arXiv subjects

Richard E. Turner

Publications and source records attributed to Richard E. Turner.

At least 73 records · Page 4Linked to original sources

arXiv2023

The Neural Process Family: Survey, Applications and Perspectives

The standard approaches to neural network implementation yield powerful function approximation capabilities but are limited in their abilities to learn meta representations and reason probabilistic uncertainties in their predictions. Gaussian processes, on the other hand, adopt the Bayesian learning scheme to estimate such uncertainties but are constrained by their efficiency and approximation capacity. The Neural Processes Family (NPF) intends to offer the best of both worlds by leveraging neural networks for meta-learning predictive uncertainties. Such potential has brought substantial research activity to the family in recent years. Therefore, a comprehensive survey of NPF models is needed to organize and relate their motivation, methodology, and experiments. This paper intends to address this gap while digging deeper into the formulation, research themes, and applications concerning the family members. We shed light on their potential to bring several recent advances in other deep learning domains under one umbrella. We then provide a rigorous taxonomy of the family and empirically demonstrate their capabilities for modeling data generating functions operating on 1-d, 2-d, and 3-d input domains. We conclude by discussing our perspectives on the promising directions that can fuel the research advances in the field. Code for our experiments will be made available at https://github.com/srvCodes/neural-processes-survey.

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arXiv2023

Beyond Intuition, a Framework for Applying GPs to Real-World Data

Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple low-dimensional datasets. We propose a framework to identify the suitability of GPs to a given problem and how to set up a robust and well-specified GP model. The guidelines formalise the decisions of experienced GP practitioners, with an emphasis on kernel design and options for computational scalability. The framework is then applied to a case study of glacier elevation change yielding more accurate results at test time.

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arXiv2023

Kernel Learning for Explainable Climate Science

The Upper Indus Basin, Himalayas provides water for 270 million people and countless ecosystems. However, precipitation, a key component to hydrological modelling, is poorly understood in this area. A key challenge surrounding this uncertainty comes from the complex spatial-temporal distribution of precipitation across the basin. In this work we propose Gaussian processes with structured non-stationary kernels to model precipitation patterns in the UIB. Previous attempts to quantify or model precipitation in the Hindu Kush Karakoram Himalayan region have often been qualitative or include crude assumptions and simplifications which cannot be resolved at lower resolutions. This body of research also provides little to no error propagation. We account for the spatial variation in precipitation with a non-stationary Gibbs kernel parameterised with an input dependent lengthscale. This allows the posterior function samples to adapt to the varying precipitation patterns inherent in the distinct underlying topography of the Indus region. The input dependent lengthscale is governed by a latent Gaussian process with a stationary squared-exponential kernel to allow the function level hyperparameters to vary smoothly. In ablation experiments we motivate each component of the proposed kernel by demonstrating its ability to model the spatial covariance, temporal structure and joint spatio-temporal reconstruction. We benchmark our model with a stationary Gaussian process and a Deep Gaussian processes.

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arXiv2023

Geometric Neural Diffusion Processes

Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many problems in the natural sciences incorporate symmetries and involve data living in non-Euclidean spaces. In this work, we extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We do so by a) constructing a noising process which admits, as limiting distribution, a geometric Gaussian process that transforms under the symmetry group of interest, and b) approximating the score with a neural network that is equivariant w.r.t. this group. We show that with these conditions, the generative functional model admits the same symmetry. We demonstrate scalability and capacity of the model, using a novel Langevin-based conditional sampler, to fit complex scalar and vector fields, with Euclidean and spherical codomain, on synthetic and real-world weather data.

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arXiv2023

Comparing the Efficacy of Fine-Tuning and Meta-Learning for Few-Shot Policy Imitation

In this paper we explore few-shot imitation learning for control problems, which involves learning to imitate a target policy by accessing a limited set of offline rollouts. This setting has been relatively under-explored despite its relevance to robotics and control applications. State-of-the-art methods developed to tackle few-shot imitation rely on meta-learning, which is expensive to train as it requires access to a distribution over tasks (rollouts from many target policies and variations of the base environment). Given this limitation we investigate an alternative approach, fine-tuning, a family of methods that pretrain on a single dataset and then fine-tune on unseen domain-specific data. Recent work has shown that fine-tuners outperform meta-learners in few-shot image classification tasks, especially when the data is out-of-domain. Here we evaluate to what extent this is true for control problems, proposing a simple yet effective baseline which relies on two stages: (i) training a base policy online via reinforcement learning (e.g. Soft Actor-Critic) on a single base environment, (ii) fine-tuning the base policy via behavioral cloning on a few offline rollouts of the target policy. Despite its simplicity this baseline is competitive with meta-learning methods on a variety of conditions and is able to imitate target policies trained on unseen variations of the original environment. Importantly, the proposed approach is practical and easy to implement, as it does not need any complex meta-training protocol. As a further contribution, we release an open source dataset called iMuJoCo (iMitation MuJoCo) consisting of 154 variants of popular OpenAI-Gym MuJoCo environments with associated pretrained target policies and rollouts, which can be used by the community to study few-shot imitation learning and offline reinforcement learning.

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arXiv2023

Environmental Sensor Placement with Convolutional Gaussian Neural Processes

Environmental sensors are crucial for monitoring weather conditions and the impacts of climate change. However, it is challenging to place sensors in a way that maximises the informativeness of their measurements, particularly in remote regions like Antarctica. Probabilistic machine learning models can suggest informative sensor placements by finding sites that maximally reduce prediction uncertainty. Gaussian process (GP) models are widely used for this purpose, but they struggle with capturing complex non-stationary behaviour and scaling to large datasets. This paper proposes using a convolutional Gaussian neural process (ConvGNP) to address these issues. A ConvGNP uses neural networks to parameterise a joint Gaussian distribution at arbitrary target locations, enabling flexibility and scalability. Using simulated surface air temperature anomaly over Antarctica as training data, the ConvGNP learns spatial and seasonal non-stationarities, outperforming a non-stationary GP baseline. In a simulated sensor placement experiment, the ConvGNP better predicts the performance boost obtained from new observations than GP baselines, leading to more informative sensor placements. We contrast our approach with physics-based sensor placement methods and propose future steps towards an operational sensor placement recommendation system. Our work could help to realise environmental digital twins that actively direct measurement sampling to improve the digital representation of reality.

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arXiv2023

Differentially private partitioned variational inference

Learning a privacy-preserving model from sensitive data which are distributed across multiple devices is an increasingly important problem. The problem is often formulated in the federated learning context, with the aim of learning a single global model while keeping the data distributed. Moreover, Bayesian learning is a popular approach for modelling, since it naturally supports reliable uncertainty estimates. However, Bayesian learning is generally intractable even with centralised non-private data and so approximation techniques such as variational inference are a necessity. Variational inference has recently been extended to the non-private federated learning setting via the partitioned variational inference algorithm. For privacy protection, the current gold standard is called differential privacy. Differential privacy guarantees privacy in a strong, mathematically clearly defined sense. In this paper, we present differentially private partitioned variational inference, the first general framework for learning a variational approximation to a Bayesian posterior distribution in the federated learning setting while minimising the number of communication rounds and providing differential privacy guarantees for data subjects. We propose three alternative implementations in the general framework, one based on perturbing local optimisation runs done by individual parties, and two based on perturbing updates to the global model (one using a version of federated averaging, the second one adding virtual parties to the protocol), and compare their properties both theoretically and empirically.

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arXiv2023

Autoregressive Conditional Neural Processes

Conditional neural processes (CNPs; Garnelo et al., 2018a) are attractive meta-learning models which produce well-calibrated predictions and are trainable via a simple maximum likelihood procedure. Although CNPs have many advantages, they are unable to model dependencies in their predictions. Various works propose solutions to this, but these come at the cost of either requiring approximate inference or being limited to Gaussian predictions. In this work, we instead propose to change how CNPs are deployed at test time, without any modifications to the model or training procedure. Instead of making predictions independently for every target point, we autoregressively define a joint predictive distribution using the chain rule of probability, taking inspiration from the neural autoregressive density estimator (NADE) literature. We show that this simple procedure allows factorised Gaussian CNPs to model highly dependent, non-Gaussian predictive distributions. Perhaps surprisingly, in an extensive range of tasks with synthetic and real data, we show that CNPs in autoregressive (AR) mode not only significantly outperform non-AR CNPs, but are also competitive with more sophisticated models that are significantly more computationally expensive and challenging to train. This performance is remarkable given that AR CNPs are not trained to model joint dependencies. Our work provides an example of how ideas from neural distribution estimation can benefit neural processes, and motivates research into the AR deployment of other neural process models.

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arXiv2023

Contextual Squeeze-and-Excitation for Efficient Few-Shot Image Classification

Recent years have seen a growth in user-centric applications that require effective knowledge transfer across tasks in the low-data regime. An example is personalization, where a pretrained system is adapted by learning on small amounts of labeled data belonging to a specific user. This setting requires high accuracy under low computational complexity, therefore the Pareto frontier of accuracy vs. adaptation cost plays a crucial role. In this paper we push this Pareto frontier in the few-shot image classification setting with a key contribution: a new adaptive block called Contextual Squeeze-and-Excitation (CaSE) that adjusts a pretrained neural network on a new task to significantly improve performance with a single forward pass of the user data (context). We use meta-trained CaSE blocks to conditionally adapt the body of a network and a fine-tuning routine to adapt a linear head, defining a method called UpperCaSE. UpperCaSE achieves a new state-of-the-art accuracy relative to meta-learners on the 26 datasets of VTAB+MD and on a challenging real-world personalization benchmark (ORBIT), narrowing the gap with leading fine-tuning methods with the benefit of orders of magnitude lower adaptation cost.

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arXiv2022

Adversarial Attacks are a Surprisingly Strong Baseline for Poisoning Few-Shot Meta-Learners

This paper examines the robustness of deployed few-shot meta-learning systems when they are fed an imperceptibly perturbed few-shot dataset. We attack amortized meta-learners, which allows us to craft colluding sets of inputs that are tailored to fool the system's learning algorithm when used as training data. Jointly crafted adversarial inputs might be expected to synergistically manipulate a classifier, allowing for very strong data-poisoning attacks that would be hard to detect. We show that in a white box setting, these attacks are very successful and can cause the target model's predictions to become worse than chance. However, in opposition to the well-known transferability of adversarial examples in general, the colluding sets do not transfer well to different classifiers. We explore two hypotheses to explain this: 'overfitting' by the attack, and mismatch between the model on which the attack is generated and that to which the attack is transferred. Regardless of the mitigation strategies suggested by these hypotheses, the colluding inputs transfer no better than adversarial inputs that are generated independently in the usual way.

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arXiv2022

Ice Core Dating using Probabilistic Programming

Ice cores record crucial information about past climate. However, before ice core data can have scientific value, the chronology must be inferred by estimating the age as a function of depth. Under certain conditions, chemicals locked in the ice display quasi-periodic cycles that delineate annual layers. Manually counting these noisy seasonal patterns to infer the chronology can be an imperfect and time-consuming process, and does not capture uncertainty in a principled fashion. In addition, several ice cores may be collected from a region, introducing an aspect of spatial correlation between them. We present an exploration of the use of probabilistic models for automatic dating of ice cores, using probabilistic programming to showcase its use for prototyping, automatic inference and maintainability, and demonstrate common failure modes of these tools.

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arXiv2022

Continual Novelty Detection

Novelty Detection methods identify samples that are not representative of a model's training set thereby flagging misleading predictions and bringing a greater flexibility and transparency at deployment time. However, research in this area has only considered Novelty Detection in the offline setting. Recently, there has been a growing realization in the computer vision community that applications demand a more flexible framework - Continual Learning - where new batches of data representing new domains, new classes or new tasks become available at different points in time. In this setting, Novelty Detection becomes more important, interesting and challenging. This work identifies the crucial link between the two problems and investigates the Novelty Detection problem under the Continual Learning setting. We formulate the Continual Novelty Detection problem and present a benchmark, where we compare several Novelty Detection methods under different Continual Learning settings. We show that Continual Learning affects the behaviour of novelty detection algorithms, while novelty detection can pinpoint insights in the behaviour of a continual learner. We further propose baselines and discuss possible research directions. We believe that the coupling of the two problems is a promising direction to bring vision models into practice.

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arXiv2022

Practical Conditional Neural Processes Via Tractable Dependent Predictions

Conditional Neural Processes (CNPs; Garnelo et al., 2018a) are meta-learning models which leverage the flexibility of deep learning to produce well-calibrated predictions and naturally handle off-the-grid and missing data. CNPs scale to large datasets and train with ease. Due to these features, CNPs appear well-suited to tasks from environmental sciences or healthcare. Unfortunately, CNPs do not produce correlated predictions, making them fundamentally inappropriate for many estimation and decision making tasks. Predicting heat waves or floods, for example, requires modelling dependencies in temperature or precipitation over time and space. Existing approaches which model output dependencies, such as Neural Processes (NPs; Garnelo et al., 2018b) or the FullConvGNP (Bruinsma et al., 2021), are either complicated to train or prohibitively expensive. What is needed is an approach which provides dependent predictions, but is simple to train and computationally tractable. In this work, we present a new class of Neural Process models that make correlated predictions and support exact maximum likelihood training that is simple and scalable. We extend the proposed models by using invertible output transformations, to capture non-Gaussian output distributions. Our models can be used in downstream estimation tasks which require dependent function samples. By accounting for output dependencies, our models show improved predictive performance on a range of experiments with synthetic and real data.

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arXiv2022

Multi-disciplinary fairness considerations in machine learning for clinical trials

While interest in the application of machine learning to improve healthcare has grown tremendously in recent years, a number of barriers prevent deployment in medical practice. A notable concern is the potential to exacerbate entrenched biases and existing health disparities in society. The area of fairness in machine learning seeks to address these issues of equity; however, appropriate approaches are context-dependent, necessitating domain-specific consideration. We focus on clinical trials, i.e., research studies conducted on humans to evaluate medical treatments. Clinical trials are a relatively under-explored application in machine learning for healthcare, in part due to complex ethical, legal, and regulatory requirements and high costs. Our aim is to provide a multi-disciplinary assessment of how fairness for machine learning fits into the context of clinical trials research and practice. We start by reviewing the current ethical considerations and guidelines for clinical trials and examine their relationship with common definitions of fairness in machine learning. We examine potential sources of unfairness in clinical trials, providing concrete examples, and discuss the role machine learning might play in either mitigating potential biases or exacerbating them when applied without care. Particular focus is given to adaptive clinical trials, which may employ machine learning. Finally, we highlight concepts that require further investigation and development, and emphasize new approaches to fairness that may be relevant to the design of clinical trials.

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arXiv2022

Partitioned Variational Inference: A Framework for Probabilistic Federated Learning

The proliferation of computing devices has brought about an opportunity to deploy machine learning models on new problem domains using previously inaccessible data. Traditional algorithms for training such models often require data to be stored on a single machine with compute performed by a single node, making them unsuitable for decentralised training on multiple devices. This deficiency has motivated the development of federated learning algorithms, which allow multiple data owners to train collaboratively and use a shared model whilst keeping local data private. However, many of these algorithms focus on obtaining point estimates of model parameters, rather than probabilistic estimates capable of capturing model uncertainty, which is essential in many applications. Variational inference (VI) has become the method of choice for fitting many modern probabilistic models. In this paper we introduce partitioned variational inference (PVI), a general framework for performing VI in the federated setting. We develop new supporting theory for PVI, demonstrating a number of properties that make it an attractive choice for practitioners; use PVI to unify a wealth of fragmented, yet related literature; and provide empirical results that showcase the effectiveness of PVI in a variety of federated settings.

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arXiv2022

Modelling Non-Smooth Signals with Complex Spectral Structure

The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth signals. Moreover, inference in the GPCM currently requires (1) a mean-field assumption, resulting in poorly calibrated uncertainties, and (2) a tedious variational optimisation of large covariance matrices. We redesign the GPCM model to induce a richer distribution over the spectrum with relaxed assumptions about smoothness: the Causal Gaussian Process Convolution Model (CGPCM) introduces a causality assumption into the GPCM, and the Rough Gaussian Process Convolution Model (RGPCM) can be interpreted as a Bayesian nonparametric generalisation of the fractional Ornstein-Uhlenbeck process. We also propose a more effective variational inference scheme, going beyond the mean-field assumption: we design a Gibbs sampler which directly samples from the optimal variational solution, circumventing any variational optimisation entirely. The proposed variations of the GPCM are validated in experiments on synthetic and real-world data, showing promising results.

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arXiv2022

Bayesian Neural Network Priors Revisited

Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using stochastic gradient descent (SGD). We find that convolutional neural network (CNN) and ResNet weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. We show that building these observations into priors can lead to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.

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arXiv2022

How Tight Can PAC-Bayes be in the Small Data Regime?

In this paper, we investigate the question: Given a small number of datapoints, for example N = 30, how tight can PAC-Bayes and test set bounds be made? For such small datasets, test set bounds adversely affect generalisation performance by withholding data from the training procedure. In this setting, PAC-Bayes bounds are especially attractive, due to their ability to use all the data to simultaneously learn a posterior and bound its generalisation risk. We focus on the case of i.i.d. data with a bounded loss and consider the generic PAC-Bayes theorem of Germain et al. While their theorem is known to recover many existing PAC-Bayes bounds, it is unclear what the tightest bound derivable from their framework is. For a fixed learning algorithm and dataset, we show that the tightest possible bound coincides with a bound considered by Catoni; and, in the more natural case of distributions over datasets, we establish a lower bound on the best bound achievable in expectation. Interestingly, this lower bound recovers the Chernoff test set bound if the posterior is equal to the prior. Moreover, to illustrate how tight these bounds can be, we study synthetic one-dimensional classification tasks in which it is feasible to meta-learn both the prior and the form of the bound to numerically optimise for the tightest bounds possible. We find that in this simple, controlled scenario, PAC-Bayes bounds are competitive with comparable, commonly used Chernoff test set bounds. However, the sharpest test set bounds still lead to better guarantees on the generalisation error than the PAC-Bayes bounds we consider.

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