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 reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.

Extreme events are evolving as a direct consequence of climate change, leading to the emergence of new, previously unobserved phenomena [1, 2]. In remote regions like the Arctic, where in-situ measurements are sparse, scientists must increasingly depend on analytical and numerical models to explore these events. However, modeling in such regions presents significant challenges due to the uncertainties in the data required to calibrate and validate these models [3]. Consequently, large simplifications are often necessary, resulting in substantial discrepancies between observed and modeled phenomena. The mysterious 10.88 mHz very-long-period (VLP) seismic signal, which appeared following a tsunamigenic landslide in the Dickson Fjord, Greenland, on September 16th, 2023, and the subsequent interdisciplinary scientific efforts to determine its origin, underscore these challenges. Two independent studies [4, 5] have hypothesized that the signal was driven by a standing wave, or seiche, which formed in the aftermath of the tsunami. While it is well-documented that seiches can form in resonant enclosed and semi-enclosed basins [6], the loading-induced tilt they produce has only been observed locally (< 30 km) and for short durations (< 1 hour)[5, 7]. Moreover, no prior evidence exists of persistent fluid sloshing (lasting several days) without an external driver.

Machine learning enables unbinned, highly-differential cross section measurements. A recent idea uses generative models to morph a starting simulation into the unfolded data. We show how to extend two morphing techniques, Schr\"odinger Bridges and Direct Diffusion, in order to ensure that the models learn the correct conditional probabilities. This brings distribution mapping to a similar level of accuracy as the state-of-the-art conditional generative unfolding methods. Numerical results are presented with a standard benchmark dataset of single jet substructure as well as for a new dataset describing a 22-dimensional phase space of Z + 2-jets.

Amortized simulation-based inference (SBI) methods train neural networks on simulated data to perform Bayesian inference. While this approach avoids the need for tractable likelihoods, it often requires a large number of simulations and has been challenging to scale to time-series data. Scientific simulators frequently emulate real-world dynamics through thousands of single-state transitions over time. We propose an SBI framework that can exploit such Markovian simulators by locally identifying parameters consistent with individual state transitions. We then compose these local results to obtain a posterior over parameters that align with the entire time series observation. We focus on applying this approach to neural posterior score estimation but also show how it can be applied, e.g., to neural likelihood (ratio) estimation. We demonstrate that our approach is more simulation-efficient than directly estimating the global posterior on several synthetic benchmark tasks and simulators used in ecology and epidemiology. Numerical simulations are a central approach for tackling problems in a wide range of scientific and engineering disciplines, including physics (Brehmer & Cranmer, 2022; Dax et al., 2021), molecular dynamics (Hollingsworth & Dror, 2018), neuroscience (Gonçalves et al., 2020) and climate science (Watson-Parris et al., 2021). Simulators often include at least some parameters that cannot be measured experimentally. Inferring such parameters from observed data is a fundamental challenge. Bayesian inference provides a principled approach to identifying parameters that align with empirical observations. Standard algorithms for Bayesian inference, such as Markov Chain Monte Carlo (MCMC) (Gilks et al., 1995) and variational inference (Beal, 2003), generally require access to the likelihoods p(x|θ). However, for many simulators, directly evaluating the likelihood remains intractable, rendering conventional Bayesian approaches inapplicable.

Deep neural network ensembles are powerful tools for uncertainty quantification, which have recently been re-interpreted from a Bayesian perspective. However, current methods inadequately leverage second-order information of the loss landscape, despite the recent availability of efficient Hessian approximations. We propose a novel approximate Bayesian inference method that modifies deep ensembles to incorporate Stein Variational Newton updates. Our approach uniquely integrates scalable modern Hessian approximations, achieving faster convergence and more accurate posterior distribution approximations. We validate the effectiveness of our method on diverse regression and classification tasks, demonstrating superior performance with a significantly reduced number of training epochs compared to existing ensemble-based methods, while enhancing uncertainty quantification and robustness against overfitting.

Most methods in explainable AI (XAI) focus on providing reasons for the prediction of a given set of features. However, we solve an inverse explanation problem, i.e., given the deviation of a label, find the reasons of this deviation. We use a Bayesian framework to recover the ``true'' features, conditioned on the observed label value. We efficiently explain the deviation of a label value from the mode, by identifying and ranking the influential features using the ``distances'' in the ANOVA functional decomposition. We show that the new method is more human-intuitive and robust than methods based on mean values, e.g., SHapley Additive exPlanations (SHAP values). The extra costs of solving a Bayesian inverse problem are dimension-independent.

When interacting with each other, humans adjust their behavior based on perceived trust. However, to achieve similar adaptability, robots must accurately estimate human trust at sufficiently granular timescales during the human-robot collaboration task. A beta reputation is a popular way to formalize a mathematical estimation of human trust. However, it relies on binary performance, which updates trust estimations only after each task concludes. Additionally, manually crafting a reward function is the usual method of building a performance indicator, which is labor-intensive and time-consuming. These limitations prevent efficiently capturing continuous changes in trust at more granular timescales throughout the collaboration task. Therefore, this paper presents a new framework for the estimation of human trust using a beta reputation at fine-grained timescales. To achieve granularity in beta reputation, we utilize continuous reward values to update trust estimations at each timestep of a task. We construct a continuous reward function using maximum entropy optimization to eliminate the need for the laborious specification of a performance indicator. The proposed framework improves trust estimations by increasing accuracy, eliminating the need for manually crafting a reward function, and advancing toward developing more intelligent robots. The source code is publicly available. https://github.com/resuldagdanov/robot-learning-human-trust

A common way to drive progress of AI models and agents is to compare their performance on standardized benchmarks. Comparing the performance of general agents requires aggregating their individual performances across a potentially wide variety of different tasks. In this paper, we describe a novel ranking scheme inspired by social choice frameworks, called Soft Condorcet Optimization (SCO), to compute the optimal ranking of agents: the one that makes the fewest mistakes in predicting the agent comparisons in the evaluation data. This optimal ranking is the maximum likelihood estimate when evaluation data (which we view as votes) are interpreted as noisy samples from a ground truth ranking, a solution to Condorcet's original voting system criteria. SCO ratings are maximal for Condorcet winners when they exist, which we show is not necessarily true for the classical rating system Elo. We propose three optimization algorithms to compute SCO ratings and evaluate their empirical performance. When serving as an approximation to the Kemeny-Young voting method, SCO rankings are on average 0 to 0.043 away from the optimal ranking in normalized Kendall-tau distance across 865 preference profiles from the PrefLib open ranking archive. In a simulated noisy tournament setting, SCO achieves accurate approximations to the ground truth ranking and the best among several baselines when 59\% or more of the preference data is missing. Finally, SCO ranking provides the best approximation to the optimal ranking, measured on held-out test sets, in a problem containing 52,958 human players across 31,049 games of the classic seven-player game of Diplomacy.

This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the $t$-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.