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High dimensional learning with theoretical guarantees

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  • Full or part time
    Dr A Kaban
  • Application Deadline
    No more applications being accepted
  • Funded PhD Project (European/UK Students Only)
    Funded PhD Project (European/UK Students Only)

Project Description

A PhD position is available in the area of high dimensional machine learning, to develop novel algorithms with theoretical guarantees on performance. In many application areas of machine learning, data sets become increasingly high dimensional while the sample size remains moderate. In such conditions learning to make predictions and generalisation from data is provably impossible in general - yet, machine learning algorithms are expected and often do perform in applications. When and how can this be rigorously guaranteed?

The successful candidate will join our research on FORGING: Fortuitous Geometries and Compressive Learning (, where we develop new ways to formalise the intuition that high dimensional data is often not truly high dimensional in the sense that it may possess some hidden low complexity or otherwise benign structure. We seek to take advantage of such naturally occurring structures to both sharpen theoretical guarantees, and to improve learning algorithms. Examples of benign geometric structures include margin and margin distribution, effective and intrinsic dimension, sparsity, and others, which we capture into a generic novel complexity term.

We seek a highly motivated PhD student with an excellent MSc/MSci degree in a numerate subject to conduct theoretical analyses for specific classes of learning problems, and based on the insights gained to devise better learning algorithms. There is ample opportunity to develop interdisciplinary collaborations -- in particular, we envisage an application in healthcare, where algorithms that can provably learn from a limited sample size are expected to contribute to improving early diagnosis of patients.

Funding Notes

The position offered is for four years of part time (75%) study with 456 teaching hours per year. The value of the award is £18,552 pa.

Eligibility: 2:1 Honours undergraduate degree and/or postgraduate degree with Distinction (or an international equivalent) in a numerate subject, such as Mathematics, Statistics, Computer Science or Physics. Excellent problem solving skills and programming skills are required.

If your first language is not English and you have not studied in an English-speaking country, you will have to provide an English language qualification.


A. Kaban. Dimension-free error bounds from random projections. 33rd AAAI Conference on Artificial Intelligence (AAAI 2019), to appear.

A. Kaban, Y. Thummanusarn. Tighter guarantees for the compressive multi-layer perceptron. 7th International Conference on the Theory and Practice of Natural Computing (TPNC18), Dublin, Ireland, December 12-14, 2018.

A. Kaban, R.J. Durrant. Structure-aware error bounds for linear classification with the zero-one loss. arXiv:1709.09782

A. Kaban. On Compressive Ensemble Induced Regularization: How Close is the Finite Ensemble Precision Matrix to the Infinite Ensemble? The 28th International Conference on Algorithmic Learning Theory (ALT 2017), Kyoto University, Japan, 15-17 October 2017.

R.J. Durrant, A. Kaban. Random projections as regularizers: Learning a linear discriminant from fewer observations than dimensions. Machine Learning 99(2), pp. 257-286, 2015.

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