arXiv subjects

Chris Holmes

Publications and source records attributed to Chris Holmes.

At least 37 records · Page 2Linked to original sources

arXiv2024

Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective

In-context learning (ICL) has emerged as a particularly remarkable characteristic of Large Language Models (LLM): given a pretrained LLM and an observed dataset, LLMs can make predictions for new data points from the same distribution without fine-tuning. Numerous works have postulated ICL as approximately Bayesian inference, rendering this a natural hypothesis. In this work, we analyse this hypothesis from a new angle through the martingale property, a fundamental requirement of a Bayesian learning system for exchangeable data. We show that the martingale property is a necessary condition for unambiguous predictions in such scenarios, and enables a principled, decomposed notion of uncertainty vital in trustworthy, safety-critical systems. We derive actionable checks with corresponding theory and test statistics which must hold if the martingale property is satisfied. We also examine if uncertainty in LLMs decreases as expected in Bayesian learning when more data is observed. In three experiments, we provide evidence for violations of the martingale property, and deviations from a Bayesian scaling behaviour of uncertainty, falsifying the hypothesis that ICL is Bayesian.

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arXiv2024

Approximations to the Fisher Information Metric of Deep Generative Models for Out-Of-Distribution Detection

Likelihood-based deep generative models such as score-based diffusion models and variational autoencoders are state-of-the-art machine learning models approximating high-dimensional distributions of data such as images, text, or audio. One of many downstream tasks they can be naturally applied to is out-of-distribution (OOD) detection. However, seminal work by Nalisnick et al. which we reproduce showed that deep generative models consistently infer higher log-likelihoods for OOD data than data they were trained on, marking an open problem. In this work, we analyse using the gradient of a data point with respect to the parameters of the deep generative model for OOD detection, based on the simple intuition that OOD data should have larger gradient norms than training data. We formalise measuring the size of the gradient as approximating the Fisher information metric. We show that the Fisher information matrix (FIM) has large absolute diagonal values, motivating the use of chi-square distributed, layer-wise gradient norms as features. We combine these features to make a simple, model-agnostic and hyperparameter-free method for OOD detection which estimates the joint density of the layer-wise gradient norms for a given data point. We find that these layer-wise gradient norms are weakly correlated, rendering their combined usage informative, and prove that the layer-wise gradient norms satisfy the principle of (data representation) invariance. Our empirical results indicate that this method outperforms the Typicality test for most deep generative models and image dataset pairings.

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arXiv2024

On the Stability of General Bayesian Inference

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from the decision-maker but a level of interpolation is required to arrive at a likelihood model. As a result, an often computationally convenient canonical form is used in place of the decision-maker's true beliefs. Equally, in practice, observational datasets often contain unforeseen heterogeneities and recording errors and therefore do not necessarily correspond to how the process was idealised by the decision-maker. Acknowledging such imprecisions, a faithful Bayesian analysis should ideally be stable across reasonable equivalence classes of such inputs. We are able to guarantee that traditional Bayesian updating provides stability across only a very strict class of likelihood models and data generating processes, requiring the decision-maker to elicit their beliefs and understand how the data was generated with an unreasonable degree of accuracy. On the other hand, a generalised Bayesian alternative using the $β$-divergence loss function is shown to be stable across practical and interpretable neighbourhoods, providing assurances that posterior inferences are not overly dependent on accidentally introduced spurious specifications or data collection errors. We illustrate this in linear regression, binary classification, and mixture modelling examples, showing that stable updating does not compromise the ability to learn about the data generating process. These stability results provide a compelling justification for using generalised Bayes to facilitate inference under simplified canonical models.

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arXiv2024

Hierarchical Bias-Driven Stratification for Interpretable Causal Effect Estimation

Interpretability and transparency are essential for incorporating causal effect models from observational data into policy decision-making. They can provide trust for the model in the absence of ground truth labels to evaluate the accuracy of such models. To date, attempts at transparent causal effect estimation consist of applying post hoc explanation methods to black-box models, which are not interpretable. Here, we present BICauseTree: an interpretable balancing method that identifies clusters where natural experiments occur locally. Our approach builds on decision trees with a customized objective function to improve balancing and reduce treatment allocation bias. Consequently, it can additionally detect subgroups presenting positivity violations, exclude them, and provide a covariate-based definition of the target population we can infer from and generalize to. We evaluate the method's performance using synthetic and realistic datasets, explore its bias-interpretability tradeoff, and show that it is comparable with existing approaches.

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arXiv2024

Explainable AI for survival analysis: a median-SHAP approach

With the adoption of machine learning into routine clinical practice comes the need for Explainable AI methods tailored to medical applications. Shapley values have sparked wide interest for locally explaining models. Here, we demonstrate their interpretation strongly depends on both the summary statistic and the estimator for it, which in turn define what we identify as an 'anchor point'. We show that the convention of using a mean anchor point may generate misleading interpretations for survival analysis and introduce median-SHAP, a method for explaining black-box models predicting individual survival times.

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arXiv2024

A Unified Framework for U-Net Design and Analysis

U-Nets are a go-to, state-of-the-art neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper, we provide a framework for designing and analysing general U-Net architectures. We present theoretical results which characterise the role of the encoder and decoder in a U-Net, their high-resolution scaling limits and their conjugacy to ResNets via preconditioning. We propose Multi-ResNets, U-Nets with a simplified, wavelet-based encoder without learnable parameters. Further, we show how to design novel U-Net architectures which encode function constraints, natural bases, or the geometry of the data. In diffusion models, our framework enables us to identify that high-frequency information is dominated by noise exponentially faster, and show how U-Nets with average pooling exploit this. In our experiments, we demonstrate how Multi-ResNets achieve competitive and often superior performance compared to classical U-Nets in image segmentation, PDE surrogate modelling, and generative modelling with diffusion models. Our U-Net framework paves the way to study the theoretical properties of U-Nets and design natural, scalable neural architectures for a multitude of problems beyond the square.

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arXiv2023

A large-scale and PCR-referenced vocal audio dataset for COVID-19

The UK COVID-19 Vocal Audio Dataset is designed for the training and evaluation of machine learning models that classify SARS-CoV-2 infection status or associated respiratory symptoms using vocal audio. The UK Health Security Agency recruited voluntary participants through the national Test and Trace programme and the REACT-1 survey in England from March 2021 to March 2022, during dominant transmission of the Alpha and Delta SARS-CoV-2 variants and some Omicron variant sublineages. Audio recordings of volitional coughs, exhalations, and speech were collected in the 'Speak up to help beat coronavirus' digital survey alongside demographic, self-reported symptom and respiratory condition data, and linked to SARS-CoV-2 test results. The UK COVID-19 Vocal Audio Dataset represents the largest collection of SARS-CoV-2 PCR-referenced audio recordings to date. PCR results were linked to 70,794 of 72,999 participants and 24,155 of 25,776 positive cases. Respiratory symptoms were reported by 45.62% of participants. This dataset has additional potential uses for bioacoustics research, with 11.30% participants reporting asthma, and 27.20% with linked influenza PCR test results.

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arXiv2023

Differentially Private Statistical Inference through $β$-Divergence One Posterior Sampling

Differential privacy guarantees allow the results of a statistical analysis involving sensitive data to be released without compromising the privacy of any individual taking part. Achieving such guarantees generally requires the injection of noise, either directly into parameter estimates or into the estimation process. Instead of artificially introducing perturbations, sampling from Bayesian posterior distributions has been shown to be a special case of the exponential mechanism, producing consistent, and efficient private estimates without altering the data generative process. The application of current approaches has, however, been limited by their strong bounding assumptions which do not hold for basic models, such as simple linear regressors. To ameliorate this, we propose $β$D-Bayes, a posterior sampling scheme from a generalised posterior targeting the minimisation of the $β$-divergence between the model and the data generating process. This provides private estimation that is generally applicable without requiring changes to the underlying model and consistently learns the data generating parameter. We show that $β$D-Bayes produces more precise inference estimation for the same privacy guarantees, and further facilitates differentially private estimation via posterior sampling for complex classifiers and continuous regression models such as neural networks for the first time.

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arXiv2023

PWSHAP: A Path-Wise Explanation Model for Targeted Variables

Predictive black-box models can exhibit high accuracy but their opaque nature hinders their uptake in safety-critical deployment environments. Explanation methods (XAI) can provide confidence for decision-making through increased transparency. However, existing XAI methods are not tailored towards models in sensitive domains where one predictor is of special interest, such as a treatment effect in a clinical model, or ethnicity in policy models. We introduce Path-Wise Shapley effects (PWSHAP), a framework for assessing the targeted effect of a binary (e.g.~treatment) variable from a complex outcome model. Our approach augments the predictive model with a user-defined directed acyclic graph (DAG). The method then uses the graph alongside on-manifold Shapley values to identify effects along causal pathways whilst maintaining robustness to adversarial attacks. We establish error bounds for the identified path-wise Shapley effects and for Shapley values. We show PWSHAP can perform local bias and mediation analyses with faithfulness to the model. Further, if the targeted variable is randomised we can quantify local effect modification. We demonstrate the resolution, interpretability, and true locality of our approach on examples and a real-world experiment.

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arXiv2023

Challenges and Opportunities of Shapley values in a Clinical Context

With the adoption of machine learning-based solutions in routine clinical practice, the need for reliable interpretability tools has become pressing. Shapley values provide local explanations. The method gained popularity in recent years. Here, we reveal current misconceptions about the ``true to the data'' or ``true to the model'' trade-off and demonstrate its importance in a clinical context. We show that the interpretation of Shapley values, which strongly depends on the choice of a reference distribution for modeling feature removal, is often misunderstood. We further advocate that for applications in medicine, the reference distribution should be tailored to the underlying clinical question. Finally, we advise on the right reference distributions for specific medical use cases.

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arXiv2023

Semiparametric posterior corrections

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate low-dimensional functionals of interest without being restricted by the holistic Bayesian formalism. Starting from a conventional nonparametric posterior, we target the functional of interest by transforming the entire distribution with a Bayesian bootstrap correction. We provide conditions for the resulting $\textit{one-step posterior}$ to possess calibrated frequentist properties and specialize the results for several canonical examples: the integrated squared density, the mean of a missing-at-random outcome, and the average causal treatment effect on the treated. The procedure is computationally attractive, requiring only a simple, efficient post-processing step that can be attached onto any arbitrary posterior sampling algorithm. Using the ACIC 2016 causal data analysis competition, we illustrate that our approach can outperform the existing state-of-the-art through the propagation of Bayesian uncertainty.

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arXiv2023

Bayesian Lesion Estimation with a Structured Spike-and-Slab Prior

Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding aging and inflammatory diseases. We propose a scalable hierarchical Bayesian spatial model, called BLESS, capable of handling binary responses by placing continuous spike-and-slab mixture priors on spatially-varying parameters and enforcing spatial dependency on the parameter dictating the amount of sparsity within the probability of inclusion. The use of mean-field variational inference with dynamic posterior exploration, which is an annealing-like strategy that improves optimization, allows our method to scale to large sample sizes. Our method also accounts for underestimation of posterior variance due to variational inference by providing an approximate posterior sampling approach based on Bayesian bootstrap ideas and spike-and-slab priors with random shrinkage targets. Besides accurate uncertainty quantification, this approach is capable of producing novel cluster size based imaging statistics, such as credible intervals of cluster size, and measures of reliability of cluster occurrence. Lastly, we validate our results via simulation studies and an application to the UK Biobank, a large-scale lesion mapping study with a sample size of 40,000 subjects.

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arXiv2023

Learning from data with structured missingness

Missing data are an unavoidable complication in many machine learning tasks. When data are `missing at random' there exist a range of tools and techniques to deal with the issue. However, as machine learning studies become more ambitious, and seek to learn from ever-larger volumes of heterogeneous data, an increasingly encountered problem arises in which missing values exhibit an association or structure, either explicitly or implicitly. Such `structured missingness' raises a range of challenges that have not yet been systematically addressed, and presents a fundamental hindrance to machine learning at scale. Here, we outline the current literature and propose a set of grand challenges in learning from data with structured missingness.

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arXiv2023

Audio-based AI classifiers show no evidence of improved COVID-19 screening over simple symptoms checkers

Recent work has reported that AI classifiers trained on audio recordings can accurately predict severe acute respiratory syndrome coronavirus 2 (SARSCoV2) infection status. Here, we undertake a large scale study of audio-based deep learning classifiers, as part of the UK governments pandemic response. We collect and analyse a dataset of audio recordings from 67,842 individuals with linked metadata, including reverse transcription polymerase chain reaction (PCR) test outcomes, of whom 23,514 tested positive for SARS CoV 2. Subjects were recruited via the UK governments National Health Service Test-and-Trace programme and the REal-time Assessment of Community Transmission (REACT) randomised surveillance survey. In an unadjusted analysis of our dataset AI classifiers predict SARS-CoV-2 infection status with high accuracy (Receiver Operating Characteristic Area Under the Curve (ROCAUC) 0.846 [0.838, 0.854]) consistent with the findings of previous studies. However, after matching on measured confounders, such as age, gender, and self reported symptoms, our classifiers performance is much weaker (ROC-AUC 0.619 [0.594, 0.644]). Upon quantifying the utility of audio based classifiers in practical settings, we find them to be outperformed by simple predictive scores based on user reported symptoms.

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arXiv2023

Statistical Design and Analysis for Robust Machine Learning: A Case Study from COVID-19

Since early in the coronavirus disease 2019 (COVID-19) pandemic, there has been interest in using artificial intelligence methods to predict COVID-19 infection status based on vocal audio signals, for example cough recordings. However, existing studies have limitations in terms of data collection and of the assessment of the performances of the proposed predictive models. This paper rigorously assesses state-of-the-art machine learning techniques used to predict COVID-19 infection status based on vocal audio signals, using a dataset collected by the UK Health Security Agency. This dataset includes acoustic recordings and extensive study participant meta-data. We provide guidelines on testing the performance of methods to classify COVID-19 infection status based on acoustic features and we discuss how these can be extended more generally to the development and assessment of predictive methods based on public health datasets.

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arXiv2023

Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the posterior predictive of the Dirichlet process mixture model. In general, direct estimation of the posterior predictive is intractable and so methods typically resort to approximating the posterior distribution as an intermediate step. The recent development of quasi-Bayesian predictive copula updates, however, has made it possible to perform tractable predictive density estimation without the need for posterior approximation. Although these estimators are computationally appealing, they tend to struggle on non-smooth data distributions. This is due to the comparatively restrictive form of the likelihood models from which the proposed copula updates were derived. To address this shortcoming, we consider a Bayesian nonparametric model with an autoregressive likelihood decomposition and a Gaussian process prior. While the predictive update of such a model is typically intractable, we derive a quasi-Bayesian predictive update that achieves state-of-the-art results in small-data regimes.

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arXiv2023

A Multi-Resolution Framework for U-Nets with Applications to Hierarchical VAEs

U-Net architectures are ubiquitous in state-of-the-art deep learning, however their regularisation properties and relationship to wavelets are understudied. In this paper, we formulate a multi-resolution framework which identifies U-Nets as finite-dimensional truncations of models on an infinite-dimensional function space. We provide theoretical results which prove that average pooling corresponds to projection within the space of square-integrable functions and show that U-Nets with average pooling implicitly learn a Haar wavelet basis representation of the data. We then leverage our framework to identify state-of-the-art hierarchical VAEs (HVAEs), which have a U-Net architecture, as a type of two-step forward Euler discretisation of multi-resolution diffusion processes which flow from a point mass, introducing sampling instabilities. We also demonstrate that HVAEs learn a representation of time which allows for improved parameter efficiency through weight-sharing. We use this observation to achieve state-of-the-art HVAE performance with half the number of parameters of existing models, exploiting the properties of our continuous-time formulation.

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arXiv2022

Generating the right evidence at the right time: Principles of a new class of flexible augmented clinical trial designs

The past few years have seen an increasing number of initiatives aimed at integrating information generated outside of confirmatory randomised clinical trials (RCTs) into drug development. However, data generated non-concurrently and through observational studies can provide results that are difficult to compare with randomised trial data. Moreover, the scientific questions these data can serve to answer often remain vague. Our starting point is to use clearly defined objectives for evidence generation, which are formulated towards early discussion with health technology assessment (HTA) bodies and are additional to regulatory requirements for authorisation of a new treatment. We propose FACTIVE (Flexible Augmented Clinical Trial for Improved eVidencE generation), a new class of study designs enabling flexible augmentation of confirmatory randomised controlled trials with concurrent and close-to-real-world elements. These enabling designs facilitate estimation of certain treatment effects in the confirmatory part and other, complementary treatment effects in a concurrent real-world part. Each stakeholder should use the evidence that is relevant within their own decision-making framework. High quality data are generated under one single protocol and the use of randomisation ensures rigorous statistical inference and interpretation within and between the different parts of the experiment. Evidence for the decision-making of HTA bodies could be available earlier than is currently the case.

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