Stephen J. Roberts

TMLR Journal 2023 Journal Article

On the Sample Complexity of Lipschitz Constant Estimation

• Julien Walden Huang
• Stephen J. Roberts
• Jan-Peter Calliess

Estimating the Lipschitz constant of a function, also known as Lipschitz learning, is a fundamental problem with broad applications in fields such as control and global optimization. In this paper, we study the Lipschitz learning problem with minimal parametric assumptions on the target function. As a first theoretical contribution, we derive novel lower bounds on the sample complexity of this problem for both noise-free and noisy settings under mild assumptions. Moreover, we propose a simple Lipschitz learning algorithm called $\textit{Lipschitz Constant Estimation by Least Squares Regression}$ (referred to as LCLS). We show that LCLS is asymptotically consistent for general noise assumptions and offers finite sample guarantees that can be translated to new upper bounds on the sample complexity of the Lipschitz learning problem. Our analysis shows that the sample complexity rates derived in this paper are optimal in both the noise-free setting and in the noisy setting when the noise is assumed to follow a Gaussian distribution and that LCLS is a sample-optimal algorithm in both cases. Finally, we show that by design, the LCLS algorithm is computationally faster than existing theoretically consistent methods, and can be readily adapted to various noise assumptions with little to no prior knowledge of the target function properties or noise distribution.

AAMAS Conference 2022 Conference Paper

On-the-fly Strategy Adaptation for ad-hoc Agent Coordination

• Jaleh Zand
• Jack Parker-Holder
• Stephen J. Roberts

Training agents in cooperative settings offers the promise of AI agents able to interact effectively with humans (and other agents) in the real world. Multi-agent reinforcement learning (MARL) has the potential to achieve this goal, demonstrating success in a series of challenging problems. However, whilst these advances are significant, the vast majority of focus has been on the self-play paradigm. This often results in a coordination problem, caused by agents learning to make use of arbitrary conventions when playing with themselves. This means that even the strongest self-play agents may have very low cross-play with other agents, including other initializations of the same algorithm. In this paper we propose to solve this problem by adapting agent strategies on the fly, using a posterior belief over the other agents’ strategy. Concretely, we consider the problem of selecting a strategy from a finite set of previously trained agents, to play with an unknown partner. We propose an extension of the classic statistical technique, Gibbs sampling, to update beliefs about other agents and obtain close to optimal ad-hoc performance. Despite its simplicity, our method is able to achieve strong cross-play with unseen partners in the challenging card game of Hanabi, achieving successful ad-hoc coordination without knowledge of the partner’s strategy a priori.

ICLR Conference 2022 Conference Paper

Revisiting Design Choices in Offline Model Based Reinforcement Learning

• Cong Lu
• Philip J. Ball
• Jack Parker-Holder
• Michael A. Osborne
• Stephen J. Roberts

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.

ICLR Conference 2022 Conference Paper

Robust and Scalable SDE Learning: A Functional Perspective

• Scott Alexander Cameron
• Tyron Luke Cameron
• Arnu Pretorius
• Stephen J. Roberts

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. This facilitates the effective use of large-scale parallel hardware for massive decreases in computation time.

AAAI Conference 2022 Conference Paper

Same State, Different Task: Continual Reinforcement Learning without Interference

• Samuel Kessler
• Jack Parker-Holder
• Philip Ball
• Stefan Zohren
• Stephen J. Roberts

Continual Learning (CL) considers the problem of training an agent sequentially on a set of tasks while seeking to retain performance on all previous tasks. A key challenge in CL is catastrophic forgetting, which arises when performance on a previously mastered task is reduced when learning a new task. While a variety of methods exist to combat forgetting, in some cases tasks are fundamentally incompatible with each other and thus cannot be learnt by a single policy. This can occur, in reinforcement learning (RL) when an agent may be rewarded for achieving different goals from the same observation. In this paper we formalize this “interference” as distinct from the problem of forgetting. We show that existing CL methods based on single neural network predictors with shared replay buffers fail in the presence of interference. Instead, we propose a simple method, OWL, to address this challenge. OWL learns a factorized policy, using shared feature extraction layers, but separate heads, each specializing on a new task. The separate heads in OWL are used to prevent interference. At test time, we formulate policy selection as a multi-armed bandit problem, and show it is possible to select the best policy for an unknown task using feedback from the environment. The use of bandit algorithms allows the OWL agent to constructively re-use different continually learnt policies at different times during an episode. We show in multiple RL environments that existing replay based CL methods fail, while OWL is able to achieve close to optimal performance when training sequentially.

ICML Conference 2022 Conference Paper

Stabilizing Off-Policy Deep Reinforcement Learning from Pixels

• Edoardo Cetin
• Philip J. Ball
• Stephen J. Roberts
• Oya Çeliktutan

Off-policy reinforcement learning (RL) from pixel observations is notoriously unstable. As a result, many successful algorithms must combine different domain-specific practices and auxiliary losses to learn meaningful behaviors in complex environments. In this work, we provide novel analysis demonstrating that these instabilities arise from performing temporal-difference learning with a convolutional encoder and low-magnitude rewards. We show that this new visual deadly triad causes unstable training and premature convergence to degenerate solutions, a phenomenon we name catastrophic self-overfitting. Based on our analysis, we propose A-LIX, a method providing adaptive regularization to the encoder’s gradients that explicitly prevents the occurrence of catastrophic self-overfitting using a dual objective. By applying A-LIX, we significantly outperform the prior state-of-the-art on the DeepMind Control and Atari benchmarks without any data augmentation or auxiliary losses.

ICML Conference 2021 Conference Paper

Augmented World Models Facilitate Zero-Shot Dynamics Generalization From a Single Offline Environment

• Philip J. Ball
• Cong Lu
• Jack Parker-Holder
• Stephen J. Roberts

Reinforcement learning from large-scale offline datasets provides us with the ability to learn policies without potentially unsafe or impractical exploration. Significant progress has been made in the past few years in dealing with the challenge of correcting for differing behavior between the data collection and learned policies. However, little attention has been paid to potentially changing dynamics when transferring a policy to the online setting, where performance can be up to 90% reduced for existing methods. In this paper we address this problem with Augmented World Models (AugWM). We augment a learned dynamics model with simple transformations that seek to capture potential changes in physical properties of the robot, leading to more robust policies. We not only train our policy in this new setting, but also provide it with the sampled augmentation as a context, allowing it to adapt to changes in the environment. At test time we learn the context in a self-supervised fashion by approximating the augmentation which corresponds to the new environment. We rigorously evaluate our approach on over 100 different changed dynamics settings, and show that this simple approach can significantly improve the zero-shot generalization of a recent state-of-the-art baseline, often achieving successful policies where the baseline fails.

UAI Conference 2021 Conference Paper

Hierarchical Indian buffet neural networks for Bayesian continual learning

• Samuel Kessler
• Vu Nguyen
• Stefan Zohren
• Stephen J. Roberts

We place an Indian Buffet process (IBP) prior over the structure of a Bayesian Neural Network (BNN), thus allowing the complexity of the BNN to increase and decrease automatically. We further extend this model such that the prior on the structure of each hidden layer is shared globally across all layers, using a Hierarchical-IBP (H-IBP). We apply this model to the problem of resource allocation in Continual Learning (CL) where new tasks occur and the network requires extra resources. Our model uses online variational inference with reparameterisation of the Bernoulli and Beta distributions, which constitute the IBP and H-IBP priors. As we automatically learn the number of weights in each layer of the BNN, overfitting and underfitting problems are largely overcome. We show empirically that our approach offers a competitive edge over existing methods in CL.

ICLR Conference 2021 Conference Paper

Improving VAEs' Robustness to Adversarial Attack

• Matthew Willetts
• Alexander Camuto
• Tom Rainforth
• Stephen J. Roberts
• Chris C. Holmes

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.

UAI Conference 2021 Conference Paper

Towards tractable optimism in model-based reinforcement learning

• Aldo Pacchiano
• Philip J. Ball
• Jack Parker-Holder
• Krzysztof Choromanski
• Stephen J. Roberts

The principle of optimism in the face of uncertainty is prevalent throughout sequential decision making problems such as multi-armed bandits and reinforcement learning (RL). To be successful, an optimistic RL algorithm must over-estimate the true value function (optimism) but not by so much that it is inaccurate (estimation error). In the tabular setting, many state-of-the-art methods produce the required optimism through approaches which are intractable when scaling to deep RL. We re-interpret these scalable optimistic model-based algorithms as solving a tractable noise augmented MDP. This formulation achieves a competitive regret bound: $\tilde{\mathcal{O}}( |\mathcal{S}|H\sqrt{|\mathcal{A}| T } )$ when augmenting using Gaussian noise, where $T$ is the total number of environment steps. We also explore how this trade-off changes in the deep RL setting, where we show empirically that estimation error is significantly more troublesome. However, we also show that if this error is reduced, optimistic model-based RL algorithms can match state-of-the-art performance in continuous control problems.

ICML Conference 2020 Conference Paper

Bayesian Optimisation over Multiple Continuous and Categorical Inputs

• Bin Xin Ru
• Ahsan S. Alvi
• Vu Nguyen
• Michael A. Osborne
• Stephen J. Roberts

Efficient optimisation of black-box problems that comprise both continuous and categorical inputs is important, yet poses significant challenges. Current approaches, like one-hot encoding, severely increase the dimension of the search space, while separate modelling of category-specific data is sample-inefficient. Both frameworks are not scalable to practical applications involving multiple categorical variables, each with multiple possible values. We propose a new approach, Continuous and Categorical Bayesian Optimisation (CoCaBO), which combines the strengths of multi-armed bandits and Bayesian optimisation to select values for both categorical and continuous inputs. We model this mixed-type space using a Gaussian Process kernel, designed to allow sharing of information across multiple categorical variables; this allows CoCaBO to leverage all available data efficiently. We extend our method to the batch setting and propose an efficient selection procedure that dynamically balances exploration and exploitation whilst encouraging batch diversity. We demonstrate empirically that our method outperforms existing approaches on both synthetic and real-world optimisation tasks with continuous and categorical inputs.

NeurIPS Conference 2020 Conference Paper

Effective Diversity in Population Based Reinforcement Learning

• Jack Parker-Holder
• Aldo Pacchiano
• Krzysztof M. Choromanski
• Stephen J. Roberts

Exploration is a key problem in reinforcement learning, since agents can only learn from data they acquire in the environment. With that in mind, maintaining a population of agents is an attractive method, as it allows data be collected with a diverse set of behaviors. This behavioral diversity is often boosted via multi-objective loss functions. However, those approaches typically leverage mean field updates based on pairwise distances, which makes them susceptible to cycling behaviors and increased redundancy. In addition, explicitly boosting diversity often has a detrimental impact on optimizing already fruitful behaviors for rewards. As such, the reward-diversity trade off typically relies on heuristics. Finally, such methods require behavioral representations, often handcrafted and domain specific. In this paper, we introduce an approach to optimize all members of a population simultaneously. Rather than using pairwise distance, we measure the volume of the entire population in a behavioral manifold, defined by task-agnostic behavioral embeddings. In addition, our algorithm Diversity via Determinants (DvD), adapts the degree of diversity during training using online learning techniques. We introduce both evolutionary and gradient-based instantiations of DvD and show they effectively improve exploration without reducing performance when better exploration is not required.

NeurIPS Conference 2020 Conference Paper

Explicit Regularisation in Gaussian Noise Injections

• Alexander Camuto
• Matthew Willetts
• Umut Simsekli
• Stephen J. Roberts
• Chris C. Holmes

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.

NeurIPS Conference 2020 Conference Paper

Provably Efficient Online Hyperparameter Optimization with Population-Based Bandits

• Jack Parker-Holder
• Vu Nguyen
• Stephen J. Roberts

Many of the recent triumphs in machine learning are dependent on well-tuned hyperparameters. This is particularly prominent in reinforcement learning (RL) where a small change in the configuration can lead to failure. Despite the importance of tuning hyperparameters, it remains expensive and is often done in a naive and laborious way. A recent solution to this problem is Population Based Training (PBT) which updates both weights and hyperparameters in a \emph{single training run} of a population of agents. PBT has been shown to be particularly effective in RL, leading to widespread use in the field. However, PBT lacks theoretical guarantees since it relies on random heuristics to explore the hyperparameter space. This inefficiency means it typically requires vast computational resources, which is prohibitive for many small and medium sized labs. In this work, we introduce the first provably efficient PBT-style algorithm, Population-Based Bandits (PB2). PB2 uses a probabilistic model to guide the search in an efficient way, making it possible to discover high performing hyperparameter configurations with far fewer agents than typically required by PBT. We show in a series of RL experiments that PB2 is able to achieve high performance with a modest computational budget.

ICML Conference 2020 Conference Paper

Ready Policy One: World Building Through Active Learning

• Philip J. Ball
• Jack Parker-Holder
• Aldo Pacchiano
• Krzysztof Choromanski
• Stephen J. Roberts

Model-Based Reinforcement Learning (MBRL) offers a promising direction for sample efficient learning, often achieving state of the art results for continuous control tasks. However many existing MBRL methods rely on combining greedy policies with exploration heuristics, and even those which utilize principled exploration bonuses construct dual objectives in an ad hoc fashion. In this paper we introduce Ready Policy One (RP1), a framework that views MBRL as an active learning problem, where we aim to improve the world model in the fewest samples possible. RP1 achieves this by utilizing a hybrid objective function, which crucially adapts during optimization, allowing the algorithm to trade off reward v. s. exploration at different stages of learning. In addition, we introduce a principled mechanism to terminate sample collection once we have a rich enough trajectory batch to improve the model. We rigorously evaluate our method on a variety of continuous control tasks, and demonstrate statistically significant gains over existing approaches.

ICML Conference 2019 Conference Paper

Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation

• Ahsan S. Alvi
• Bin Xin Ru
• Jan-P. Calliess
• Stephen J. Roberts
• Michael A. Osborne

Batch Bayesian optimisation (BO) has been successfully applied to hyperparameter tuning using parallel computing, but it is wasteful of resources: workers that complete jobs ahead of others are left idle. We address this problem by developing an approach, Penalising Locally for Asynchronous Bayesian Optimisation on K Workers (PLAyBOOK), for asynchronous parallel BO. We demonstrate empirically the efficacy of PLAyBOOK and its variants on synthetic tasks and a real-world problem. We undertake a comparison between synchronous and asynchronous BO, and show that asynchronous BO often outperforms synchronous batch BO in both wall-clock time and sample efficiency.

JBHI Journal 2019 Journal Article

Gaussian Processes for Personalized Interpretable Volatility Metrics in the Step-Down Ward

• Glen Wright Colopy
• Stephen J. Roberts
• David A. Clifton

Patients in a hospital step-down unit require a level of care that is between that of the intensive care unit (ICU) and that of the general ward. While many patients remain physiologically stabilized, others will suffer clinical emergencies and be readmitted to the ICU, with a subsequent high risk of mortality. Had the associated physiological deterioration been detected early, the emergency may have been less severe or avoided entirely. Current clinical monitoring is largely heuristic, requiring manual calculation of risk scores and the use of heuristic decision criteria. Technical drawbacks include ignoring the time-series dynamics of physiological measurements, and lacking patient-specificity (i. e. , personalization of models to the individual patient). In this paper, we demonstrate how Gaussian process regression models can supplement current monitoring practice by providing interpretable and intuitive illustrations of erratic vital-sign volatility. These personalized volatility metrics may provide significantly advanced warning of deterioration, while minimizing the false alarms that induce so-called alarm fatigue. While many AI-based approaches to healthcare are criticized for being uninterpretable “black-box” methods, the cause of alarms generated from the proposed methods are explicitly interpretable and intuitive. We conclude that intelligent computational inference using methods such as those proposed can enhance current clinical decision making and potentially save lives.

JBHI Journal 2018 Journal Article

Bayesian Optimization of Personalized Models for Patient Vital-Sign Monitoring

• Glen Wright Colopy
• Stephen J. Roberts
• David A. Clifton

Gaussian process regression (GPR) provides a means to generate flexible personalized models of time series of patient vital signs. These models can perform useful clinical inference in ways that population-based models cannot. A challenge for the use of personalized models is that they must be amenable to a wide range of parameterizations, to accommodate the plausible physiology of any patient in the population. Additionally, optimal performance is typically achieved when models are regularized in light of the knowledge of the physiology of the individual patient. In this paper, we describe a method to build GP models with varying complexity (via covariance kernels) and regularization (via fixed priors over hyperparameters) on a patient-specific level, for the purpose of robust vital-sign forecasting. To this end, our results present evidence in support of two main hypotheses: 1) the use of patient-specific models can outperform population-based models for useful clinical tasks, such as vital-sign forecasting; and 2) the optimal values of (hyper)parameters of these models are best determined by sophisticated methods of optimization, due to high correlation between dimensions of the search space. The resulting models are sufficiently robust to inform clinicians of a patient's vital-sign trajectory and warn of imminent deterioration.

UAI Conference 2018 Conference Paper

Improved Stochastic Trace Estimation using Mutually Unbiased Bases

• Jack K. Fitzsimons
• Michael A. Osborne
• Stephen J. Roberts
• Joseph F. Fitzsimons

The paper begins by introducing the definition and construction of mutually unbiased bases, which are a widely used concept in quantum information processing but have received little to no attention in the machine learning and statistics literature. We demonstrate their usefulness by using them to create a new sampling technique which offers an improvement on the previously well established bounds of stochastic trace estimation. This approach offers a new state of the art single shot sampling variance while requiring O(log(n)) random bits for x ∈ Rn which significantly improves on traditional methods such as fixed basis methods, Hutchinson’s and Gaussian estimators in terms of the number of random bits required and worst case sample variance.

ICML Conference 2018 Conference Paper

Optimization, Fast and Slow: Optimally Switching between Local and Bayesian Optimization

• Mark McLeod
• Stephen J. Roberts
• Michael A. Osborne

We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on expected regret. This pairing allows us to obtain the best characteristics of both local and Bayesian optimization, making efficient use of function evaluations while yielding superior convergence to the global minimum on a selection of optimization problems, and also halting optimization once a principled and intuitive stopping condition has been fulfilled.

UAI Conference 2017 Conference Paper

Bayesian Inference of Log Determinants

• Jack K. Fitzsimons
• Kurt Cutajar
• Maurizio Filippone
• Michael A. Osborne
• Stephen J. Roberts

The log determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few thousands. In the spirit of probabilistic numerics, we reinterpret the problem of computing the log determinant as a Bayesian inference problem. In particular, we combine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain probabilistic estimates for the log determinant and its associated uncertainty within a given computational budget. Beyond its novelty and theoretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log determinant, while also quantifying the uncertainty due to budgetconstrained evidence.

JMLR Journal 2016 Journal Article

String and Membrane Gaussian Processes

• Yves-Laurent Kom Samo
• Stephen J. Roberts

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as string Gaussian processes ( string GPs which are not to be mistaken for Gaussian processes operating on text). We construct string GPs so that their finite- dimensional marginals exhibit suitable local conditional independence structures, which allow for scalable, distributed, and flexible nonparametric Bayesian inference, without resorting to approximations, and while ensuring some mild global regularity constraints. Furthermore, string GP priors naturally cope with heterogeneous input data, and the gradient of the learned latent function is readily available for explanatory analysis. Secondly, we provide some theoretical results relating our approach to the standard GP paradigm. In particular, we prove that some string GPs are Gaussian processes, which provides a complementary global perspective on our framework. Finally, we derive a scalable and distributed MCMC scheme for supervised learning tasks under string GP priors. The proposed MCMC scheme has computational time complexity $\mathcal{O}(N)$ and memory requirement $\mathcal{O}(dN)$, where $N$ is the data size and $d$ the dimension of the input space. We illustrate the efficacy of the proposed approach on several synthetic and real-world data sets, including a data set with $6$ millions input points and $8$ attributes. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

ICML Conference 2015 Conference Paper

Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes

• Yves-Laurent Kom Samo
• Stephen J. Roberts

In this paper we propose an efficient, scalable non-parametric Gaussian process model for inference on Poisson point processes. Our model does not resort to gridding the domain or to introducing latent thinning points. Unlike competing models that scale as O(n^3) over n data points, our model has a complexity O(nk^2) where k << n. We propose a MCMC sampler and show that the model obtained is faster, more accurate and generates less correlated samples than competing approaches on both synthetic and real-life data. Finally, we show that our model easily handles data sizes not considered thus far by alternate approaches.

ICML Conference 2015 Conference Paper

Variational Inference for Gaussian Process Modulated Poisson Processes

• Chris M. Lloyd
• Tom Gunter
• Michael A. Osborne
• Stephen J. Roberts

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Our scheme: requires no discretisation of the domain; scales linearly in the number of observed events; and is many orders of magnitude faster than previous sampling based approaches. The resulting algorithm is shown to outperform standard methods on synthetic examples, coal mining disaster data and in the prediction of Malaria incidences in Kenya.

UAI Conference 2014 Conference Paper

Efficient Bayesian Nonparametric Modelling of Structured Point Processes

• Tom Gunter
• Chris M. Lloyd
• Michael A. Osborne
• Stephen J. Roberts

This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer latent structure, and cope with large numbers of observed processes. A further novel contribution enables the model to work effectively in higher dimensional spaces. Using this method, we achieve vastly improved predictive performance on both 2D and 1D real data, validating our structured approach.

SoCS Conference 2013 Conference Paper

Multi-Agent Planning with Mixed-Integer Programming and Adaptive Interaction Constraint Generation (Extended Abstract)

• Jan-P. Calliess
• Stephen J. Roberts

We consider multi-agent planning in which the agents

ICML Conference 2009 Conference Paper

Sequential Bayesian prediction in the presence of changepoints

• Roman Garnett
• Michael A. Osborne
• Stephen J. Roberts