Learning an ordering of items based on noisy pairwise comparisons is useful when item-specific labels are difficult to assign, for example, when annotators have to make subjective assessments. Algorithms have been proposed for actively sampling comparisons of items to minimize the number of annotations necessary for learning an accurate ordering. However, many ignore shared structure between items, treating them as unrelated, limiting sample efficiency and precluding generalization to new items. In this work, we study active learning with pairwise preference feedback for ordering items with contextual attributes, both in- and out-of-sample. We give an upper bound on the expected ordering error incurred by active learning strategies under a logistic preference model, in terms of the aleatoric and epistemic uncertainty in comparisons, and propose two algorithms designed to greedily minimize this bound. We evaluate these algorithms in two realistic image ordering tasks, including one with comparisons made by human annotators, and demonstrate superior sample efficiency compared to non-contextual ranking approaches and active preference learning baselines.

Autonomous exploration of unknown environments using a team of mobile robots demands distributed perception and planning strategies to enable efficient and scalable performance. Ideally, each robot should update its map and plan its motion not only relying on its own observations, but also considering the observations of its peers. Centralized solutions to multi-robot coordination are susceptible to central node failure and require a sophisticated communication infrastructure for reliable operation. Current decentralized active mapping methods consider simplistic robot models with linear-Gaussian observations and Euclidean robot states. In this work, we present a distributed multi-robot mapping and planning method, called Riemannian Optimization for Active Mapping (ROAM). We formulate an optimization problem over a graph with node variables belonging to a Riemannian manifold and a consensus constraint requiring feasible solutions to agree on the node variables. We develop a distributed Riemannian optimization algorithm that relies only on one-hop communication to solve the problem with consensus and optimality guarantees. We show that multi-robot active mapping can be achieved via two applications of our distributed Riemannian optimization over different manifolds: distributed estimation of a 3-D semantic map and distributed planning of SE(3) trajectories that minimize map uncertainty. We demonstrate the performance of ROAM in simulation and real-world experiments using a team of robots with RGB-D cameras.

This thesis aims to study some of the mathematical challenges that arise in the analysis of statistical sequential decision-making algorithms for postoperative patients follow-up. Stochastic bandits (multiarmed, contextual) model the learning of a sequence of actions (policy) by an agent in an uncertain environment in order to maximise observed rewards. To learn optimal policies, bandit algorithms have to balance the exploitation of current knowledge and the exploration of uncertain actions. Such algorithms have largely been studied and deployed in industrial applications with large datasets, low-risk decisions and clear modelling assumptions, such as clickthrough rate maximisation in online advertising. By contrast, digital health recommendations call for a whole new paradigm of small samples, risk-averse agents and complex, nonparametric modelling. To this end, we developed new safe, anytime-valid concentration bounds, (Bregman, empirical Chernoff), introduced a new framework for risk-aware contextual bandits (with elicitable risk measures) and analysed a novel class of nonparametric bandit algorithms under weak assumptions (Dirichlet sampling). In addition to the theoretical guarantees, these results are supported by in-depth empirical evidence. Finally, as a first step towards personalised postoperative follow-up recommendations, we developed with medical doctors and surgeons an interpretable machine learning model to predict the long-term weight trajectories of patients after bariatric surgery.

Social agents with finitely nested opponent models are vulnerable to manipulation by agents with deeper reasoning and more sophisticated opponent modelling. This imbalance, rooted in logic and the theory of recursive modelling frameworks, cannot be solved directly. We propose a computational framework, $\aleph$-IPOMDP, augmenting model-based RL agents' Bayesian inference with an anomaly detection algorithm and an out-of-belief policy. Our mechanism allows agents to realize they are being deceived, even if they cannot understand how, and to deter opponents via a credible threat. We test this framework in both a mixed-motive and zero-sum game. Our results show the $\aleph$ mechanism's effectiveness, leading to more equitable outcomes and less exploitation by more sophisticated agents. We discuss implications for AI safety, cybersecurity, cognitive science, and psychiatry.

This paper introduces "Semantic Scaling," a novel method for ideal point estimation from text. I leverage large language models to classify documents based on their expressed stances and extract survey-like data. I then use item response theory to scale subjects from these data. Semantic Scaling significantly improves on existing text-based scaling methods, and allows researchers to explicitly define the ideological dimensions they measure. This represents the first scaling approach that allows such flexibility outside of survey instruments and opens new avenues of inquiry for populations difficult to survey. Additionally, it works with documents of varying length, and produces valid estimates of both mass and elite ideology. I demonstrate that the method can differentiate between policy preferences and in-group/out-group affect. Among the public, Semantic Scaling out-preforms Tweetscores according to human judgement; in Congress, it recaptures the first dimension DW-NOMINATE while allowing for greater flexibility in resolving construct validity challenges.

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter learning, often neglecting the potential of knowledge-intensive learning, a particular issue in data-scarce/knowledge-rich domains such as healthcare. To bridge this gap, we propose a novel unified framework that can systematically integrate diverse domain knowledge into the parameter learning process of PCs. Experiments on several benchmarks as well as real world datasets show that our proposed framework can both effectively and efficiently leverage domain knowledge to achieve superior performance compared to purely data-driven learning approaches.

Computed Tomography (CT) is pivotal in industrial quality control and medical diagnostics. Sparse-view CT, offering reduced ionizing radiation, faces challenges due to its under-sampled nature, leading to ill-posed reconstruction problems. Recent advancements in Implicit Neural Representations (INRs) have shown promise in addressing sparse-view CT reconstruction. Recognizing that CT often involves scanning similar subjects, we propose a novel approach to improve reconstruction quality through joint reconstruction of multiple objects using INRs. This approach can potentially leverage both the strengths of INRs and the statistical regularities across multiple objects. While current INR joint reconstruction techniques primarily focus on accelerating convergence via meta-initialization, they are not specifically tailored to enhance reconstruction quality. To address this gap, we introduce a novel INR-based Bayesian framework integrating latent variables to capture the inter-object relationships. These variables serve as a dynamic reference throughout the optimization, thereby enhancing individual reconstruction fidelity. Our extensive experiments, which assess various key factors such as reconstruction quality, resistance to overfitting, and generalizability, demonstrate significant improvements over baselines in common numerical metrics. This underscores a notable advancement in CT reconstruction methods.

This work is focused on the morphological classification of galaxies following the Hubble sequence in which the different classes are arranged in a hierarchy. The proposed method, BCNN, is composed of two main modules. First, a convolutional neural network (CNN) is trained with images of the different classes of galaxies (image augmentation is carried out to balance some classes); the CNN outputs the probability for each class of the hierarchy, and its outputs/predictions feed the second module. The second module consists of a Bayesian network that represents the hierarchy and helps to improve the prediction accuracy by combining the predictions of the first phase while maintaining the hierarchical constraint (in a hierarchy, an instance associated with a node must be associated to all its ancestors), through probabilistic inference over the Bayesian network so that a consistent prediction is obtained. Different images from the Hubble telescope have been collected and labeled by experts, which are used to perform the experiments. The results show that BCNN performed better than several CNNs in multiple evaluation measures, reaching the next scores: 67% in exact match, 78% in accuracy, and 83% in hierarchical F-measure.

In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such improvements were measured were accurately capturing the intended goal, whether the numerical differences in the resulting values were significant, or whether uncertainty played a role in this study and if it should have been taken into account, was of secondary importance. Whereas probability theory, be it frequentist or Bayesian, used to be the gold standard in science before the advent of the supercomputer, it was quickly replaced in favor of black box models and sheer computing power because of their ability to handle large data sets. This evolution sadly happened at the expense of interpretability and trustworthiness. However, while people are still trying to improve the predictive power of their models, the community is starting to realize that for many applications it is not so much the exact prediction that is of importance, but rather the variability or uncertainty. The work in this dissertation tries to further the quest for a world where everyone is aware of uncertainty, of how important it is and how to embrace it instead of fearing it. A specific, though general, framework that allows anyone to obtain accurate uncertainty estimates is singled out and analysed. Certain aspects and applications of the framework -- dubbed `conformal prediction' -- are studied in detail. Whereas many approaches to uncertainty quantification make strong assumptions about the data, conformal prediction is, at the time of writing, the only framework that deserves the title `distribution-free'. No parametric assumptions have to be made and the nonparametric results also hold without having to resort to the law of large numbers in the asymptotic regime.

Predicting the remaining useful life (RUL) of ball bearings plays an important role in predictive maintenance. A common definition of the RUL is the time until a bearing is no longer functional, which we denote as an event, and many data-driven methods have been proposed to predict the RUL. However, few studies have addressed the problem of censored data, where this event of interest is not observed, and simply ignoring these observations can lead to an overestimation of the failure risk. In this paper, we propose a probabilistic estimation of RUL using survival analysis that supports censored data. First, we analyze sensor readings from ball bearings in the frequency domain and annotate when a bearing starts to deteriorate by calculating the Kullback-Leibler (KL) divergence between the probability density function (PDF) of the current process and a reference PDF. Second, we train several survival models on the annotated bearing dataset, capable of predicting the RUL over a finite time horizon using the survival function. This function is guaranteed to be strictly monotonically decreasing and is an intuitive estimation of the remaining lifetime. We demonstrate our approach in the XJTU-SY dataset using cross-validation and find that Random Survival Forests consistently outperforms both non-neural networks and neural networks in terms of the mean absolute error (MAE). Our work encourages the inclusion of censored data in predictive maintenance models and highlights the unique advantages that survival analysis offers when it comes to probabilistic RUL estimation and early fault detection.