Terence J. O'Kane

Xuhui Fan, Edwin V. Bonilla, Terence J. O'Kane et al.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

Stephen G. Dale, Nikita Kazeev, Alastair J. A. Price et al.

Artificial intelligence and machine learning are reshaping how we approach scientific discovery, not by replacing established methods but by extending what researchers can probe, predict, and design. In this roadmap we provide a forward-looking view of AI-enabled science across biology, chemistry, climate science, mathematics, materials science, physics, self-driving laboratories and unconventional computing. Several shared themes emerge: the need for diverse and trustworthy data, transferable electronic-structure and interatomic models, AI systems integrated into end-to-end scientific workflows that connect simulations to experiments and generative systems grounded in synthesisability rather than purely idealised phases. Across domains, we highlight how large foundation models, active learning and self-driving laboratories can close loops between prediction and validation while maintaining reproducibility and physical interpretability. Taken together, these perspectives outline where AI-enabled science stands today, identify bottlenecks in data, methods and infrastructure, and chart concrete directions for building AI systems that are not only more powerful but also more transparent and capable of accelerating discovery in complex real-world environments.

He Zhao, Vassili Kitsios, Terence J. O'Kane et al.

We study the problem of automatically discovering Granger causal relations from observational multivariate time-series data.Vector autoregressive (VAR) models have been time-tested for this problem, including Bayesian variants and more recent developments using deep neural networks. Most existing VAR methods for Granger causality use sparsity-inducing penalties/priors or post-hoc thresholds to interpret their coefficients as Granger causal graphs. Instead, we propose a new Bayesian VAR model with a hierarchical factorised prior distribution over binary Granger causal graphs, separately from the VAR coefficients. We develop an efficient algorithm to infer the posterior over binary Granger causal graphs. Comprehensive experiments on synthetic, semi-synthetic, and climate data show that our method is more uncertainty aware, has less hyperparameters, and achieves better performance than competing approaches, especially in low-data regimes where there are less observations.

Davide Bassetti, Lukáš Pospíšil, Michael Groom et al.

Progress of AI has led to very successful, but by no means humble models and tools, especially regarding (i) the huge and further exploding costs and resources they demand, and (ii) the over-confidence of these tools with the answers they provide. Here we introduce a novel mathematical framework for a non-equilibrium entropy-optimizing reformulation of Boltzmann machines based on the exact law of total probability and the exact convex polytope representations. We show that it results in the highly-performant, but much cheaper, gradient-descent-free learning framework with mathematically-justified existence and uniqueness criteria, and cheaply-computable confidence/reliability measures for both the model inputs and the outputs. Comparisons to state-of-the-art AI tools in terms of performance, cost and the model descriptor lengths on a broad set of synthetic and real-world problems with varying complexity reveal that the proposed method results in more performant and slim models, with the descriptor lengths being very close to the intrinsic complexity scaling bounds for the underlying problems. Applying this framework to historical climate data results in models with systematically higher prediction skills for the onsets of important La Niña and El Niño climate phenomena, requiring just few years of climate data for training - a small fraction of what is necessary for contemporary climate prediction tools.