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Researcher profile

Chris Holmes

Chris Holmes contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer VisionCryptography and Securitycs.CYeess.SPMethodologyApplicationsComputationphysics.soc-phPopulations and Evolution

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Published work

12 published item(s)

preprint2026arXiv

Variational predictive resampling

Bayesian inference provides principled uncertainty quantification, but accurate posterior sampling with MCMC can be computationally prohibitive for modern applications. Variational inference (VI) offers a scalable alternative and often yields accurate predictive distributions, but cheap variational families such as mean-field (MF) can produce over-concentrated approximations that miss posterior dependence. We propose variational predictive resampling (VPR), a scalable posterior sampling method that exploits VI's predictive strength within a predictive-resampling framework to better approximate the Bayesian posterior. Given a prior-likelihood pair, VPR repeatedly imputes future observations from the current variational predictive, updates the variational approximation after each imputation, and records the parameter value implied by the completed sample. We establish conditions under which the law of the parameter returned by VPR is well defined and show that its finite-horizon approximation converges to this limit. In a tractable Gaussian location model, we show that VPR with MF variational predictives converges to the exact Bayesian posterior, whereas the optimal MF-VI approximation retains a non-vanishing asymptotic gap. Experiments on linear regression, logistic regression, and hierarchical linear mixed-effects models demonstrate that VPR substantially improves posterior uncertainty quantification and recovers posterior dependence missed by MF-VI, while remaining computationally competitive with, and often more efficient than, MCMC.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Causal predictive inference and target trial emulation

Causal inference from observational data can be viewed as a missing data problem arising from a hypothetical population-scale randomized trial matched to the observational study. This links a target trial protocol with a corresponding generative predictive model for inference, providing a complete framework for transparent communication of causal assumptions and statistical uncertainty on treatment effects, without the need for counterfactuals. The intuitive foundation for the work is that a whole population randomized trial would provide answers to any observable causal question with certainty. Thus, our fundamental problem of causal inference is the missingness of the hypothetical target trial data, which we solve through repeated imputation from a generative predictive model conditioned on the observational data. Causal assumptions map to intuitive conditions on the transportability of predictive models across populations and conditions. We demonstrate our approach on a real data application to studying the effects of maternal smoking on birthweights using extensions of Bayesian additive regression trees and inverse probability weighting.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mitigating Statistical Bias within Differentially Private Synthetic Data

Increasing interest in privacy-preserving machine learning has led to new and evolved approaches for generating private synthetic data from undisclosed real data. However, mechanisms of privacy preservation can significantly reduce the utility of synthetic data, which in turn impacts downstream tasks such as learning predictive models or inference. We propose several re-weighting strategies using privatised likelihood ratios that not only mitigate statistical bias of downstream estimators but also have general applicability to differentially private generative models. Through large-scale empirical evaluation, we show that private importance weighting provides simple and effective privacy-compliant augmentation for general applications of synthetic data.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Deep Generative Pattern-Set Mixture Models for Nonignorable Missingness

We propose a variational autoencoder architecture to model both ignorable and nonignorable missing data using pattern-set mixtures as proposed by Little (1993). Our model explicitly learns to cluster the missing data into missingness pattern sets based on the observed data and missingness masks. Underpinning our approach is the assumption that the data distribution under missingness is probabilistically semi-supervised by samples from the observed data distribution. Our setup trades off the characteristics of ignorable and nonignorable missingness and can thus be applied to data of both types. We evaluate our method on a wide range of data sets with different types of missingness and achieve state-of-the-art imputation performance. Our model outperforms many common imputation algorithms, especially when the amount of missing data is high and the missingness mechanism is nonignorable.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Explicit Regularisation in Gaussian Noise Injections

We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Improving VAEs' Robustness to Adversarial Attack

Variational autoencoders (VAEs) have recently been shown to be vulnerable to adversarial attacks, wherein they are fooled into reconstructing a chosen target image. However, how to defend against such attacks remains an open problem. We make significant advances in addressing this issue by introducing methods for producing adversarially robust VAEs. Namely, we first demonstrate that methods proposed to obtain disentangled latent representations produce VAEs that are more robust to these attacks. However, this robustness comes at the cost of reducing the quality of the reconstructions. We ameliorate this by applying disentangling methods to hierarchical VAEs. The resulting models produce high-fidelity autoencoders that are also adversarially robust. We confirm their capabilities on several different datasets and with current state-of-the-art VAE adversarial attacks, and also show that they increase the robustness of downstream tasks to attack.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Learning Bijective Feature Maps for Linear ICA

Separating high-dimensional data like images into independent latent factors, i.e independent component analysis (ICA), remains an open research problem. As we show, existing probabilistic deep generative models (DGMs), which are tailor-made for image data, underperform on non-linear ICA tasks. To address this, we propose a DGM which combines bijective feature maps with a linear ICA model to learn interpretable latent structures for high-dimensional data. Given the complexities of jointly training such a hybrid model, we introduce novel theory that constrains linear ICA to lie close to the manifold of orthogonal rectangular matrices, the Stiefel manifold. By doing so we create models that converge quickly, are easy to train, and achieve better unsupervised latent factor discovery than flow-based models, linear ICA, and Variational Autoencoders on images.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Relaxed-Responsibility Hierarchical Discrete VAEs

Successfully training Variational Autoencoders (VAEs) with a hierarchy of discrete latent variables remains an area of active research. Vector-Quantised VAEs are a powerful approach to discrete VAEs, but naive hierarchical extensions can be unstable when training. Leveraging insights from classical methods of inference we introduce \textit{Relaxed-Responsibility Vector-Quantisation}, a novel way to parameterise discrete latent variables, a refinement of relaxed Vector-Quantisation that gives better performance and more stable training. This enables a novel approach to hierarchical discrete variational autoencoders with numerous layers of latent variables (here up to 32) that we train end-to-end. Within hierarchical probabilistic deep generative models with discrete latent variables trained end-to-end, we achieve state-of-the-art bits-per-dim results for various standard datasets. % Unlike discrete VAEs with a single layer of latent variables, we can produce samples by ancestral sampling: it is not essential to train a second autoregressive generative model over the learnt latent representations to then sample from and then decode. % Moreover, that latter approach in these deep hierarchical models would require thousands of forward passes to generate a single sample. Further, we observe different layers of our model become associated with different aspects of the data.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Towards a Theoretical Understanding of the Robustness of Variational Autoencoders

We make inroads into understanding the robustness of Variational Autoencoders (VAEs) to adversarial attacks and other input perturbations. While previous work has developed algorithmic approaches to attacking and defending VAEs, there remains a lack of formalization for what it means for a VAE to be robust. To address this, we develop a novel criterion for robustness in probabilistic models: $r$-robustness. We then use this to construct the first theoretical results for the robustness of VAEs, deriving margins in the input space for which we can provide guarantees about the resulting reconstruction. Informally, we are able to define a region within which any perturbation will produce a reconstruction that is similar to the original reconstruction. To support our analysis, we show that VAEs trained using disentangling methods not only score well under our robustness metrics, but that the reasons for this can be interpreted through our theoretical results.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Inferring proximity from Bluetooth Low Energy RSSI with Unscented Kalman Smoothers

The Covid-19 pandemic has resulted in a variety of approaches for managing infection outbreaks in international populations. One example is mobile phone applications, which attempt to alert infected individuals and their contacts by automatically inferring two key components of infection risk: the proximity to an individual who may be infected, and the duration of proximity. The former component, proximity, relies on Bluetooth Low Energy (BLE) Received Signal Strength Indicator(RSSI) as a distance sensor, and this has been shown to be problematic; not least because of unpredictable variations caused by different device types, device location on-body, device orientation, the local environment and the general noise associated with radio frequency propagation. In this paper, we present an approach that infers posterior probabilities over distance given sequences of RSSI values. Using a single-dimensional Unscented Kalman Smoother (UKS) for non-linear state space modelling, we outline several Gaussian process observation transforms, including: a generative model that directly captures sources of variation; and a discriminative model that learns a suitable observation function from training data using both distance and infection risk as optimisation objective functions. Our results show that good risk prediction can be achieved in $\mathcal{O}(n)$ time on real-world data sets, with the UKS outperforming more traditional classification methods learned from the same training data.

0 citations0 reviewsNo code linkedOpen access