Differential Model Inference with Missing Data

In the vast majority of real-world scenarios, data used for modelling and inference is imperfect and incomplete. This can take a variety of forms whether it be random due to errors in the data collection or processing procedure, or systematic due to the design of experiments or real-world limitations. Despite this abundance, most model inference procedures have no natural ability to adapt to the presence of missing or corrupted data. One area where this is especially prescient is the area of differential model estimation. Differential model estimation is the broad range of method whose focus is the difference or ratios of two objects. This can be a difference between or within distributions, random variables or functions. This area has seen a great deal of attention due to its relative flexibility when compared to singular model estimation allowing us to model more complicated objects than would be feasible with direct model estimation. Another potential benefit to this approach is often the relative simplicity of the difference which is the core philosophy behind many estimands of interest.
In this project our aim to take popular differential model estimation paradigms and either adapt them to missing data or extend their pre-existing adaptations to missing data. Specifically, we focus on three popular areas: density ratio estimation, score matching, and heterogeneous treatment effect analysis. Density ratio estimation focusses on estimating the ratio between two probability densities while score matching estimates the gradient of the log of a singular density. Both of these approaches allow us to model objects adjacent to the while being significantly easier to model than the density itself. Heterogeneous treatment effect aims to learn the difference two outcomes for individuals both on and off a binary treatment with the hypothesis that this difference will be simpler than the outcomes themselves.

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.