The mapping from sound to neural activity that underlies hearing is highly non-linear. The first few stages of this mapping in the cochlea have been modelled successfully, with biophysical models built by hand and, more recently, with DNN models trained on datasets simulated by biophysical models. Modelling the auditory brain has been a challenge because central auditory processing is too complex for models to be built by hand, and datasets for training DNN models directly have not been available. Recent work has taken advantage of large-scale high resolution neural recordings from the auditory midbrain to build a DNN model of normal hearing with great success. But this model assumes that auditory processing is the same in all brains, and therefore it cannot capture the widely varying effects of hearing loss. We propose a novel variational-conditional model to learn to encode the space of hearing loss directly from recordings of neural activity in the auditory midbrain of healthy and noise exposed animals. With hearing loss parametrised by only 6 free parameters per animal, our model accurately predicts 62\% of the explainable variance in neural responses from normal hearing animals and 68% for hearing impaired animals, within a few percentage points of state of the art animal specific models. We demonstrate that the model can be used to simulate realistic activity from out of sample animals by fitting only the learned conditioning parameters with Bayesian optimisation, achieving crossentropy loss within 2% of the optimum in 15-30 iterations. Including more animals in the training data slightly improved the performance on unseen animals. This model will enable future development of parametrised hearing loss compensation models trained to directly restore normal neural coding in hearing impaired brains, which can be quickly fitted for a new user by human in the loop optimisation.
Large Language Models (LLMs) struggle with complex reasoning due to limited diversity and inefficient search. We propose Soft Reasoning, an embedding-based search framework that optimises the embedding of the first token to guide generation. It combines (1) embedding perturbation for controlled exploration and (2) Bayesian optimisation to refine embeddings via a verifier-guided objective, balancing exploration and exploitation. This approach improves reasoning accuracy and coherence while avoiding reliance on heuristic search. Experiments demonstrate superior correctness with minimal computation, making it a scalable, model-agnostic solution.
In the context of global warming, even relatively cooler countries like the UK are experiencing a rise in cooling demand, particularly in southern regions such as London. This growing demand, especially during the summer months, presents significant challenges for energy management systems. Accurately predicting cooling demand in urban domestic buildings is essential for maintaining energy efficiency. This study introduces a generalised framework for developing high-resolution Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks using physical model-based summer cooling demand data. To maximise the predictive capability and generalisation ability of the models under limited data scenarios, four distinct data partitioning strategies were implemented, including the extrapolation, month-based interpolation, global interpolation, and day-based interpolation. Bayesian Optimisation (BO) was then applied to fine-tune the hyper-parameters, substantially improving the framework predictive accuracy. Results show that the day-based interpolation GRU model demonstrated the best performance due to its ability to retain both the data randomness and the time sequence continuity characteristics. This optimal model achieves a Root Mean Squared Error (RMSE) of 2.22%, a Mean Absolute Error (MAE) of 0.87%, and a coefficient of determination (R square) of 0.9386 on the test set. The generalisation ability of this framework was further evaluated by forecasting.
This study proposes a novel few-shot crack image classification model based on CLIP and Bayesian optimization. By combining multimodal information and Bayesian approach, the model achieves efficient classification of crack images in a small number of training samples. The CLIP model employs its robust feature extraction capabilities to facilitate precise classification with a limited number of samples. In contrast, Bayesian optimisation enhances the robustness and generalization of the model, while reducing the reliance on extensive labelled data. The results demonstrate that the model exhibits robust performance across a diverse range of dataset scales, particularly in the context of small sample sets. The study validates the potential of the method in civil engineering crack classification.
This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then demonstrate empirically that our proposed method does indeed require fewer samples to estimate nested expectations on real-world applications including Bayesian optimisation, option pricing, and health economics.
We address the problem of optimising the average payoff for a large number of cooperating agents, where the payoff function is unknown and treated as a black box. While standard Bayesian Optimisation (BO) methods struggle with the scalability required for high-dimensional input spaces, we demonstrate how leveraging the mean-field assumption on the black-box function can transform BO into an efficient and scalable solution. Specifically, we introduce MF-GP-UCB, a novel efficient algorithm designed to optimise agent payoffs in this setting. Our theoretical analysis establishes a regret bound for MF-GP-UCB that is independent of the number of agents, contrasting sharply with the exponential dependence observed when naive BO methods are applied. We evaluate our algorithm on a diverse set of tasks, including real-world problems, such as optimising the location of public bikes for a bike-sharing programme, distributing taxi fleets, and selecting refuelling ports for maritime vessels. Empirical results demonstrate that MF-GP-UCB significantly outperforms existing benchmarks, offering substantial improvements in performance and scalability, constituting a promising solution for mean-field, black-box optimisation. The code is available at https://github.com/petarsteinberg/MF-BO.
As we transition from Narrow Artificial Intelligence towards Artificial Super Intelligence, users are increasingly concerned about their privacy and the trustworthiness of machine learning (ML) technology. A common denominator for the metrics of trustworthiness is the quantification of uncertainty inherent in DL algorithms, and specifically in the model parameters, input data, and model predictions. One of the common approaches to address privacy-related issues in DL is to adopt distributed learning such as federated learning (FL), where private raw data is not shared among users. Despite the privacy-preserving mechanisms in FL, it still faces challenges in trustworthiness. Specifically, the malicious users, during training, can systematically create malicious model parameters to compromise the models predictive and generative capabilities, resulting in high uncertainty about their reliability. To demonstrate malicious behaviour, we propose a novel model poisoning attack method named Delphi which aims to maximise the uncertainty of the global model output. We achieve this by taking advantage of the relationship between the uncertainty and the model parameters of the first hidden layer of the local model. Delphi employs two types of optimisation , Bayesian Optimisation and Least Squares Trust Region, to search for the optimal poisoned model parameters, named as Delphi-BO and Delphi-LSTR. We quantify the uncertainty using the KL Divergence to minimise the distance of the predictive probability distribution towards an uncertain distribution of model output. Furthermore, we establish a mathematical proof for the attack effectiveness demonstrated in FL. Numerical results demonstrate that Delphi-BO induces a higher amount of uncertainty than Delphi-LSTR highlighting vulnerability of FL systems to model poisoning attacks.
Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to emulate a black-box computational model with the aim of efficiently searching for the global minimum. However, Gaussian processes have limited applicability for engineering problems with many design variables. Their scalability can be significantly improved by identifying a low-dimensional vector of latent variables that serve as inputs to the Gaussian process. In this paper, we introduce a multi-view learning strategy that considers both the input design variables and output data representing the objective or constraint functions, to identify a low-dimensional space of latent variables. Adopting a fully probabilistic viewpoint, we use probabilistic partial least squares (PPLS) to learn an orthogonal mapping from the design variables to the latent variables using training data consisting of inputs and outputs of the black-box computational model. The latent variables and posterior probability densities of the probabilistic partial least squares and Gaussian process models are determined sequentially and iteratively, with retraining occurring at each adaptive sampling iteration. We compare the proposed probabilistic partial least squares Bayesian optimisation (PPLS-BO) strategy to its deterministic counterpart, partial least squares Bayesian optimisation (PLS-BO), and classical Bayesian optimisation, demonstrating significant improvements in convergence to the global minimum.
Bayesian Optimisation (BO) is a state-of-the-art global optimisation technique for black-box problems where derivative information is unavailable, and sample efficiency is crucial. However, improving the general scalability of BO has proved challenging. Here, we explore Latent Space Bayesian Optimisation (LSBO), that applies dimensionality reduction to perform BO in a reduced-dimensional subspace. While early LSBO methods used (linear) random projections (Wang et al., 2013), we employ Variational Autoencoders (VAEs) to manage more complex data structures and general DR tasks. Building on Grosnit et. al. (2021), we analyse the VAE-based LSBO framework, focusing on VAE retraining and deep metric loss. We suggest a few key corrections in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes. Our numerical results show that structured latent manifolds improve BO performance. Additionally, we examine the use of the Mat\'{e}rn-$\frac{5}{2}$ kernel for Gaussian Processes in this LSBO context. We also integrate Sequential Domain Reduction (SDR), a standard global optimization efficiency strategy, into BO. SDR is included in a GPU-based environment using \textit{BoTorch}, both in the original and VAE-generated latent spaces, marking the first application of SDR within LSBO.
Unconstrained global optimisation aims to optimise expensive-to-evaluate black-box functions without gradient information. Bayesian optimisation, one of the most well-known techniques, typically employs Gaussian processes as surrogate models, leveraging their probabilistic nature to balance exploration and exploitation. However, Gaussian processes become computationally prohibitive in high-dimensional spaces. Recent alternatives, based on inverse distance weighting (IDW) and radial basis functions (RBFs), offer competitive, computationally lighter solutions. Despite their efficiency, both traditional global and Bayesian optimisation strategies suffer from the myopic nature of their acquisition functions, which focus solely on immediate improvement neglecting future implications of the sequential decision making process. Nonmyopic acquisition functions devised for the Bayesian setting have shown promise in improving long-term performance. Yet, their use in deterministic strategies with IDW and RBF remains unexplored. In this work, we introduce novel nonmyopic acquisition strategies tailored to IDW- and RBF-based global optimisation. Specifically, we develop dynamic programming-based paradigms, including rollout and multi-step scenario-based optimisation schemes, to enable lookahead acquisition. These methods optimise a sequence of query points over a horizon (instead of only at the next step) by predicting the evolution of the surrogate model, inherently managing the exploration-exploitation trade-off in a systematic way via optimisation techniques. The proposed approach represents a significant advance in extending nonmyopic acquisition principles, previously confined to Bayesian optimisation, to the deterministic framework. Empirical results on synthetic and hyperparameter tuning benchmark problems demonstrate that these nonmyopic methods outperform conventional myopic approaches.
We introduce Agent K v1.0, an end-to-end autonomous data science agent designed to automate, optimise, and generalise across diverse data science tasks. Fully automated, Agent K v1.0 manages the entire data science life cycle by learning from experience. It leverages a highly flexible structured reasoning framework to enable it to dynamically process memory in a nested structure, effectively learning from accumulated experience stored to handle complex reasoning tasks. It optimises long- and short-term memory by selectively storing and retrieving key information, guiding future decisions based on environmental rewards. This iterative approach allows it to refine decisions without fine-tuning or backpropagation, achieving continuous improvement through experiential learning. We evaluate our agent's apabilities using Kaggle competitions as a case study. Following a fully automated protocol, Agent K v1.0 systematically addresses complex and multimodal data science tasks, employing Bayesian optimisation for hyperparameter tuning and feature engineering. Our new evaluation framework rigorously assesses Agent K v1.0's end-to-end capabilities to generate and send submissions starting from a Kaggle competition URL. Results demonstrate that Agent K v1.0 achieves a 92.5\% success rate across tasks, spanning tabular, computer vision, NLP, and multimodal domains. When benchmarking against 5,856 human Kaggle competitors by calculating Elo-MMR scores for each, Agent K v1.0 ranks in the top 38\%, demonstrating an overall skill level comparable to Expert-level users. Notably, its Elo-MMR score falls between the first and third quartiles of scores achieved by human Grandmasters. Furthermore, our results indicate that Agent K v1.0 has reached a performance level equivalent to Kaggle Grandmaster, with a record of 6 gold, 3 silver, and 7 bronze medals, as defined by Kaggle's progression system.
We study the problem of globally optimising a target variable of an unknown causal graph on which a sequence of soft or hard interventions can be performed. The problem of optimising the target variable associated with a causal graph is formalised as Causal Bayesian Optimisation (CBO). We study the CBO problem under the cumulative regret objective with unknown causal graphs for two settings, namely structural causal models with hard interventions and function networks with soft interventions. We propose Graph Agnostic Causal Bayesian Optimisation (GACBO), an algorithm that actively discovers the causal structure that contributes to achieving optimal rewards. GACBO seeks to balance exploiting the actions that give the best rewards against exploring the causal structures and functions. To the best of our knowledge, our work is the first to study causal Bayesian optimization with cumulative regret objectives in scenarios where the graph is unknown or partially known. We show our proposed algorithm outperforms baselines in simulated experiments and real-world applications.
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued functions, as well as vector fields. We target data inherently supported on manifolds, which is too complex for shallow Gaussian processes thereon. For example, while the latter perform well on high-altitude wind data, they struggle with the more intricate, nonstationary patterns at low altitudes. Our models significantly improve performance in these settings, enhancing prediction quality and uncertainty calibration, and remain robust to overfitting, reverting to shallow models when additional complexity is unneeded. We further showcase our models on Bayesian optimisation problems on manifolds, using stylised examples motivated by robotics, and obtain substantial improvements in later stages of the optimisation process. Finally, we show our models to have potential for speeding up inference for non-manifold data, when, and if, it can be mapped to a proxy manifold well enough.
Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of transformations. We show that vanilla and constrained BO algorithms are inefficient when optimising such invariant objectives, and provide a method for incorporating group invariances into the kernel of the GP to produce invariance-aware algorithms that achieve significant improvements in sample efficiency. We derive a bound on the maximum information gain of these invariant kernels, and provide novel upper and lower bounds on the number of observations required for invariance-aware BO algorithms to achieve $\epsilon$-optimality. We demonstrate our method's improved performance on a range of synthetic invariant and quasi-invariant functions. We also apply our method in the case where only some of the invariance is incorporated into the kernel, and find that these kernels achieve similar gains in sample efficiency at significantly reduced computational cost. Finally, we use invariant BO to design a current drive system for a nuclear fusion reactor, finding a high-performance solution where non-invariant methods failed.
Accurate uncertainty quantification for causal effects is essential for robust decision making in complex systems, but remains challenging in non-parametric settings. One promising framework represents conditional distributions in a reproducing kernel Hilbert space and places Gaussian process priors on them to infer posteriors on causal effects, but requires restrictive nuclear dominant kernels and approximations that lead to unreliable uncertainty estimates. In this work, we introduce a method, IMPspec, that addresses these limitations via a spectral representation of the Hilbert space. We show that posteriors in this model can be obtained explicitly, by extending a result in Hilbert space regression theory. We also learn the spectral representation to optimise posterior calibration. Our method achieves state-of-the-art performance in uncertainty quantification and causal Bayesian optimisation across simulations and a healthcare application.
Bayesian optimisation for real-world problems is often performed interactively with human experts, and integrating their domain knowledge is key to accelerate the optimisation process. We consider a setup where experts provide advice on the next query point through binary accept/reject recommendations (labels). Experts' labels are often costly, requiring efficient use of their efforts, and can at the same time be unreliable, requiring careful adjustment of the degree to which any expert is trusted. We introduce the first principled approach that provides two key guarantees. (1) Handover guarantee: similar to a no-regret property, we establish a sublinear bound on the cumulative number of experts' binary labels. Initially, multiple labels per query are needed, but the number of expert labels required asymptotically converges to zero, saving both expert effort and computation time. (2) No-harm guarantee with data-driven trust level adjustment: our adaptive trust level ensures that the convergence rate will not be worse than the one without using advice, even if the advice from experts is adversarial. Unlike existing methods that employ a user-defined function that hand-tunes the trust level adjustment, our approach enables data-driven adjustments. Real-world applications empirically demonstrate that our method not only outperforms existing baselines, but also maintains robustness despite varying labelling accuracy, in tasks of battery design with human experts.
Bayesian Optimization (BO) is widely used for optimising black-box functions but requires us to specify the length scale hyperparameter, which defines the smoothness of the functions the optimizer will consider. Most current BO algorithms choose this hyperparameter by maximizing the marginal likelihood of the observed data, albeit risking misspecification if the objective function is less smooth in regions we have not yet explored. The only prior solution addressing this problem with theoretical guarantees was A-GP-UCB, proposed by Berkenkamp et al. (2019). This algorithm progressively decreases the length scale, expanding the class of functions considered by the optimizer. However, A-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow convergence. To overcome this, we introduce Length scale Balancing (LB) - a novel approach, aggregating multiple base surrogate models with varying length scales. LB intermittently adds smaller length scale candidate values while retaining longer scales, balancing exploration and exploitation. We formally derive a cumulative regret bound of LB and compare it with the regret of an oracle BO algorithm using the optimal length scale. Denoting the factor by which the regret bound of A-GP-UCB was away from oracle as $g(T)$, we show that LB is only $\log g(T)$ away from oracle regret. We also empirically evaluate our algorithm on synthetic and real-world benchmarks and show it outperforms A-GP-UCB, maximum likelihood estimation and MCMC.
Autonomous tuning of particle accelerators is an active and challenging field of research with the goal of enabling novel accelerator technologies cutting-edge high-impact applications, such as physics discovery, cancer research and material sciences. A key challenge with autonomous accelerator tuning remains that the most capable algorithms require an expert in optimisation, machine learning or a similar field to implement the algorithm for every new tuning task. In this work, we propose the use of large language models (LLMs) to tune particle accelerators. We demonstrate on a proof-of-principle example the ability of LLMs to successfully and autonomously tune a particle accelerator subsystem based on nothing more than a natural language prompt from the operator, and compare the performance of our LLM-based solution to state-of-the-art optimisation algorithms, such as Bayesian optimisation (BO) and reinforcement learning-trained optimisation (RLO). In doing so, we also show how LLMs can perform numerical optimisation of a highly non-linear real-world objective function. Ultimately, this work represents yet another complex task that LLMs are capable of solving and promises to help accelerate the deployment of autonomous tuning algorithms to the day-to-day operations of particle accelerators.
This research paper introduces innovative approaches for multivariate time series forecasting based on different variations of the combined regression strategy. We use specific data preprocessing techniques which makes a radical change in the behaviour of prediction. We compare the performance of the model based on two types of hyper-parameter tuning Bayesian optimisation (BO) and Usual Grid search. Our proposed methodologies outperform all state-of-the-art comparative models. We illustrate the methodologies through eight time series datasets from three categories: cryptocurrency, stock index, and short-term load forecasting.
Rock mass classification systems are crucial for assessing stability and risk in underground construction globally and guiding support and excavation design. However, these systems, developed primarily in the 1970s, lack access to modern high-resolution data and advanced statistical techniques, limiting their effectiveness as decision-support systems. We outline these limitations and describe how a data-driven system, based on drilling data, can overcome them. Using statistical information extracted from thousands of MWD-data values in one-meter sections of a tunnel profile, acting as a signature of the rock mass, we demonstrate that well-defined clusters can form a foundational basis for various classification systems. Representation learning was used to reduce the dimensionality of 48-value vectors via a nonlinear manifold learning technique (UMAP) and linear principal component analysis (PCA) to enhance clustering. Unsupervised machine learning methods (HDBSCAN, Agglomerative Clustering, K-means) clustered the data, with hyperparameters optimised through multi-objective Bayesian optimisation. Domain knowledge improved clustering by adding extra features to core MWD-data clusters. We structured and correlated these clusters with physical rock properties, including rock type and quality, and analysed cumulative distributions of key MWD-parameters to determine if clusters meaningfully differentiate rock masses. The ability of MWD data to form distinct rock mass clusters suggests substantial potential for future classification systems using this objective, data-driven methodology, minimising human bias.