Andrew Thompson

Andrew Thompson, Vivek Desai

We propose the Variation Calibration Error (VCE) metric for assessing the calibration of machine learning classifiers. The metric can be viewed as an extension of the well-known Expected Calibration Error (ECE) which assesses the calibration of the maximum probability or confidence. Other ways of measuring the variation of a probability distribution exist which have the advantage of taking into account the full probability distribution, for example the Shannon entropy. We show how the ECE approach can be extended from assessing confidence calibration to assessing the calibration of any metric of variation. We present numerical examples upon synthetic predictions which are perfectly calibrated by design, demonstrating that, in this scenario, the VCE has the desired property of approaching zero as the number of data samples increases, in contrast to another entropy-based calibration metric (the UCE) which has been proposed in the literature.

Andrew Thompson, Miles McCrory

We give analytical results for propagation of uncertainty through trained multi-layer perceptrons (MLPs) with a single hidden layer and ReLU activation functions. More precisely, we give expressions for the mean and variance of the output when the input is multivariate Gaussian. In contrast to previous results, we obtain exact expressions without resort to a series expansion.

Ciaran Bench, Oskar Pfeffer, Vivek Desai et al.

In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there is considerable risk of poor performance when deployed in practical measurement scenarios leading to negative patient outcomes. Reliable uncertainties accompanying predictions can provide guidance to clinicians in their interpretation of the trustworthiness of model outputs. It is therefore of interest to compare the effectiveness of different approaches. Here we implement an unprecedented set of eight uncertainty quantification (UQ) techniques to models trained on two clinically relevant prediction tasks: Atrial Fibrillation (AF) detection (classification), and two variants of blood pressure regression. We formulate a comprehensive evaluation procedure to enable a rigorous comparison of these approaches. We observe a complex picture of uncertainty reliability across the different techniques, where the most optimal for a given task depends on the chosen expression of uncertainty, evaluation metric, and scale of reliability assessed. We find that assessing local calibration and adaptivity provides practically relevant insights about model behaviour that otherwise cannot be acquired using more commonly implemented global reliability metrics. We emphasise that criteria for evaluating UQ techniques should cater to the model's practical use case, where the use of a small number of measurements per patient places a premium on achieving small-scale reliability for the chosen expression of uncertainty, while preserving as much predictive performance as possible.

Alicia Russell-Gilbert, Alexander Sommers, Andrew Thompson et al.

For data-constrained, complex and dynamic industrial environments, there is a critical need for transferable and multimodal methodologies to enhance anomaly detection and therefore, prevent costs associated with system failures. Typically, traditional PdM approaches are not transferable or multimodal. This work examines the use of Large Language Models (LLMs) for anomaly detection in complex and dynamic manufacturing systems. The research aims to improve the transferability of anomaly detection models by leveraging Large Language Models (LLMs) and seeks to validate the enhanced effectiveness of the proposed approach in data-sparse industrial applications. The research also seeks to enable more collaborative decision-making between the model and plant operators by allowing for the enriching of input series data with semantics. Additionally, the research aims to address the issue of concept drift in dynamic industrial settings by integrating an adaptability mechanism. The literature review examines the latest developments in LLM time series tasks alongside associated adaptive anomaly detection methods to establish a robust theoretical framework for the proposed architecture. This paper presents a novel model framework (AAD-LLM) that doesn't require any training or finetuning on the dataset it is applied to and is multimodal. Results suggest that anomaly detection can be converted into a "language" task to deliver effective, context-aware detection in data-constrained industrial applications. This work, therefore, contributes significantly to advancements in anomaly detection methodologies.

Reva Schwartz, Rumman Chowdhury, Akash Kundu et al.

Conventional AI evaluation approaches concentrated within the AI stack exhibit systemic limitations for exploring, navigating and resolving the human and societal factors that play out in real world deployment such as in education, finance, healthcare, and employment sectors. AI capability evaluations can capture detail about first-order effects, such as whether immediate system outputs are accurate, or contain toxic, biased or stereotypical content, but AI's second-order effects, i.e. any long-term outcomes and consequences that may result from AI use in the real world, have become a significant area of interest as the technology becomes embedded in our daily lives. These secondary effects can include shifts in user behavior, societal, cultural and economic ramifications, workforce transformations, and long-term downstream impacts that may result from a broad and growing set of risks. This position paper argues that measuring the indirect and secondary effects of AI will require expansion beyond static, single-turn approaches conducted in silico to include testing paradigms that can capture what actually materializes when people use AI technology in context. Specifically, we describe the need for data and methods that can facilitate contextual awareness and enable downstream interpretation and decision making about AI's secondary effects, and recommend requirements for a new ecosystem.

Andrew Thompson

Machine learning (ML) models are increasingly being used in metrology applications. However, for ML models to be credible in a metrology context they should be accompanied by principled uncertainty quantification. This paper addresses the challenge of uncertainty propagation through trained/fixed machine learning (ML) regression models. Analytical expressions for the mean and variance of the model output are obtained/presented for certain input data distributions and for a variety of ML models. Our results cover several popular ML models including linear regression, penalised linear regression, kernel ridge regression, Gaussian Processes (GPs), support vector machines (SVMs) and relevance vector machines (RVMs). We present numerical experiments in which we validate our methods and compare them with a Monte Carlo approach from a computational efficiency point of view. We also illustrate our methods in the context of a metrology application, namely modelling the state-of-health of lithium-ion cells based upon Electrical Impedance Spectroscopy (EIS) data

Samuel Bilson, Andrew Thompson, Declan Tucker et al.

Thermocouples are in widespread use in industry, but they are particularly susceptible to calibration drift in harsh environments. Self-validating thermocouples aim to address this issue by using a miniature phase-change cell (fixed-point) in close proximity to the measurement junction (tip) of the thermocouple. The fixed point is a crucible containing an ingot of metal with a known melting temperature. When the process temperature being monitored passes through the melting temperature of the ingot, the thermocouple output exhibits a "plateau" during melting. Since the melting temperature of the ingot is known, the thermocouple can be recalibrated in situ. Identifying the melting plateau to determine the onset of melting is reasonably well established but requires manual intervention involving zooming in on the region around the actual melting temperature, a process which can depend on the shape of the melting plateau. For the first time, we present a novel machine learning approach to recognize and identify the characteristic shape of the melting plateau and once identified, to quantity the point at which melting begins, along with its associated uncertainty. This removes the need for human intervention in locating and characterizing the melting point. Results from test data provided by CCPI Europe show 100% accuracy of melting plateau detection. They also show a cross-validated R2 of 0.99 on predictions of calibration drift.

Samuel Bilson, Maurice Cox, Anna Pustogvar et al.

Machine learning (ML) classification models are increasingly being used in a wide range of applications where it is important that predictions are accompanied by uncertainties, including in climate and earth observation, medical diagnosis and bioaerosol monitoring. The output of an ML classification model is a type of categorical variable known as a nominal property in the International Vocabulary of Metrology (VIM). However, concepts related to uncertainty evaluation for nominal properties are not defined in the VIM, nor is such evaluation addressed by the Guide to the Expression of Uncertainty in Measurement (GUM). In this paper we propose a metrological conceptual uncertainty evaluation framework for nominal properties. This framework is based on probability mass functions and summary statistics thereof, and it is applicable to ML classification. We also illustrate its use in the context of two applications that exemplify the issues and have significant societal impact, namely, climate and earth observation and medical diagnosis. Our framework would enable an extension of the GUM to uncertainty for nominal properties, which would make both applicable to ML classification models.

Mohammad Moulaeifard, Loic Coquelin, Mantas Rinkevičius et al.

Photoplethysmography (PPG) is a widely used non-invasive physiological sensing technique, suitable for various clinical applications. Such clinical applications are increasingly supported by machine learning methods, raising the question of the most appropriate input representation and model choice. Comprehensive comparisons, in particular across different input representations, are scarce. We address this gap in the research landscape by a comprehensive benchmarking study covering three kinds of input representations, interpretable features, image representations and raw waveforms, across prototypical regression and classification use cases: blood pressure and atrial fibrillation prediction. In both cases, the best results are achieved by deep neural networks operating on raw time series as input representations. Within this model class, best results are achieved by modern convolutional neural networks (CNNs). but depending on the task setup, shallow CNNs are often also very competitive. We envision that these results will be insightful for researchers to guide their choice on machine learning tasks for PPG data, even beyond the use cases presented in this work.

Andrew Thompson, Alexander Sommers, Alicia Russell-Gilbert et al.

Predictive maintenance has been used to optimize system repairs in the industrial, medical, and financial domains. This technique relies on the consistent ability to detect and predict anomalies in critical systems. AI models have been trained to detect system faults, improving predictive maintenance efficiency. Typically there is a lack of fault data to train these models, due to organizations working to keep fault occurrences and down time to a minimum. For newly installed systems, no fault data exists since they have yet to fail. By using diffusion models for synthetic data generation, the complex training datasets for these predictive models can be supplemented with high level synthetic fault data to improve their performance in anomaly detection. By learning the relationship between healthy and faulty data in similar systems, a diffusion model can attempt to apply that relationship to healthy data of a newly installed system that has no fault data. The diffusion model would then be able to generate useful fault data for the new system, and enable predictive models to be trained for predictive maintenance. The following paper demonstrates a system for generating useful, multivariate synthetic data for predictive maintenance, and how it can be applied to systems that have yet to fail.

Tameem Adel, Sam Bilson, Mark Levene et al.

We review research at the National Physical Laboratory (NPL) in the area of trustworthy artificial intelligence (TAI), and more specifically trustworthy machine learning (TML), in the context of metrology, the science of measurement. We describe three broad themes of TAI: technical, socio-technical and social, which play key roles in ensuring that the developed models are trustworthy and can be relied upon to make responsible decisions. From a metrology perspective we emphasise uncertainty quantification (UQ), and its importance within the framework of TAI to enhance transparency and trust in the outputs of AI systems. We then discuss three research areas within TAI that we are working on at NPL, and examine the certification of AI systems in terms of adherence to the characteristics of TAI.

Sandy Schoettler, Andrew Thompson, Rakshith Gopalakrishna et al.

Trigger-action platforms are a new type of system that connect IoT devices with web services. For example, the popular IFTTT platform can connect Fitbit with Google Calendar to add a bedtime reminder based on sleep history. However, these platforms present confidentiality and integrity risks as they run on public cloud infrastructure and compute over sensitive user data. This paper describes the design, implementation, and evaluation of Walnut, a low-trust trigger-action platform that mimics the functionality of IFTTT, while ensuring confidentiality of data and correctness of computation, at a low resource cost. The key enabler for Walnut is a new two-party secure computation protocol that (i) efficiently performs strings substitutions, which is a common computation in trigger-action platform workloads, and (ii) replicates computation over heterogeneous trusted-hardware machines from different vendors to ensure correctness of computation output as long as one of the machines is not compromised. An evaluation of Walnut demonstrates its plausible deployability and low overhead relative to a non-secure baseline--3.6x in CPU and 4.3x in network for all but a small percentage of programs.

Melanie Beckerleg, Andrew Thompson

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the form of binary factors which represent a decomposition of the matrix into tiles. Our approach is inspired by a popular algorithm from the data mining community called PROXIMUS: it adopts the same recursive partitioning approach while extending to missing data. The algorithm relies upon rank-one approximations of incomplete binary matrices, and we propose a linear programming (LP) approach for solving this subproblem. We also prove a $2$-approximation result for the LP approach which holds for any level of subsampling and for any subsampling pattern. Our numerical experiments show that TBMC outperforms existing methods on recommender systems arising in the context of real datasets.

Yin Xian, Yunchen Pu, Zhe Gan et al.

In this paper, we investigate DCTNet for audio signal classification. Its output feature is related to Cohen's class of time-frequency distributions. We introduce the use of adaptive DCTNet (A-DCTNet) for audio signals feature extraction. The A-DCTNet applies the idea of constant-Q transform, with its center frequencies of filterbanks geometrically spaced. The A-DCTNet is adaptive to different acoustic scales, and it can better capture low frequency acoustic information that is sensitive to human audio perception than features such as Mel-frequency spectral coefficients (MFSC). We use features extracted by the A-DCTNet as input for classifiers. Experimental results show that the A-DCTNet and Recurrent Neural Networks (RNN) achieve state-of-the-art performance in bird song classification rate, and improve artist identification accuracy in music data. They demonstrate A-DCTNet's applicability to signal processing problems.

Yin Xian, Andrew Thompson, Xiaobai Sun et al.

We introduce the use of DCTNet, an efficient approximation and alternative to PCANet, for acoustic signal classification. In PCANet, the eigenfunctions of the local sample covariance matrix (PCA) are used as filterbanks for convolution and feature extraction. When the eigenfunctions are well approximated by the Discrete Cosine Transform (DCT) functions, each layer of of PCANet and DCTNet is essentially a time-frequency representation. We relate DCTNet to spectral feature representation methods, such as the the short time Fourier transform (STFT), spectrogram and linear frequency spectral coefficients (LFSC). Experimental results on whale vocalization data show that DCTNet improves classification rate, demonstrating DCTNet's applicability to signal processing problems such as underwater acoustics.

Yang Cao, Andrew Thompson, Meng Wang et al.

We study sequential change-point detection procedures based on linear sketches of high-dimensional signal vectors using generalized likelihood ratio (GLR) statistics. The GLR statistics allow for an unknown post-change mean that represents an anomaly or novelty. We consider both fixed and time-varying projections, derive theoretical approximations to two fundamental performance metrics: the average run length (ARL) and the expected detection delay (EDD); these approximations are shown to be highly accurate by numerical simulations. We further characterize the relative performance measure of the sketching procedure compared to that without sketching and show that there can be little performance loss when the signal strength is sufficiently large, and enough number of sketches are used. Finally, we demonstrate the good performance of sketching procedures using simulation and real-data examples on solar flare detection and failure detection in power networks.

Qiang Qiu, Andrew Thompson, Robert Calderbank et al.

The Weyl transform is introduced as a rich framework for data representation. Transform coefficients are connected to the Walsh-Hadamard transform of multiscale autocorrelations, and different forms of dyadic periodicity in a signal are shown to appear as different features in its Weyl coefficients. The Weyl transform has a high degree of symmetry with respect to a large group of multiscale transformations, which allows compact yet discriminative representations to be obtained by pooling coefficients. The effectiveness of the Weyl transform is demonstrated through the example of textured image classification.