Theory and applications of probabilistic machine learning

The probabilistic framework to machine learning is one of the main theoretical and practical approaches for designing systems that learn from past data. Using the tools of probability theory to represent and manipulate uncertainty we can tackle important questions such as:
Q1 (prediction): Given some data, what is the best prediction about an outcome?
Q2 (model selection): What is the best model for an underlying process, given some data generated by it?
Q3 (experimental design): What measurements should be performed next?

The aim of this DPhil thesis is to explore one or more of these key questions. One direction of research aims to tackle Q3: designing experiments in a way that maximizes the information gathered about an underlying process.

Bayesian optimal experimental design (BOED) is a principled, model-based framework for choosing designs optimally (Lindley, 1956). It has been applied to a wide range of scientific fields, including bioinformatics, physics, pharmacology. The true power of the BOED framework is realised when it is used to design a sequence of experiments in an adaptive manner: we utilize the information gathered from past experiments to tailor each successive design. As a concrete example, suppose that a chemical contaminant has accidentally been released and is spreading rapidly. In order to discover its source we can select a location (this is our design) at which to measure the contaminant concentration level (this is our observation). Using past design-observation pairs we can select the next design to narrow in on the source, provided that we can perform the necessary computations sufficiently quickly. Unfortunately, traditional approaches to constructing adaptive design strategies necessitate significant computation at each step, meaning that it is infeasible to run adaptive BOED in real-time, unless the model is unusually simple (see Ryan et al 2016 for a review).

In this thesis we develop Deep Adaptive Design (DAD) - a novel method which addresses this restriction for a certain class of models (Foster et al 2021). The key idea is to train a design network upfront, before the beginning of the experiment, then use it to quickly run multiple adaptive experiments at deployment time. The design network therefore represents a policy, which takes as inputs the data from previous steps and outputs the next design using a single forward pass.

We also introduce implicit Deep Adaptive Design (iDAD), a method for learning adaptive design policy networks for a considerably larger class of models than DAD, namely models without an analytic likelihood function (Ivanova et al 2021). iDAD is the first method in the literature that can practically perform real-time adaptive BOED for implicit models.

Part of this thesis will be devoted to applying the developed methodology to a range of real-world experimental design problems. An exciting potential application which we are currently exploring is experimental design for quantum processing unit (QPU) calibration.

This project falls within the EPSRC "Artificial intelligence and robotics" research area. Current collaborators include academics and PhD students from the department of Statistics at the University of Oxford and the School of Informatics at the University of Edinburgh.

References:
Foster A*, D R Ivanova*, I Malik, and T Rainforth. Deep adaptive design: Amortizing sequential Bayesian experimental design. ICML 2021.
*Equal contribution

Ivanova D R, A Foster, S Kleinegesse, M Gutmann and T Rainforth. Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods. Accepted at NeurIPS 2021.

Lindley D V. On a measure of the information provided by an experiment. The Annals of Mathematical Statistics, 1956.

Ryan E G, C C Drovandi, J M McGree, and A N Pettitt. A review of modern computational algorithms for Bayesian optimal design. International Statistical Review, 2016.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.