STOR-i student, Lancaster University
I am a PhD student at STOR-i, a centre for doctoral training at Lancaster University. My research focuses on the development of novel supervised machine learning methods with applications in phylogenetics.
In phylogenetics, a phylogenetic tree is a representation of the evolutionary history between species. Tree leaves are labelled with extant species, and internal nodes representing ancestral species are unlabelled. Recent technological advancements in genetics and genomics have led to cheap and fast genome data generation. This, in turn, has paved the way for the development of phylogenomics, a new field that applies tools in phylogenetics to conduct comparative analyses on genome data.
Our goal is to develop statistical methods over the space of phylogenetic trees, which coincides with the ultrametric space and conforms to spaces from tropical geometry. I have developed a “tropical” version of logistic regression, which classifies sampled gene trees into two classes characterized by a species tree, which is treated as a statistical parameter to be inferred. The model is easily generalised to a tropical version of generalised linear models, which can be stacked to create a “tropical” neural network. Using simulated gene trees, we have shown that our models are significantly better at classification than classical models.
For my undergraduate degree I attended the Mathematical Tripos in Cambridge, followed by an MSc in Mathematical Modelling and Scientific Computing in Oxford from which I graduated with Distinction. My master’s thesis was in the area of mathematical biology focusing on modelling tumour growth as a system of PDEs. During those years I developed an interest in Probability and Measure Theory with applications to Mathematical Finance and ecological dynamics, which I explored through projects in deriving and calculating the VIX index and stochastically simulating populations in a tritrophic food chain.
I also got a chance to spend a year with Silvaco, a company that produces software for semiconductor design (TCAD). My work there focused on PDE numerical solvers, but also on statistical inference of the distribution of ions in the wafer and the optimisation of statistical parameters for the fitting of the two dimensional distribution.
The MRes part of STOR-i is a great opportunity for me to explore those aforementioned research interest before deciding the topic of specialization. I look forward to the next four years of statistical research in STOR-i.
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