13 TESI DI DOTTORATO

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13 - Tesi di dottorato 869

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Advances in Bayesian cross-validation and tensor modelling

The first chapter presents a work I undertook with my supervisor Giacomo Zanella. We propose a novel estimator for the log pointwise predictive density(lppd) of a Bayesian model. The naive method to calculate this quantity would require running n markov chain Monte Carlo (MCMC) chains, resulting in an unfeasible computational cost. A classical approach to overcome such a problem is to leverage importance sampling, which although solves the computational hurdle results in a estimator that can...

Sequential skew-symmetric posterior approximations

Deterministic approximations of analytically intractable posterior distributions are a common tool in Bayesian analysis. However, accurate extensions of these methods to situations in which data stream in rapidly and sequentially are still under-explored. In this thesis, we cover this gap by deriving a general and provably-accurate skew-symmetric approximation of a target posterior whose parameters can be evaluated via novel window-type estimators that make computations effectively online. Th...

Contributions to dependent processes in Bayesian nonparametrics

Random measures represent the fundamental building blocks for defining flexible priors in Bayesian nonparametric models. Over the last three decades, there has been a widespread diffusion of proposals aimed at introducing dependence among different random measures, in order to properly account for various forms of heterogeneity in the observations while preserving the possibility to borrow information across them. The first part of the thesis focuses on vectors of dependent random measures de...

Topics in scalable Bayesian posterior estimation

As the complexity and dimensionality of data continue to increase, it is becoming fundamental to develop advanced strategies for statistical inference and to explore their computational properties (Bishop, 2006). This thesis considers Bayesian models, known for their ability to frame prediction and uncertainty within a coherent probabilistic framework. However, achieving accurate estimates of posterior quantities within these models generally requires innovative techniques to accommodate the ...

Essays in Economics of Artificial Intelligence

This thesis embodies three chapters on the economics and applications of artificial intelligence (AI). The first chapter explores the economic underpinnings of open-source contributions in AI by for-profit companies, focusing on large language models (LLMs). Three main findings emerge: (1) LLMs align well with the R&D portfolios of diverse technologically advanced firms, (2) models developed by large technology companies are more likely to be open-sourced, and (3) open-sourcing advanced LLMs ...

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