Román Marchant

Roman Marchant, Dario Draca, Gilad Francis et al.

Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often violated in real-world applications. In such cases, using a single network structure for inference can be misleading, as it may not capture sub-population differences. To address this, we propose a novel approach of modelling a mixture of Bayesian networks where component probabilities depend on individual characteristics. Our method identifies both network structures and demographic predictors of sub-population membership, aiding personalised interventions. We evaluate our method through simulations and a youth mental health case study, demonstrating its potential to improve tailored interventions in health, education, and social policy.

Kim Bente, Roman Marchant, Fabio Ramos

To reliably project future sea level rise, ice sheet models require inputs that respect physics. Embedding physical principles like mass conservation into models that interpolate Antarctic ice flow vector fields from sparse & noisy measurements not only promotes physical adherence but can also improve accuracy and robustness. While physics-informed neural networks (PINNs) impose physics as soft penalties, offering flexibility but no physical guarantees, we instead propose divergence-free neural networks (dfNNs), which enforce local mass conservation exactly via a vector calculus trick. Our comparison of dfNNs, PINNs, and unconstrained NNs on ice flux interpolation over Byrd Glacier suggests that "mass conservation on rails" yields more reliable estimates, and that directional guidance, a learning strategy leveraging continent-wide satellite velocity data, boosts performance across models.

Philippe Morere, Roman Marchant, Fabio Ramos

Bayesian Optimisation has gained much popularity lately, as a global optimisation technique for functions that are expensive to evaluate or unknown a priori. While classical BO focuses on where to gather an observation next, it does not take into account practical constraints for a robotic system such as where it is physically possible to gather samples from, nor the sequential nature of the problem while executing a trajectory. In field robotics and other real-life situations, physical and trajectory constraints are inherent problems. This paper addresses these issues by formulating Bayesian Optimisation for continuous trajectories within a Partially Observable Markov Decision Process (POMDP) framework. The resulting POMDP is solved using Monte-Carlo Tree Search (MCTS), which we adapt to using a reward function balancing exploration and exploitation. Experiments on monitoring a spatial phenomenon with a UAV illustrate how our BO-POMDP algorithm outperforms competing techniques.

Gilad Francis, Lionel Ott, Roman Marchant et al.

We propose a novel holistic approach for safe autonomous exploration and map building based on constrained Bayesian optimisation. This method finds optimal continuous paths instead of discrete sensing locations that inherently satisfy motion and safety constraints. Evaluating both the objective and constraints functions requires forward simulation of expected observations. As such evaluations are costly, the Bayesian optimiser proposes only paths which are likely to yield optimal results and satisfy the constraints with high confidence. By balancing the reward and risk associated with each path, the optimiser minimises the number of expensive function evaluations. We demonstrate the effectiveness of our approach in a series of experiments both in simulation and with a real ground robot and provide comparisons to other exploration techniques. Evidently, each method has its specific favourable conditions, where it outperforms all other techniques. Yet, by reasoning on the usefulness of the entire path instead of its end point, our method provides a robust and consistent performance through all tests and performs better than or as good as the other leading methods.