Estimating sparse patterns from sparse data.

This project is focused on the problem of 'group testing' in information theory, which aims to identify the (hopefully) small number of individuals carrying a disease in a large population via as few "group" tests as possible (potentially due to lack of population-scale testing resources); these group tests involve pooling together samples from different subsets of individuals into a small number of pooled tests (each pooled test has a positive test outcome if and only if at least one individual whose sample was included was a disease carrier) and inferring the set of diseased individuals from the set of test outcomes. This problem of group-testing is one example of nonlinear sparse signal estimation, wherein a sparse (mostly zero) input is to be inferred from a small number of outputs, where the input-output relationship is non-linear. Fundamental limits (on the minimum number of tests required for reliable estimation) for the classical group-testing problem have only recently been obtained; new insights regarding List Decoding (in which we allow a list of possible sets of diseased individuals) and exploring the trade off and applications of such techniques. Exploring the novel problem which is related to our testing function (as a property of the dilution of the disease in the blood sample), exploring results and developing methods for such functions. Applications of group testing span a wide variety of subjects, from confidential counting of diseased individuals to machine learning and DNA testing> the applications of our research would allow us to improve upon previous applications by allowing more flexibility in the methodologies, for example list-decoding would allow us to reduce the number of tests needed to fit in with any physical limitations. While exploring different tests functions would allow us to understand how to use these methods with different testing apparatus.

This project falls within the EPSRC Mathematical Sciences research area.

The COMPASS Centre for Doctoral Training will have the following impact.

Doctoral Students Impact.

I1. Recruit and train over 55 students and provide them with a broad and comprehensive education in contemporary Computational Statistics & Data Science, leading to the award of a PhD. The training environment will be built around a set of multilevel cohorts: a variety of group sizes, within and across year cohort activities, within and across disciplinary boundaries with internal and external partners, where statistics and computation are the common focus, but remaining sensitive to disciplinary needs. Our novel doctoral training environment will powerfully impact on students, opening their eyes to not only a range of modern technical benefits and opportunities, but on the power of team-working with people from a range of backgrounds to solve the most important problems of the day. They will learn to apply their skills to achieve impact by collaborative working with internal and external partners, such as via our Rapid Response Teams, Policy Workshops & Statistical Clinics.

I2. As well as advanced training in computational statistics and data science, our students will be impacted by exposure to, and training in, important cognate topics such as ethics, responsible innovation, equality, diversity and inclusion, policy, effective communication and dissemination, enterprise, impact and consultancy skills. It is vital for our students to understand that their training will enable them to have a powerful impact on the wider world, so, e.g., AI algorithms they develop should not be discriminatory, and statistical methodologies should be reproducible, and statistical results accurately and comprehensibly communicated to the general public and policymakers.

I3. The students will gain experience via collaborations with academic partners within the University in cognate disciplines, and a wide range of external industrial & government partners. The students will be impacted by the structured training programmes of the UK Academy of Postgraduate Training in Statistics, the Bristol Doctoral College, the Jean Golding Institute, the Alan Turing Institute and the Heilbronn Institute for Mathematical Sciences, which will be integrated into our programme.

I4. Having received an excellent training, the students will then impact powerfully on the world in their future fruitful careers, spreading excellence.

Impact on our Partners & ourselves.

I5. Direct impacts will be achieved by students engaging with, and working on projects with, our academic partners, with discipline-specific problems arising in engineering, education, medicine, economics, earth sciences, life sciences and geographical sciences, and our external partners Adarga, the Atomic Weapons Establishment, CheckRisk, EDF, GCHQ, GSK, the Office for National Statistics, Sciex, Shell UK, Trainline and the UK Space Agency. The students will demonstrate a wide range of innovation with these partners, will attract engagement from new partners, and often provide attractive future employment matches for students and partners alike.

Wider Societal Impact

I6. COMPASS will greatly benefit the UK by providing over 55 highly trained PhD graduates in an area that is known to be suffering from extreme, well-known, shortages in the people pipeline nationally. COMPASS CDT graduates will be equipped for jobs in sectors of high economic value and national priority, including data science, analytics, pharmaceuticals, security, energy, communications, government, and indeed all research labs that deal with data. Through their training, they will enable these organisations to make well-informed and statistically principled decisions that will allow them to maximise their international competitiveness and contribution to societal well-being. COMPASS will also impact positively on the wider student community, both now and sustainably into the future.