Comparing Heterogeneous Data Using Embeddings

In the realm of data analysis and machine learning, comparing datasets with vastly different structures poses a significant challenge. There is currently little existing research in comparing datasets with very different structures. Our previous work in this field has attempted to adapt existing embedding methods for anomaly detection between simulated datasets with mixed results. While some of the results were promising, they were not reliable enough to provide a recommendation for users. This project hopes to develop novel methodologies for both anomaly detection and more general comparisons. Firstly, we will provide mathematical proofs to provide a rigorous backing for the reliability of our methods. Secondly, we will establish the empirical success of our methods using both simulated and real-world datasets to validate the effectiveness of our methodologies. Finally, we will develop software to make these methodologies accessible to users. The anticipated impacts of this project are far-reaching, with potential applications spanning various domains. One prominent area we expect to benefit significantly is interdisciplinary statistics-a rapidly growing field reliant on the comparisons mentioned. Some interesting case studies we might include in this project are: 1. The science of genetic and linguistic histories: The study of genetic and linguistic histories involves comparing complex datasets that differ in structure. Genetic data, comprising DNA sequences and genetic markers, often needs to be correlated with linguistic data, such as language evolution timelines and migration patterns. 2. The link between cultural values and economic markers of countries: Cultural datasets, encompassing values, beliefs, and customs, vary greatly in structure from economic datasets, which include quantitative economic indicators. Specifically in the case of anomaly detection, we want to demonstrate the need and effectiveness of these methods in the economic context. Traditional methods for detecting economic anomalies often rely on structured financial data. However, anomalies can emerge from various sources and may not always conform to a structured pattern. In summary, this project represents a significant step forward in the realm of comparative analysis and anomaly detection for datasets with diverse structures. By establishing mathematical foundations, conducting empirical testing, and offering accessible software tools, we aim to empower researchers across multiple disciplines to extract meaningful insights from their data.

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.