Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

Integrated communication and learning towards autonomous mobile radio networks

The integration of distributed and ubiquitous intelligence has emerged over the last years as the mainspring of transformative advancements in mobile radio networks. As we approach the era of “mobile for intelligence”, next-generation wireless networks are poised to undergo significant and profound changes. Notably, the overarching challenge that lies ahead is the development and implementation of integrated communication and learning mechanisms that will enable the realization of autonomous mobile radio networks. The ultimate pursuit of eliminating human-in-the-loop constitutes an ambitious challenge, necessitating a meticulous delineation of the fundamental characteristics that artificial intelligence (AI) should possess to effectively achieve this objective. This challenge represents a paradigm shift in the design, deployment, and operation of wireless networks, where conventional, static configurations give way to dynamic, adaptive, and AI-native systems capable of self-optimization, self-sustainment, and learning. This thesis aims to provide a comprehensive exploration of the fundamental principles and practical approaches required to create autonomous mobile radio networks that seamlessly integrate communication and learning components. The first chapter of this thesis introduces the notion of Predictive Quality of Service (PQoS) and adaptive optimization and expands upon the challenge to achieve adaptable, reliable, and robust network performance in dynamic and ever-changing environments. The subsequent chapter delves into the revolutionary role of generative AI in shaping next-generation autonomous networks. This chapter emphasizes achieving trustworthy uncertainty-aware generation processes with the use of approximate Bayesian methods and aims to show how generative AI can improve generalization while reducing data communication costs. Finally, the thesis embarks on the topic of distributed learning over wireless networks. Distributed learning and its declinations, including multi-agent reinforcement learning systems and federated learning, have the potential to meet the scalability demands of modern data-driven applications, enabling efficient and collaborative model training across dynamic scenarios while ensuring data privacy and reducing communication overhead.