Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Machine learning tools for protein annotation: the cases of transmembrane β-barrel and myristoylated proteins

Biology is now a “Big Data Science” thanks to technological advancements allowing the characterization of the whole macromolecular content of a cell or a collection of cells. This opens interesting perspectives, but only a small portion of this data may be experimentally characterized. From this derives the demand of accurate and efficient computational tools for automatic annotation of biological molecules. This is even more true when dealing with membrane proteins, on which my research project is focused leading to the development of two machine learning-based methods: BetAware-Deep and SVMyr. BetAware-Deep is a tool for the detection and topology prediction of transmembrane beta-barrel proteins found in Gram-negative bacteria. These proteins are involved in many biological processes and primary candidates as drug targets. BetAware-Deep exploits the combination of a deep learning framework (bidirectional long short-term memory) and a probabilistic graphical model (grammatical-restrained hidden conditional random field). Moreover, it introduced a modified formulation of the hydrophobic moment, designed to include the evolutionary information. BetAware-Deep outperformed all the available methods in topology prediction and reported high scores in the detection task. Glycine myristoylation in Eukaryotes is the binding of a myristic acid on an N-terminal glycine. SVMyr is a fast method based on support vector machines designed to predict this modification in dataset of proteomic scale. It uses as input octapeptides and exploits computational scores derived from experimental examples and mean physicochemical features. SVMyr outperformed all the available methods for co-translational myristoylation prediction. In addition, it allows (as a unique feature) the prediction of post-translational myristoylation. Both the tools here described are designed having in mind best practices for the development of machine learning-based tools outlined by the bioinformatics community. Moreover, they are made available via user-friendly web servers. All this make them valuable tools for filling the gap between sequential and annotated data.

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.