New approaches to open problems in gene expression microarray data

In the past decade, the advent of efficient genome sequencing tools and high-throughput experimental biotechnology has lead to enormous progress in the life science. Among the most important innovations is the microarray tecnology. It allows to quantify the expression for thousands of genes simultaneously by measurin the hybridization from a tissue of interest to probes on a small glass or plastic slide. The characteristics of these data include a fair amount of random noise, a predictor dimension in the thousand, and a sample noise in the dozens. One of the most exciting areas to which microarray technology has been applied is the challenge of deciphering complex disease such as cancer. In these studies, samples are taken from two or more groups of individuals with heterogeneous phenotypes, pathologies, or clinical outcomes. these samples are hybridized to microarrays in an effort to find a small number of genes which are strongly correlated with the group of individuals. Eventhough today methods to analyse the data are welle developed and close to reach a standard organization (through the effort of preposed International project like Microarray Gene Expression Data -MGED- Society [1]) it is not unfrequant to stumble in a clinician's question that do not have a compelling statistical method that could permit to answer it.The contribution of this dissertation in deciphering disease regards the development of new approaches aiming at handle open problems posed by clinicians in handle specific experimental designs. In Chapter 1 starting from a biological necessary introduction, we revise the microarray tecnologies and all the important steps that involve an experiment from the production of the array, to the quality controls ending with preprocessing steps that will be used into the data analysis in the rest of the dissertation. While in Chapter 2 a critical review of standard analysis methods are provided stressing most of problems that In Chapter 3 is introduced a method to adress the issue of unbalanced design of miacroarray experiments. In microarray experiments, experimental design is a crucial starting-point for obtaining reasonable results. In a two-class problem, an equal or similar number of samples it should be collected between the two classes. However in some cases, e.g. rare pathologies, the approach to be taken is less evident. We propose to address this issue by applying a modified version of SAM [2]. MultiSAM consists in a reiterated application of a SAM analysis, comparing the less populated class (LPC) with 1,000 random samplings of the same size from the more populated class (MPC) A list of the differentially expressed genes is generated for each SAM application. After 1,000 reiterations, each single probe given a "score" ranging from 0 to 1,000 based on its recurrence in the 1,000 lists as differentially expressed. The performance of MultiSAM was compared to the performance of SAM and LIMMA [3] over two simulated data sets via beta and exponential distribution. The results of all three algorithms over low- noise data sets seems acceptable However, on a real unbalanced two-channel data set reagardin Chronic Lymphocitic Leukemia, LIMMA finds no significant probe, SAM finds 23 significantly changed probes but cannot separate the two classes, while MultiSAM finds 122 probes with score >300 and separates the data into two clusters by hierarchical clustering. We also report extra-assay validation in terms of differentially expressed genes Although standard algorithms perform well over low-noise simulated data sets, multi-SAM seems to be the only one able to reveal subtle differences in gene expression profiles on real unbalanced data. In Chapter 4 a method to adress similarities evaluation in a three-class prblem by means of Relevance Vector Machine [4] is described. In fact, looking at microarray data in a prognostic and diagnostic clinical framework, not only differences could have a crucial role. In some cases similarities can give useful and, sometimes even more, important information. The goal, given three classes, could be to establish, with a certain level of confidence, if the third one is similar to the first or the second one. In this work we show that Relevance Vector Machine (RVM) [2] could be a possible solutions to the limitation of standard supervised classification. In fact, RVM offers many advantages compared, for example, with his well-known precursor (Support Vector Machine - SVM [3]). Among these advantages, the estimate of posterior probability of class membership represents a key feature to address the similarity issue. This is a highly important, but often overlooked, option of any practical pattern recognition system. We focused on Tumor-Grade-three-class problem, so we have 67 samples of grade I (G1), 54 samples of grade 3 (G3) and 100 samples of grade 2 (G2). The goal is to find a model able to separate G1 from G3, then evaluate the third class G2 as test-set to obtain the probability for samples of G2 to be member of class G1 or class G3. The analysis showed that breast cancer samples of grade II have a molecular profile more similar to breast cancer samples of grade I. Looking at the literature this result have been guessed, but no measure of significance was gived before.

Multi-functional electrocatalysts for CO2 reduction reaction: towards the modulation of selectivity

The electrocatalytic reduction of CO2 (CO2RR) is a captivating strategy for the conversion of CO2 into fuels, to realize a carbon neutral circular economy. In the recent years, research has focused on the development of new materials and technology capable of capturing and converting CO2 into useful products. The main problem of CO2RR is given by its poor selectivity, which can lead to the formation of numerous reaction products, to the detriment of efficiencies. For this reason, the design of new electrocatalysts that selectively and efficiently reduce CO2 is a fundamental step for the future exploitation of this technology. Here we present a new class of electrocatalysts, designed with a modular approach, namely, deriving from the combination of different building blocks in a single nanostructure. With this approach it is possible to obtain materials with an innovative design and new functionalities, where the interconnections between the various components are essential to obtain a highly selective and efficient reduction of CO2, thus opening up new possibilities in the design of optimized electrocatalytic materials. By combining the unique physic-chemical properties of carbon nanostructures (CNS) with nanocrystalline metal oxides (MO), we were able to modulate the selectivity of CO2RR, with the production of formic acid and syngas at low overpotentials. The CNS have not only the task of stabilizing the MO nanoparticles, but the creation of an optimal interface between two nanostructures is able to improve the catalytic activity of the active phase of the material. While the presence of oxygen atoms in the MO creates defects that accelerate the reaction kinetics and stabilize certain reaction intermediates, selecting the reaction pathway. Finally, a part was dedicated to the study of the experimental parameters influencing the CO2RR, with the aim of improving the experimental setup in order to obtain commercial catalytic performances.

Applying machine learning: a multi-role perspective

Machine (and deep) learning technologies are more and more present in several fields. It is undeniable that many aspects of our society are empowered by such technologies: web searches, content filtering on social networks, recommendations on e-commerce websites, mobile applications, etc., in addition to academic research. Moreover, mobile devices and internet sites, e.g., social networks, support the collection and sharing of information in real time. The pervasive deployment of the aforementioned technological instruments, both hardware and software, has led to the production of huge amounts of data. Such data has become more and more unmanageable, posing challenges to conventional computing platforms, and paving the way to the development and widespread use of the machine and deep learning. Nevertheless, machine learning is not only a technology. Given a task, machine learning is a way of proceeding (a way of thinking), and as such can be approached from different perspectives (points of view). This, in particular, will be the focus of this research. The entire work concentrates on machine learning, starting from different sources of data, e.g., signals and images, applied to different domains, e.g., Sport Science and Social History, and analyzed from different perspectives: from a non-data scientist point of view through tools and platforms; setting a problem stage from scratch; implementing an effective application for classification tasks; improving user interface experience through Data Visualization and eXtended Reality. In essence, not only in a quantitative task, not only in a scientific environment, and not only from a data-scientist perspective, machine (and deep) learning can do the difference.

Modelling and classification with quantile-based distributions

In this work, we explore and demonstrate the potential for modeling and classification using quantile-based distributions, which are random variables defined by their quantile function. In the first part we formalize a least squares estimation framework for the class of linear quantile functions, leading to unbiased and asymptotically normal estimators. Among the distributions with a linear quantile function, we focus on the flattened generalized logistic distribution (fgld), which offers a wide range of distributional shapes. A novel naïve-Bayes classifier is proposed that utilizes the fgld estimated via least squares, and through simulations and applications, we demonstrate its competitiveness against state-of-the-art alternatives. In the second part we consider the Bayesian estimation of quantile-based distributions. We introduce a factor model with independent latent variables, which are distributed according to the fgld. Similar to the independent factor analysis model, this approach accommodates flexible factor distributions while using fewer parameters. The model is presented within a Bayesian framework, an MCMC algorithm for its estimation is developed, and its effectiveness is illustrated with data coming from the European Social Survey. The third part focuses on depth functions, which extend the concept of quantiles to multivariate data by imposing a center-outward ordering in the multivariate space. We investigate the recently introduced integrated rank-weighted (IRW) depth function, which is based on the distribution of random spherical projections of the multivariate data. This depth function proves to be computationally efficient and to increase its flexibility we propose different methods to explicitly model the projected univariate distributions. Its usefulness is shown in classification tasks: the maximum depth classifier based on the IRW depth is proven to be asymptotically optimal under certain conditions, and classifiers based on the IRW depth are shown to perform well in simulated and real data experiments.