Stor-i PhD project • June 2017 - Present
My primary area of research is detecting changepoints in multivariate time series data. Changepoints are discrete points in indexed data where the underlying properties of the data change. This includes for example financial data indexed by time or DNA sequencing data indexed by gene. Changepoint detection is a well studied problem in the statistics literature. However, much of this focus has been on detecting changepoints in univariate time series. Multivariate time series present a number of challenges that as of yet remain unaddressed.
Much of my work focuses on multivariate time series where only a subset of the variables are affected by a change. So called subset changepoints present a number of difficulties. While a number of authors have examined this issue, they typically place significant restrictions on the distribution of the data and the type of change. This significantly limits the applicability of these methods. However, in the absence of these types of assumptions standard optimisation methods such as dynamic programming become computationally infeasible in this setting, particularly as the number of variables increases. The aim of my work is to develop efficient methods that can be applied to a very wide range of datasets.
In order to reduce the computational cost of a dynamic program we have considered using a range of search space reduction methods that can reduce the computational cost of the algorithm while still calculating an exact solution. As a result we are able to exactly locate changepoints in small datasets. Although this approach is still too slow for datasets of even moderate size the exact solution is quite useful. The optimal segmentation given by this approach is useful as a ground truth which other methods can be evaluated against. This is an important step in developing effective approximate methods.
While search space reduction techniques are useful for small datasets, they are wholly inadequate for big data. Therefore we have also developed an approximate method. This method utilises an approximate test statistics with properties that mean it can be optimised easily. The result is the SPOT method which has linear computational cost when the number of changepoints is proportionate to the length of the data.
As part of my work I have also contributed software. The methods discussed above will soon be available as part of the changepoint.mv R package of which I am a contributing author.
More recently I have become interested in detecting changes in the correlation structure of multivariate data. In many applications, such as networks, we are interested in understanding the relationships between different variables. Changes in such structures are extremely important. However current methodology has a number of limitations. In particular when the relationships between variables are quite strong, common changepoint detection methods can lose statistical power. Furthermore these methods do not consider sparse changes and as such can not identify affected variates. My work will focus on addresing these issues in the high dimensional setting.
Although statistical methodology is the primary focus of my work I am interested in collaborating on relevant applied projects. Previous collaborations have examined how changepoints can be used to measure retinal degeneration in mice. If you are a practitioner interested in collaborating please use the contact form at the bottom of the page to contact me.
BSc in Mathematics • June 2016
I studied at the University of Edinburgh where I graduated in 2016. During my time there I studied a wide range of mathematical topics with a particular focus on Analysis, Optimization and Statistics (alongside some Swedish thrown in for good measure). I also completed a research project on randomized algorithms for solving large linear systems with Peter Richtárik based on papers he'd written with his PhD student Richard Gower. You can read more about this fascinating topic here
For the last four years I've been a keen Underwater Hockey player (yes it's a real thing). This is a team photo of my old club Edinburgh University Hippos which I captained in 2014/2015.
This is me and some of my many wonderful classmates graduating from Edinburgh in 2016. They were four fantastic years and I learned a lot from these guys.
University life can occasionally be a litte stressful. Thankfully there's always improptu yoga sessions on a hill to help.
The Stor-i class of 2016
A university ski trip in 2014.
During university I was a keen member of the Maths society, eventually becoming president in my final year. This picture is of me giving my farewell speech at the ball. Highlights of my time with the mathsoc include organising a speech by the legendary Sir Michael Atiyah and my final year ball.
I was a member of City of Edinburgh University Officer Training Corps (CEUOTC). Through the corp I was able to do undergo military training. This included among other things rifle handling, leadership and management and military tactics. Personal development is a key goal for the unit and through it I gained a wide variety of skills and experiences.
A photo from my recent visit to Indonesia
You betta workRupaul Charles
If you can't love yourself how in the hell are you going to love anyone elseRupaul Charles
We're all born naked and the rest is drag.Rupaul Charles
If you'd like to get in contact with me fill in the form below and I'll get back to you as soon as possible.