Matthew John Foster Willetts

• Doctor of Philosophy
• Research Fellow at University College London

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 re...

Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background could be clustered over the shape of the object and separately by the colour of the background. In t...

In this work we introduce a new approach for identifiable non-linear ICA models. Recently there has been a renaissance in identifiability results in deep generative models, not least for non-linear ICA. These prior works, however, have assumed access to a sufficiently-informative auxiliary set of observations, denoted $\mathbf{u}$. We show here how...

In this work we study Variational Autoencoders (VAEs) from the perspective of harmonic analysis. By viewing a VAE's latent space as a Gaussian Space, a variety of measure space, we derive a series of results that show that the encoder variance of a VAE controls the frequency content of the functions parameterised by the VAE encoder and decoder neur...

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 bijec...

We introduce an approach for training Variational Autoencoders (VAEs) that are certifiably robust to adversarial attack. Specifically, we first derive actionable bounds on the minimal size of an input perturbation required to change a VAE's reconstruction by more than an allowed amount, with these bounds depending on certain key parameters such as...

Successfully training Variational Autoencoders (VAEs) with a hierarchy of discrete latent variables remains an area of active research. 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-Quan...

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 marg...

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 crite...

Separating high-dimensional data like images into independent latent factors remains an open research problem. Here we develop a method that jointly learns a linear independent component analysis (ICA) model with non-linear bijective feature maps. By combining these two methods, ICA can learn interpretable latent structure for images. For non-squar...

We show that the stochasticity in training ResNets for image classification on GPUs in TensorFlow is dominated by the non-determinism from GPUs, rather than by the initialisation of the weights and biases of the network or by the sequence of minibatches given. The standard deviation of test set accuracy is 0.02 with fixed seeds, compared to 0.027 w...

In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by their colour, or by their type. Different attributes form a hierarchy, and we could wish to cluster in any of them...

Here we develop a new method for regularising neural networks where we learn a density estimator over the activations of all layers of the model. We extend recent work in data imputation using VAEs (Ivanov et al., 2018) so that we can obtain a posterior for an arbitrary subset of activations conditioned on the remainder. Our method has links both t...

This paper is concerned with the robustness of VAEs to adversarial attacks. We highlight that conventional VAEs are brittle under attack but that methods recently introduced for disentanglement such as $\beta$-TCVAE (Chen et al., 2018) improve robustness, as demonstrated through a variety of previously proposed adversarial attacks (Tabacof et al. (...

We introduce $\textit{semi-unsupervised learning}$, an extreme case of semi-supervised learning with ultra-sparse categorisation where some classes have no labels in the training set. That is, in the training data some classes are sparsely labelled and other classes appear only as unlabelled data. Many real-world datasets are conceivably of this ty...

Here we demonstrate a new deep generative model for classification. We introduce `semi-unsupervised learning', a problem regime related to transfer learning and zero/few shot learning where, in the training data, some classes are sparsely labelled and others entirely unlabelled. Models able to learn from training data of this type are potentially o...

Current public health guidelines on physical activity and sleep duration are limited by a reliance on subjective self-reported evidence. Using data from simple wrist-worn activity monitors, we developed a tailored machine learning model, using balanced random forests with Hidden Markov Models, to reliably detect a number of activity modes. We show...

Current public health guidelines on physical activity and sleep duration are limited by a reliance on subjective self-reported evidence. Using data from simple wrist-worn activity monitors, we developed a tailored machine learning model, using balanced random forests with Hidden Markov Models, to reliably detect a number of activity modes. We show...