Neil D. Lawrence

Samuel J. Bell, Neil D. Lawrence · cambridge, meta-ai

We investigate the effect of task ordering on continual learning performance. We conduct an extensive series of empirical experiments on synthetic and naturalistic datasets and show that reordering tasks significantly affects the amount of catastrophic forgetting. Connecting to the field of curriculum learning, we show that the effect of task ordering can be exploited to modify continual learning performance, and present a simple approach for doing so. Our method computes the distance between all pairs of tasks, where distance is defined as the source task curvature of a gradient step toward the target task. Using statistically rigorous methods and sound experimental design, we show that task ordering is an important aspect of continual learning that can be modified for improved performance.

Samuel J. Bell, Onno P. Kampman, Jesse Dodge et al. · allen-ai, cambridge

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis (Steegen et al., 2016) introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

Andrei Paleyes, Siyuan Guo, Bernhard Schölkopf et al. · cambridge

Component-based development is one of the core principles behind modern software engineering practices. Understanding of causal relationships between components of a software system can yield significant benefits to developers. Yet modern software design approaches make it difficult to track and discover such relationships at system scale, which leads to growing intellectual debt. In this paper we consider an alternative approach to software design, flow-based programming (FBP), and draw the attention of the community to the connection between dataflow graphs produced by FBP and structural causal models. With expository examples we show how this connection can be leveraged to improve day-to-day tasks in software projects, including fault localisation, business analysis and experimentation.

Philipp Berens, Kyle Cranmer, Neil D. Lawrence et al. · cambridge

This report documents the programme and the outcomes of Dagstuhl Seminar 22382 "Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling". Today's scientific challenges are characterised by complexity. Interconnected natural, technological, and human systems are influenced by forces acting across time- and spatial-scales, resulting in complex interactions and emergent behaviours. Understanding these phenomena -- and leveraging scientific advances to deliver innovative solutions to improve society's health, wealth, and well-being -- requires new ways of analysing complex systems. The transformative potential of AI stems from its widespread applicability across disciplines, and will only be achieved through integration across research domains. AI for science is a rendezvous point. It brings together expertise from $\mathrm{AI}$ and application domains; combines modelling knowledge with engineering know-how; and relies on collaboration across disciplines and between humans and machines. Alongside technical advances, the next wave of progress in the field will come from building a community of machine learning researchers, domain experts, citizen scientists, and engineers working together to design and deploy effective AI tools. This report summarises the discussions from the seminar and provides a roadmap to suggest how different communities can collaborate to deliver a new wave of progress in AI and its application for scientific discovery.

Christian Cabrera, Andrei Paleyes, Pierre Thodoroff et al. · cambridge

Engineers are deploying ML models as parts of real-world systems with the upsurge of AI technologies. Real-world environments challenge the deployment of such systems because these environments produce large amounts of heterogeneous data, and users require increasingly efficient responses. These requirements push prevalent software architectures to the limit when deploying ML-based systems. Data-oriented Architecture (DOA) is an emerging style that equips systems better for integrating ML models. Even though papers on deployed ML systems do not mention DOA, their authors made design decisions that implicitly follow DOA. Implicit decisions create a knowledge gap, limiting the practitioners' ability to implement ML-based systems. \hlb{This paper surveys why, how, and to what extent practitioners have adopted DOA to implement and deploy ML-based systems.} We overcome the knowledge gap by answering these questions and explicitly showing the design decisions and practices behind these systems. The survey follows a well-known systematic and semi-automated methodology for reviewing papers in software engineering. The majority of reviewed works partially adopt DOA. Such an adoption enables systems to address requirements such as Big Data management, low latency processing, resource management, security and privacy. Based on these findings, we formulate practical advice to facilitate the deployment of ML-based systems.

Andrei Paleyes, Christian Cabrera, Neil D. Lawrence · cambridge

As use of data driven technologies spreads, software engineers are more often faced with the task of solving a business problem using data-driven methods such as machine learning (ML) algorithms. Deployment of ML within large software systems brings new challenges that are not addressed by standard engineering practices and as a result businesses observe high rate of ML deployment project failures. Data Oriented Architecture (DOA) is an emerging approach that can support data scientists and software developers when addressing such challenges. However, there is a lack of clarity about how DOA systems should be implemented in practice. This paper proposes to consider Flow-Based Programming (FBP) as a paradigm for creating DOA applications. We empirically evaluate FBP in the context of ML deployment on four applications that represent typical data science projects. We use Service Oriented Architecture (SOA) as a baseline for comparison. Evaluation is done with respect to different application domains, ML deployment stages, and code quality metrics. Results reveal that FBP is a suitable paradigm for data collection and data science tasks, and is able to simplify data collection and discovery when compared with SOA. We discuss the advantages of FBP as well as the gaps that need to be addressed to increase FBP adoption as a standard design paradigm for DOA.

Andrei Paleyes, Neil D. Lawrence · cambridge

Dataflow computing was shown to bring significant benefits to multiple niches of systems engineering and has the potential to become a general-purpose paradigm of choice for data-driven application development. One of the characteristic features of dataflow computing is the natural access to the dataflow graph of the entire system. Recently it has been observed that these dataflow graphs can be treated as complete graphical causal models, opening opportunities to apply causal inference techniques to dataflow systems. In this demonstration paper we aim to provide the first practical validation of this idea with a particular focus on causal fault localisation. We provide multiple demonstrations of how causal inference can be used to detect software bugs and data shifts in multiple scenarios with three modern dataflow engines.

Aditya Ravuri, Francisco Vargas, Vidhi Lalchand et al. · cambridge

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation, noise reduction and efficient downstream processing of the data. In this work, we introduce the ProbDR variational framework, which interprets a wide range of classical DR algorithms as probabilistic inference algorithms in this framework. ProbDR encompasses PCA, CMDS, LLE, LE, MVU, diffusion maps, kPCA, Isomap, (t-)SNE, and UMAP. In our framework, a low-dimensional latent variable is used to construct a covariance, precision, or a graph Laplacian matrix, which can be used as part of a generative model for the data. Inference is done by optimizing an evidence lower bound. We demonstrate the internal consistency of our framework and show that it enables the use of probabilistic programming languages (PPLs) for DR. Additionally, we illustrate that the framework facilitates reasoning about unseen data and argue that our generative models approximate Gaussian processes (GPs) on manifolds. By providing a unified view of DR, our framework facilitates communication, reasoning about uncertainties, model composition, and extensions, particularly when domain knowledge is present.

Vidhi Lalchand, Aditya Ravuri, Emma Dann et al. · cambridge

Single-cell RNA-seq datasets are growing in size and complexity, enabling the study of cellular composition changes in various biological/clinical contexts. Scalable dimensionality reduction techniques are in need to disentangle biological variation in them, while accounting for technical and biological confounders. In this work, we extend a popular approach for probabilistic non-linear dimensionality reduction, the Gaussian process latent variable model, to scale to massive single-cell datasets while explicitly accounting for technical and biological confounders. The key idea is to use an augmented kernel which preserves the factorisability of the lower bound allowing for fast stochastic variational inference. We demonstrate its ability to reconstruct latent signatures of innate immunity recovered in Kumasaka et al. (2021) with 9x lower training time. We further analyze a COVID dataset and demonstrate across a cohort of 130 individuals, that this framework enables data integration while capturing interpretable signatures of infection. Specifically, we explore COVID severity as a latent dimension to refine patient stratification and capture disease-specific gene expression.

Sijia Li, Martín López-García, Neil D. Lawrence et al. · cambridge

Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters. However, for $n\approx p$ or $p > n$ such models are poorly determined. Kalaitzis et al. (2013) introduced the Bigraphical Lasso, an estimator for sparse precision matrices based on the Cartesian product of graphs. Unfortunately, the original Bigraphical Lasso algorithm is not applicable in case of large p and n due to memory requirements. We exploit eigenvalue decomposition of the Cartesian product graph to present a more efficient version of the algorithm which reduces memory requirements from $O(n^2p^2)$ to $O(n^2 + p^2)$. Many datasets in different application fields, such as biology, medicine and social science, come with count data, for which Gaussian based models are not applicable. Our multi-way network inference approach can be used for discrete data. Our methodology accounts for the dependencies across both instances and features, reduces the computational complexity for high dimensional data and enables to deal with both discrete and continuous data. Numerical studies on both synthetic and real datasets are presented to showcase the performance of our method.

Aditya Ravuri, Tom R. Andersson, Ieva Kazlauskaite et al. · cambridge

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.

Bogdan Ficiu, Neil D. Lawrence, Andrei Paleyes

Machine learning models are deployed as a central component in decision making and policy operations with direct impact on individuals' lives. In order to act ethically and comply with government regulations, these models need to make fair decisions and protect the users' privacy. However, such requirements can come with decrease in models' performance compared to their potentially biased, privacy-leaking counterparts. Thus the trade-off between fairness, privacy and performance of ML models emerges, and practitioners need a way of quantifying this trade-off to enable deployment decisions. In this work we interpret this trade-off as a multi-objective optimization problem, and propose PFairDP, a pipeline that uses Bayesian optimization for discovery of Pareto-optimal points between fairness, privacy and utility of ML models. We show how PFairDP can be used to replicate known results that were achieved through manual constraint setting process. We further demonstrate effectiveness of PFairDP with experiments on multiple models and datasets.

Hadi Sotoudeh, Payel Mukhopadhyay, Ruben Ohana et al.

We investigate the impact of tokeniser pretraining on the accuracy and efficiency of physics emulation. Modern high-resolution simulations produce vast volumes of data spanning diverse physical regimes and scales. Training foundation models to learn the dynamics underlying such data enables the modelling of complex multiphysics phenomena, especially in data-limited settings. The emerging class of physics foundation models typically aims to learn two tasks jointly: (i) extracting compact representations of high-resolution spatiotemporal data, and (ii) capturing governing physical dynamics. However, learning both tasks from scratch simultaneously can impede the effectiveness of either process. We show that pretraining the tokeniser with an autoencoding objective prior to training the dynamics model enhances computational efficiency for physics emulation. Notably, the magnitude of this benefit depends on domain alignment: pretraining on the same physical system as the emulation task yields the largest improvements, while pretraining on other systems provides moderate gains. In-domain pretraining reduces VRMSE by 64% after 10,500 training steps compared to training from scratch. To our knowledge, this is the first systematic investigation of tokeniser pretraining for physics foundation models. We further introduce flexible spatiotemporal compression operations that extend causal convolutions to support runtime-adjustable compression ratios, enabling efficient adaptation to diverse downstream tasks. Our findings provide practical guidance for training efficient physics emulators and highlight the importance of strategic pretraining data selection.

Andrei Paleyes, Radzim Sendyka, Diana Robinson et al.

Code generation is one of the most active areas of application of Large Language Models (LLMs). While LLMs lower barriers to writing code and accelerate development process, the overall quality of generated programs depends on the quality of given prompts. Specifically, functionality and quality of generated code can be sensitive to user's background and familiarity with software development. It is therefore important to quantify LLM's sensitivity to variations in the input. To this end we propose a synthetic evaluation pipeline for code generation with LLMs, as well as a systematic persona-based evaluation approach to expose qualitative differences of LLM responses dependent on prospective user background. Both proposed methods are completely independent from specific programming tasks and LLMs, and thus are widely applicable. We provide experimental evidence illustrating utility of our methods and share our code for the benefit of the community.

Neil D. Lawrence

The inaccessible game (Lawrence, 2025, 2026) is an information-theoretic dynamical system governed by three information loss axioms, a marginal entropy conservation constraint and maximum entropy dynamics. In this paper we look at selection in the game. Our aim is to develop a selection policy for the game rules based on a minimal set of assumptions. We seek necessary consistency constraints for self-determining dynamical systems. Specifically, we suggest that rules that quantify over distinctions they cannot internally represent risk impredicative-style circularity. Our criterion is motivated by an analogy with Russell's paradox. We formulate a no-barber principle which prohibits dynamics that appeal to external adjudicators or structure lying outside the system. To motivate our principle we examine Russell's paradox through its structural formalisation as a Lawvere diagonalisation. The marginal-entropy conservation in the game is a nontrivial entropy constraint which prohibits external structure. Through the no-barber principle we argue (i) the classical category FinProb, in which Shannon entropy is characterised, is cartesian and provides canonical diagonal (copying) maps that make Lawvere-style constructions expressible and is structurally incompatible with the no-copying instantiation of the no-barber principle studied here. (ii) the noncommutative category NCFinProb, in which von Neumann entropy is characterised, is symmetric monoidal and lacks canonical copying maps, making it a more natural candidate for the game's internal language.

Christian Cabrera, Viviana Bastidas, Jennifer Schooling et al.

Using Large Language Models (LLMs) to address critical societal problems requires adopting this novel technology into socio-technical systems. However, the complexity of such systems and the nature of LLMs challenge such a vision. It is unlikely that the solution to such challenges will come from the Artificial Intelligence (AI) community itself. Instead, the Systems Engineering approach is better equipped to facilitate the adoption of LLMs by prioritising the problems and their context before any other aspects. This paper introduces the challenges LLMs generate and surveys systems research efforts for engineering AI-based systems. We reveal how the systems engineering principles have supported addressing similar issues to the ones LLMs pose and discuss our findings to provide future directions for adopting LLMs.

Emile Dos Santos Ferreira, Neil D. Lawrence, Andrei Paleyes

The ubiquity of machine learning (ML) and the demand for ever-larger models bring an increase in energy consumption and environmental impact. However, little is known about the energy scaling laws in ML, and existing research focuses on training cost -- ignoring the larger cost of inference. Furthermore, tools for measuring the energy consumption of ML do not provide actionable feedback. To address these gaps, we developed Energy Consumption Optimiser (ECOpt): a hyperparameter tuner that optimises for energy efficiency and model performance. ECOpt quantifies the trade-off between these metrics as an interpretable Pareto frontier. This enables ML practitioners to make informed decisions about energy cost and environmental impact, while maximising the benefit of their models and complying with new regulations. Using ECOpt, we show that parameter and floating-point operation counts can be unreliable proxies for energy consumption, and observe that the energy efficiency of Transformer models for text generation is relatively consistent across hardware. These findings motivate measuring and publishing the energy metrics of ML models. We further show that ECOpt can have a net positive environmental impact and use it to uncover seven models for CIFAR-10 that improve upon the state of the art, when considering accuracy and energy efficiency together.

Oluwatomisin I. Dada, Neil D. Lawrence

Recent work has proposed machine learning (ML) approaches as fast surrogates for solving AC optimal power flow (AC-OPF), with claims of significant speed-ups and high accuracy. In this paper, we revisit these claims through a systematic evaluation of ML models against a set of simple yet carefully designed linear baselines. We introduce OPFormer-V, a transformer-based model for predicting bus voltages, and compare it to both the state-of-the-art DeepOPF-V model and simple linear methods. Our findings reveal that, while OPFormer-V improves over DeepOPF-V, the relative gains of the ML approaches considered are less pronounced than expected. Simple linear baselines can achieve comparable performance. These results highlight the importance of including strong linear baselines in future evaluations.

Aditya Ravuri, Neil D. Lawrence

We propose a probabilistic interpretation of transformers as unrolled inference steps assuming a probabilistic Laplacian Eigenmaps model from the ProbDR framework. Our derivation shows that at initialisation, transformers perform "linear" dimensionality reduction. We also show that within the transformer block, a graph Laplacian term arises from our arguments, rather than an attention matrix (which we interpret as an adjacency matrix). We demonstrate that simply subtracting the identity from the attention matrix (and thereby taking a graph diffusion step) improves validation performance on a language model and a simple vision transformer.

Aditya Ravuri, Neil D. Lawrence

Protein Language Models (PLMs) such as ESM2 have been shown to be capable of zero-shot prediction of critical scalar properties of proteins (fitness). In this work, we show that injecting a dropout layer at inference time between a PLM's featurizer/embedding layer and its transformer, and averaging its output akin to Monte-Carlo dropout increases zero-shot performance on a subset of the ProteinGym dataset. This is the case even when the model was not trained with dropouts to begin with, and does not require retraining or finetuning of the PLM. A dropout of 0.1 seems performant across all models.

Sarah Zhao, Aditya Ravuri, Vidhi Lalchand et al.

Dimensionality reduction is crucial for analyzing large-scale single-cell RNA-seq data. Gaussian Process Latent Variable Models (GPLVMs) offer an interpretable dimensionality reduction method, but current scalable models lack effectiveness in clustering cell types. We introduce an improved model, the amortized stochastic variational Bayesian GPLVM (BGPLVM), tailored for single-cell RNA-seq with specialized encoder, kernel, and likelihood designs. This model matches the performance of the leading single-cell variational inference (scVI) approach on synthetic and real-world COVID datasets and effectively incorporates cell-cycle and batch information to reveal more interpretable latent structures as we demonstrate on an innate immunity dataset.

Christian Cabrera, Andrei Paleyes, Neil D. Lawrence

Software systems impact society at different levels as they pervasively solve real-world problems. Modern software systems are often so sophisticated that their complexity exceeds the limits of human comprehension. These systems must respond to changing goals, dynamic data, unexpected failures, and security threats, among other variable factors in real-world environments. Systems' complexity challenges their interpretability and requires autonomous responses to dynamic changes. Two main research areas explore autonomous systems' responses: evolutionary computing and autonomic computing. Evolutionary computing focuses on software improvement based on iterative modifications to the source code. Autonomic computing focuses on optimising systems' performance by changing their structure, behaviour, or environment variables. Approaches from both areas rely on feedback loops that accumulate knowledge from the system interactions to inform autonomous decision-making. However, this knowledge is often limited, constraining the systems' interpretability and adaptability. This paper proposes a new concept for interpretable and adaptable software systems: self-sustaining software systems (S4). S4 builds knowledge loops between all available knowledge sources that define modern software systems to improve their interpretability and adaptability. This paper introduces and discusses the S4 concept.

Vidhi Lalchand, Aditya Ravuri, Neil D. Lawrence

Gaussian process latent variable models (GPLVM) are a flexible and non-linear approach to dimensionality reduction, extending classical Gaussian processes to an unsupervised learning context. The Bayesian incarnation of the GPLVM Titsias and Lawrence, 2010] uses a variational framework, where the posterior over latent variables is approximated by a well-behaved variational family, a factorized Gaussian yielding a tractable lower bound. However, the non-factories ability of the lower bound prevents truly scalable inference. In this work, we study the doubly stochastic formulation of the Bayesian GPLVM model amenable with minibatch training. We show how this framework is compatible with different latent variable formulations and perform experiments to compare a suite of models. Further, we demonstrate how we can train in the presence of massively missing data and obtain high-fidelity reconstructions. We demonstrate the model's performance by benchmarking against the canonical sparse GPLVM for high-dimensional data examples.

Francisco Vargas, Andrius Ovsianas, David Fernandes et al.

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schrödinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics (SGLD). Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models.

Andrei Paleyes, Mark Pullin, Maren Mahsereci et al.

Decision making in uncertain scenarios is an ubiquitous challenge in real world systems. Tools to deal with this challenge include simulations to gather information and statistical emulation to quantify uncertainty. The machine learning community has developed a number of methods to facilitate decision making, but so far they are scattered in multiple different toolkits, and generally rely on a fixed backend. In this paper, we present Emukit, a highly adaptable Python toolkit for enriching decision making under uncertainty. Emukit allows users to: (i) use state of the art methods including Bayesian optimization, multi-fidelity emulation, experimental design, Bayesian quadrature and sensitivity analysis; (ii) easily prototype new decision making methods for new problems. Emukit is agnostic to the underlying modeling framework and enables users to use their own custom models. We show how Emukit can be used on three exemplary case studies.

Samuel J. Bell, Neil D. Lawrence

In this paper we explore whether the fundamental tool of experimental psychology, the behavioral experiment, has the power to generate insight not only into humans and animals, but artificial systems too. We apply the techniques of experimental psychology to investigating catastrophic forgetting in neural networks. We present a series of controlled experiments with two-layer ReLU networks, and exploratory results revealing a new understanding of the behavior of catastrophic forgetting. Alongside our empirical findings, we demonstrate an alternative, behavior-first approach to investigating neural network phenomena.

Corinna Cortes, Neil D. Lawrence

In this paper we revisit the 2014 NeurIPS experiment that examined inconsistency in conference peer review. We determine that 50\% of the variation in reviewer quality scores was subjective in origin. Further, with seven years passing since the experiment we find that for \emph{accepted} papers, there is no correlation between quality scores and impact of the paper as measured as a function of citation count. We trace the fate of rejected papers, recovering where these papers were eventually published. For these papers we find a correlation between quality scores and impact. We conclude that the reviewing process for the 2014 conference was good for identifying poor papers, but poor for identifying good papers. We give some suggestions for improving the reviewing process but also warn against removing the subjective element. Finally, we suggest that the real conclusion of the experiment is that the community should place less onus on the notion of `top-tier conference publications' when assessing the quality of individual researchers. For NeurIPS 2021, the PCs are repeating the experiment, as well as conducting new ones.

Andrei Paleyes, Christian Cabrera, Neil D. Lawrence

Despite huge successes reported by the field of machine learning, such as voice assistants or self-driving cars, businesses still observe very high failure rate when it comes to deployment of ML in production. We argue that part of the reason is infrastructure that was not designed for data-oriented activities. This paper explores the potential of flow-based programming (FBP) for simplifying data discovery and collection in software systems. We compare FBP with the currently prevalent service-oriented paradigm to assess characteristics of each paradigm in the context of ML deployment. We develop a data processing application, formulate a subsequent ML deployment task, and measure the impact of the task implementation within both programming paradigms. Our main conclusion is that FBP shows great potential for providing data-centric infrastructural benefits for deployment of ML. Additionally, we provide an insight into the current trend that prioritizes model development over data quality management.

Francisco Vargas, Pierre Thodoroff, Neil D. Lawrence et al.

The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. We prove an equivalence between the SBP and maximum likelihood estimation enabling direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.

Andrei Paleyes, Raoul-Gabriel Urma, Neil D. Lawrence

In recent years, machine learning has transitioned from a field of academic research interest to a field capable of solving real-world business problems. However, the deployment of machine learning models in production systems can present a number of issues and concerns. This survey reviews published reports of deploying machine learning solutions in a variety of use cases, industries and applications and extracts practical considerations corresponding to stages of the machine learning deployment workflow. By mapping found challenges to the steps of the machine learning deployment workflow we show that practitioners face issues at each stage of the deployment process. The goal of this paper is to lay out a research agenda to explore approaches addressing these challenges.

Shell Xu Hu, Pablo G. Moreno, Yang Xiao et al.

We propose a meta-learning approach that learns from multiple tasks in a transductive setting, by leveraging the unlabeled query set in addition to the support set to generate a more powerful model for each task. To develop our framework, we revisit the empirical Bayes formulation for multi-task learning. The evidence lower bound of the marginal log-likelihood of empirical Bayes decomposes as a sum of local KL divergences between the variational posterior and the true posterior on the query set of each task. We derive a novel amortized variational inference that couples all the variational posteriors via a meta-model, which consists of a synthetic gradient network and an initialization network. Each variational posterior is derived from synthetic gradient descent to approximate the true posterior on the query set, although where we do not have access to the true gradient. Our results on the Mini-ImageNet and CIFAR-FS benchmarks for episodic few-shot classification outperform previous state-of-the-art methods. Besides, we conduct two zero-shot learning experiments to further explore the potential of the synthetic gradient.

Michael Thomas Smith, Mauricio A. Alvarez, Neil D. Lawrence

A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been combined with Gaussian processes through the previously published \emph{cloaking method}. In this paper we solve several shortcomings of this method, starting with the problem of predictions in regions with low data density. We experiment with the use of inducing points to provide a sparse approximation and show that these can provide robust differential privacy in outlier areas and at higher dimensions. We then look at classification, and modify the Laplace approximation approach to provide differentially private predictions. We then combine this with the sparse approximation and demonstrate the capability to perform classification in high dimensions. We finally explore the issue of hyperparameter selection and develop a method for their private selection. This paper and associated libraries provide a robust toolkit for combining differential privacy and GPs in a practical manner.

Sungsoo Ahn, Shell Xu Hu, Andreas Damianou et al.

Transferring knowledge from a teacher neural network pretrained on the same or a similar task to a student neural network can significantly improve the performance of the student neural network. Existing knowledge transfer approaches match the activations or the corresponding hand-crafted features of the teacher and the student networks. We propose an information-theoretic framework for knowledge transfer which formulates knowledge transfer as maximizing the mutual information between the teacher and the student networks. We compare our method with existing knowledge transfer methods on both knowledge distillation and transfer learning tasks and show that our method consistently outperforms existing methods. We further demonstrate the strength of our method on knowledge transfer across heterogeneous network architectures by transferring knowledge from a convolutional neural network (CNN) to a multi-layer perceptron (MLP) on CIFAR-10. The resulting MLP significantly outperforms the-state-of-the-art methods and it achieves similar performance to the CNN with a single convolutional layer.

Neil D. Lawrence

Machine learning solutions, in particular those based on deep learning methods, form an underpinning of the current revolution in "artificial intelligence" that has dominated popular press headlines and is having a significant influence on the wider tech agenda. Here we give an overview of the 3Ds of ML systems design: Data, Design and Deployment. By considering the 3Ds we can move towards \emph{data first} design.

Sebastian Flennerhag, Pablo G. Moreno, Neil D. Lawrence et al.

In complex transfer learning scenarios new tasks might not be tightly linked to previous tasks. Approaches that transfer information contained only in the final parameters of a source model will therefore struggle. Instead, transfer learning at a higher level of abstraction is needed. We propose Leap, a framework that achieves this by transferring knowledge across learning processes. We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta-learning objective that minimizes the expected length of this path. Our framework leverages only information obtained during training and can be computed on the fly at negligible cost. We demonstrate that our framework outperforms competing methods, both in meta-learning and transfer learning, on a set of computer vision tasks. Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding reinforcement learning environments (Atari) that involve millions of gradient steps.

Matthias Seeger, Asmus Hetzel, Zhenwen Dai et al.

Development systems for deep learning (DL), such as Theano, Torch, TensorFlow, or MXNet, are easy-to-use tools for creating complex neural network models. Since gradient computations are automatically baked in, and execution is mapped to high performance hardware, these models can be trained end-to-end on large amounts of data. However, it is currently not easy to implement many basic machine learning primitives in these systems (such as Gaussian processes, least squares estimation, principal components analysis, Kalman smoothing), mainly because they lack efficient support of linear algebra primitives as differentiable operators. We detail how a number of matrix decompositions (Cholesky, LQ, symmetric eigen) can be implemented as differentiable operators. We have implemented these primitives in MXNet, running on CPU and GPU in single and double precision. We sketch use cases of these new operators, learning Gaussian process and Bayesian linear regression models, where we demonstrate very substantial reductions in implementation complexity and running time compared to previous codes. Our MXNet extension allows end-to-end learning of hybrid models, which combine deep neural networks (DNNs) with Bayesian concepts, with applications in advanced Gaussian process models, scalable Bayesian optimization, and Bayesian active learning.

Simo Särkkä, Mauricio A. Álvarez, Neil D. Lawrence

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first-principles physical model part and a non-parametric GP model part. We briefly review the statistical inference and learning methods for this kind of models, introduce stochastic control methodology for the models, and provide new theoretical observability and controllability results for them.

Zhenwen Dai, Mauricio A. Álvarez, Neil D. Lawrence

Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these conditions and generalize to a new one with few data? We present a new model called Latent Variable Multiple Output Gaussian Processes (LVMOGP) and that allows to jointly model multiple conditions for regression and generalize to a new condition with a few data points at test time. LVMOGP infers the posteriors of Gaussian processes together with a latent space representing the information about different conditions. We derive an efficient variational inference method for LVMOGP, of which the computational complexity is as low as sparse Gaussian processes. We show that LVMOGP significantly outperforms related Gaussian process methods on various tasks with both synthetic and real data.

Neil D. Lawrence

In this paper we consider the nature of the machine intelligences we have created in the context of our human intelligence. We suggest that the fundamental difference between human and machine intelligence comes down to \emph{embodiment factors}. We define embodiment factors as the ratio between an entity's ability to communicate information vs compute information. We speculate on the role of embodiment factors in driving our own intelligence and consciousness. We briefly review dual process models of cognition and cast machine intelligence within that framework, characterising it as a dominant System Zero, which can drive behaviour through interfacing with us subconsciously. Driven by concerns about the consequence of such a system we suggest prophylactic courses of action that could be considered. Our main conclusion is that it is \emph{not} sentient intelligence we should fear but \emph{non-sentient} intelligence.

Neil D. Lawrence

Application of models to data is fraught. Data-generating collaborators often only have a very basic understanding of the complications of collating, processing and curating data. Challenges include: poor data collection practices, missing values, inconvenient storage mechanisms, intellectual property, security and privacy. All these aspects obstruct the sharing and interconnection of data, and the eventual interpretation of data through machine learning or other approaches. In project reporting, a major challenge is in encapsulating these problems and enabling goals to be built around the processing of data. Project overruns can occur due to failure to account for the amount of time required to curate and collate. But to understand these failures we need to have a common language for assessing the readiness of a particular data set. This position paper proposes the use of data readiness levels: it gives a rough outline of three stages of data preparedness and speculates on how formalisation of these levels into a common language for data readiness could facilitate project management.

Javier Gonzalez, Zhenwen Dai, Andreas Damianou et al.

Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimizing black-box functions where direct queries of the objective are expensive. In this paper we consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) which allows us to find the optimum of a latent function that can only be queried through pairwise comparisons, the so-called duels. PBO extends the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the winner of each duel by means of a Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments, showing that PBO needs drastically fewer comparisons for finding the optimum. According to our experiments, the way of modeling correlations in PBO is key in obtaining this advantage.

Andreas Damianou, Neil D. Lawrence, Carl Henrik Ek

We present Manifold Alignment Determination (MAD), an algorithm for learning alignments between data points from multiple views or modalities. The approach is capable of learning correspondences between views as well as correspondences between individual data-points. The proposed method requires only a few aligned examples from which it is capable to recover a global alignment through a probabilistic model. The strong, yet flexible regularization provided by the generative model is sufficient to align the views. We provide experiments on both synthetic and real data to highlight the benefit of the proposed approach.

Brenden M. Lake, Neil D. Lawrence, Joshua B. Tenenbaum

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form --- where form could be a tree, ring, chain, grid, etc. [Kemp & Tenenbaum (2008). The discovery of structural form. PNAS, 105(3), 10687-10692]. While this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model's initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist.

Michael Thomas Smith, Max Zwiessele, Neil D. Lawrence

A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the differential privacy framework with the flexibility of Gaussian processes (GPs). We propose a method using GPs to provide differentially private (DP) regression. We then improve this method by crafting the DP noise covariance structure to efficiently protect the training data, while minimising the scale of the added noise. We find that this cloaking method achieves the greatest accuracy, while still providing privacy guarantees, and offers practical DP for regression over multi-dimensional inputs. Together these methods provide a starter toolkit for combining differential privacy and GPs.

Alan D. Saul, James Hensman, Aki Vehtari et al.

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to a linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e. a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.

Andreas Damianou, Neil D. Lawrence, Carl Henrik Ek

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.

César Lincoln C. Mattos, Zhenwen Dai, Andreas Damianou et al.

We define Recurrent Gaussian Processes (RGP) models, a general family of Bayesian nonparametric models with recurrent GP priors which are able to learn dynamical patterns from sequential data. Similar to Recurrent Neural Networks (RNNs), RGPs can have different formulations for their internal states, distinct inference methods and be extended with deep structures. In such context, we propose a novel deep RGP model whose autoregressive states are latent, thereby performing representation and dynamical learning simultaneously. To fully exploit the Bayesian nature of the RGP model we develop the Recurrent Variational Bayes (REVARB) framework, which enables efficient inference and strong regularization through coherent propagation of uncertainty across the RGP layers and states. We also introduce a RGP extension where variational parameters are greatly reduced by being reparametrized through RNN-based sequential recognition models. We apply our model to the tasks of nonlinear system identification and human motion modeling. The promising obtained results indicate that our RGP model maintains its highly flexibility while being able to avoid overfitting and being applicable even when larger datasets are not available.

Javier González, Michael Osborne, Neil D. Lawrence

We present GLASSES: Global optimisation with Look-Ahead through Stochastic Simulation and Expected-loss Search. The majority of global optimisation approaches in use are myopic, in only considering the impact of the next function value; the non-myopic approaches that do exist are able to consider only a handful of future evaluations. Our novel algorithm, GLASSES, permits the consideration of dozens of evaluations into the future. This is done by approximating the ideal look-ahead loss function, which is expensive to evaluate, by a cheaper alternative in which the future steps of the algorithm are simulated beforehand. An Expectation Propagation algorithm is used to compute the expected value of the loss.We show that the far-horizon planning thus enabled leads to substantive performance gains in empirical tests.

Andreas Damianou, Neil D. Lawrence

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problems (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks.

Javier González, Zhenwen Dai, Philipp Hennig et al.

The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is desirable to simultaneously propose batches of parameter values to explore. This is particularly the case when large parallel processing facilities are available. These facilities could be computational or physical facets of the process being optimized. E.g. in biological experiments many experimental set ups allow several samples to be simultaneously processed. Batch methods, however, require modeling of the interaction between the evaluations in the batch, which can be expensive in complex scenarios. We investigate a simple heuristic based on an estimate of the Lipschitz constant that captures the most important aspect of this interaction (i.e. local repulsion) at negligible computational overhead. The resulting algorithm compares well, in running time, with much more elaborate alternatives. The approach assumes that the function of interest, $f$, is a Lipschitz continuous function. A wrap-loop around the acquisition function is used to collect batches of points of certain size minimizing the non-parallelizable computational effort. The speed-up of our method with respect to previous approaches is significant in a set of computationally expensive experiments.