Machine learning and neural computing postgraduate personal statement example

Personal statement example

My interest in machine learning began with a linear algebra problem sheet rather than anything more dramatic. We were asked to interpret the singular value decomposition of a matrix of exam marks, and I was struck that a purely algebraic operation could pull out something interpretable about the data. When I later met principal component analysis in a statistics module and realised it was the same machinery, I began looking for the mathematics underneath the methods I had been using as recipes. That habit has shaped how I want to study further: I would like to work on neural computation as a mathematical subject, not only as a toolkit.

My degree in Mathematics and Computer Science has given me the components for this. Probability and statistical inference gave me maximum likelihood, and it changed how I read loss functions; cross-entropy stopped being an arbitrary formula once I saw it as the negative log likelihood of a categorical model. Optimisation taught me convexity and gradient methods, which made the behaviour of stochastic gradient descent on very much non-convex surfaces more interesting rather than less. On the computing side, a concurrency module and a fair amount of C have given me a reasonable sense of why memory layout and batch size matter when a model is actually running, which I think is easy to lose if you only ever call a library.

My final-year project is a comparison of small convolutional networks with logistic regression and random forests on a publicly available image classification dataset. The point is not to beat any published result, but to be careful about what a fair comparison means: matching preprocessing, using a held-out test set only once, and reporting variation across random seeds rather than a single number. Two findings surprised me. First, the gap between the simple baselines and the network narrowed considerably once I tuned the baselines properly, which made me sceptical of comparisons where only one side has been optimised. Second, my early accuracy figures were optimistic because I had been selecting architectures on the test split. Redoing the experiments with a proper validation split cost me three weeks and taught me more about methodology than the modules had.

Before that I taught myself PyTorch by building a handwriting recognition tool that reads short words I write on a tablet. Reading Goodfellow, Bengio and Courville's Deep Learning alongside it helped, particularly the chapters on regularisation, which explained why my first version memorised my own handwriting and failed completely on my flatmate's. Adding augmentation and weight decay improved things; collecting samples from eleven friends improved them far more, which was a useful lesson about data.

Outside my degree I have worked Saturdays on a supermarket customer service desk for three years, handling refunds, complaints and the occasional very long queue. It has made me calmer under pressure and better at explaining decisions to people who are not pleased about them. I also help at a Saturday maths club for Year 8 and 9 pupils, where I usually take the group working on fractions and negative numbers. Explaining why dividing by a fraction makes a number larger, three different ways, is good training for writing up technical work clearly.

For postgraduate study I want deeper grounding in the theory of learning, including generalisation bounds and the optimisation behaviour of over-parameterised models, and more experience with sequence models and probabilistic methods. In the longer term I am drawn to research or research-adjacent work on evaluating models honestly, since my project convinced me that how we measure performance is as substantial a problem as how we improve it.