# Michael A. Osborne's research while affiliated with University of Oxford and other places

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## Publications (99)

Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows for Gaussian process regression in $O((n+m)\log(n+m))$ time. Our "binary tree" kernel places all data points o...

We analyze the expected behavior of an advanced artificial agent with a learned goal planning in an unknown environment. Given a few assumptions, we argue that it will encounter a fundamental ambiguity in the data about its goal. For example, if we provide a large reward to indicate that something about the world is satisfactory to us, it may hypot...

Reinforcement learning (RL) offers the potential for training generally capable agents that can interact autonomously in the real world. However, one key limitation is the brittleness of RL algorithms to core hyperparameters and network architecture choice. Furthermore, non-stationarities such as evolving training data and increased agent complexit...

Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector...

Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector...

Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector...

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed...

The discrepancies between reality and simulation impede the optimisation and scalability of solid-state quantum devices. Disorder induced by the unpredictable distribution of material defects is one of the major contributions to the reality gap. We bridge this gap using physics-aware machine learning, in particular, using an approach combining a ph...

Accumulating evidence from human-based research has highlighted that the prevalent one-size-fits-all approach for neural and behavioral interventions is inefficient. This approach can benefit one individual, but be ineffective or even detrimental for another. Studying the efficacy of the large range of different parameters for different individuals...

The potential of Si and SiGe-based devices for the scaling of quantum circuits is tainted by device variability. Each device needs to be tuned to operation conditions. We give a key step towards tackling this variability with an algorithm that, without modification, is capable of tuning a 4-gate Si FinFET, a 5-gate GeSi nanowire and a 7-gate SiGe h...

Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We provide a theoretical analysis of Deep Sets which shows that this universal approximation property is only guara...

Deep reinforcement learning is an emerging machine-learning approach that can teach a computer to learn from their actions and rewards similar to the way humans learn from experience. It offers many advantages in automating decision processes to navigate large parameter spaces. This paper proposes an approach to the efficient measurement of quantum...

Accumulating evidence from human-based research has highlighted that the prevalent one-size-fits-all approach for neural and behavioral interventions is inefficient. This approach can benefit one individual, but be ineffective or even detrimental for another. Studying the efficacy of the large range of different parameters for different individuals...

Deep reinforcement learning is an emerging machine learning approach which can teach a computer to learn from their actions and rewards similar to the way humans learn from experience. It offers many advantages in automating decision processes to navigate large parameter spaces. This paper proposes a novel approach to the efficient measurement of q...

Variability is a problem for the scalability of semiconductor quantum devices. The parameter space is large, and the operating range is small. Our statistical tuning algorithm searches for specific electron transport features in gate-defined quantum dot devices with a gate voltage space of up to eight dimensions. Starting from the full range of eac...

Device variability is a bottleneck for the scalability of semiconductor quantum devices. Increasing device control comes at the cost of a large parameter space that has to be explored in order to find the optimal operating conditions. We demonstrate a statistical tuning algorithm that navigates this entire parameter space, using just a few modellin...

Scalable quantum technologies such as quantum computers will require very large numbers of quantum devices to be characterised and tuned. As the number of devices on chip increases, this task becomes ever more time-consuming, and will be intractable on a large scale without efficient automation. We present measurements on a quantum dot device perfo...

Fairness, through its many forms and definitions, has become an important issue facing the machine learning community. In this work, we consider how to incorporate group fairness constraints into kernel regression methods, applicable to Gaussian processes, support vector machines, neural network regression and decision tree regression. Further, we...

Bayesian optimization has demonstrated impressive success in finding the optimum location $x^{*}$ and value $f^{*}=f(x^{*})=\max_{x\in\mathcal{X}}f(x)$ of the black-box function $f$. In some applications, however, the optimum value is known in advance and the goal is to find the corresponding optimum location. Existing work in Bayesian optimization...

A research frontier has emerged in scientific computation, wherein discretisation error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly deterministic) computational...

This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?" (Statist. Sci. 34 (2019) 1-22). We would first like to thank the reviewers and many of our colleagues who helped shape this paper, the Editor for selecting our paper for discussion, and of course all of the discussants for their thoughtful, i...

Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed as the cardinality of the sets under consideration increases. However, we demonstrate that the analysis leadin...

This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?" to appear in Statistical Science with discussion. We would first like to thank the reviewers and many of our colleagues who helped shape this paper, the editor for selecting our paper for discussion, and of course all of the discussants for t...

Group fairness is an important concern for machine learning researchers, developers, and regulators. However, the strictness to which models must be constrained to be considered fair is still under debate. The focus of this work is on constraining the expected outcome of subpopulations in kernel regression and, in particular, decision tree regressi...

Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of automation. We present measurements on a quantum dot device performed by a machine learning algorithm. The algorith...

Fairness, through its many forms and definitions, has become an important issue facing the machine learning community. In this work, we consider how to incorporate group fairness constraints in kernel regression methods. More specifically, we focus on examining the incorporation of these constraints in decision tree regression when cast as a form o...

Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discrete graphical models. In order t...

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given infor...

The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few thousand. In the spirit of prob...

We examine the problem of estimating the trace of a matrix $A$ when given access to an oracle which computes $x^\dagger A x$ for an input vector $x$. We make use of the basis vectors from a set of mutually unbiased bases, widely studied in the field of quantum information processing, in the selection of probing vectors $x$. This approach offers a n...

The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves the constraints on both storage (the kernel matrix need not be stored) and computation (both stochastic gradient...

Probabilistic numerical methods aim to model numerical error as a source of
epistemic uncertainty that is subject to probabilistic analysis and reasoning,
enabling the principled propagation of numerical uncertainty through a
computational pipeline. In this paper we focus on numerical methods for
integration. We present probabilistic (Bayesian) ver...

We present Blitzkriging, a new approach to fast inference for Gaussian
processes, applicable to regression, optimisation and classification.
State-of-the-art (stochastic) inference for Gaussian processes on very large
datasets scales cubically in the number of 'inducing inputs', variables
introduced to factorise the model. Blitzkriging shares state...

Online Passive-Aggressive (PA) learning is a class of online margin-based
algorithms suitable for a wide range of real-time prediction tasks, including
classification and regression. PA algorithms are formulated in terms of
deterministic point-estimation problems governed by a set of user-defined
hyperparameters: the approach fails to capture model...