assess structural differences between graphs. Despite these advancements, the theoretical properties of discrete curvature measures, such as their representational power and their relationship to graph features is yet to be fully explored. This paper studies Ollivier--Ricci curvature on graphs, providing both a discussion and empirical analysis of its expressivity, i.e. the ability to distinguish non-isomorphic graphs..