arXiv subjects

Luigi Augugliaro

Publications and source records attributed to Luigi Augugliaro.

6 recordsLinked to original sources

arXiv2026

Gaussian Graphical Models for Partially Observed Multivariate Functional Data

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependencies among these variables. It is often the case that the functional data are only partially observed. This creates additional challenges to statistical inference, since the functional principal component scores, which capture all the information from these data, cannot be computed. Under an assumption of Gaussianity and of partial separability of the covariance operator, we develop an Expectation-Maximization (EM)-type algorithm for penalized inference of a functional graphical model from multivariate functional data which are only partially observed. A simulation study and an illustration on environmental, social and governance (ESG) data show the potential of the proposed method.

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arXiv2024

Functional Gaussian Graphical Regression Models For Air Quality Data

Functional data describe a wide range of processes, such as growth curves and spectral absorption. In this study, we analyze air pollution data from the In-service Aircraft for a Global Observing System, focusing on the spatial interactions among chemicals in the atmosphere and their dependence on meteorological conditions. This requires functional regression, where both response and covariates are functional objects evolving over the troposphere. Evaluating both the functional relatedness between the response and covariates and the relatedness of a multivariate response function can be challenging. We propose a solution to these challenges by introducing a functional Gaussian graphical regression model, extending conditional Gaussian graphical models to partially separable functions. To estimate the model, we propose a doubly-penalized estimator. Additionally, we present a novel adaptation of Kullback-Leibler cross-validation tailored for graph estimators which accounts for precision and regression matrices when the population presents one or more sub-groups, named joint Kullback-Leibler cross-validation. Evaluation of model performance is done in terms of Kullback-Leibler divergence and graph recovery power.

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arXiv2022

The CDF penalty:sparse and quasi unbiased estimation in regression models

In high-dimensional regression modelling, the number of candidate covariates to be included in the predictor is quite large, and variable selection is crucial. In this work, we propose a new penalty able to guarantee both sparse variable selection, i.e. exactly zero regression coefficient estimates, and quasi-unbiasedness for the coefficients of 'selected' variables in high dimensional regression models. Simulation results suggest that our proposal performs no worse than its competitors while always ensuring that the solution is unique.

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arXiv2022

Sparse inference of the human hematopoietic system from heterogeneous and partially observed genomic data

Hematopoiesis is the process of blood cell formation, through which progenitor stem cells differentiate into mature forms, such as white and red blood cells or mature platelets. While the precursors of the mature forms share many regulatory pathways involving common cellular nuclear factors, specific networks of regulation shape their fate towards one lineage or another. In this study, we aim to analyse the complex regulatory network that drives the formation of mature red blood cells and platelets from their common precursor. To this aim, we develop a dedicated graphical model which we infer from the latest RT-qPCR genomic data. The model also accounts for the effect of external genomic data. A computationally efficient Expectation-Maximization algorithm allows regularised network inference from the high-dimensional and often only partially observed RT-qPCR data. A careful combination of alternating direction method of multipliers algorithms allows achieving sparsity in the individual lineage networks and a high sharing between these networks, together with the detection of the associations between the membrane-bound receptors and the nuclear factors. The approach will be implemented in the R package cglasso and can be used in similar applications where network inference is conducted from high-dimensional, heterogeneous and partially observed data.

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arXiv2019

The conditional censored graphical lasso estimator

In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data generated by polymerase chain reactions and flow cytometer. When the overall objective is that of network inference, at possibly different levels of a system, information coming from different sources and/or different steps of the analysis can be integrated into one model with the use of conditional graphical models. In this paper, we develop a doubly penalized inferential procedure for a conditional Gaussian graphical model when data can be subject to censoring. The computational challenges of handling censored data in high dimensionality are met with the development of an efficient Expectation-Maximization algorithm, based on approximate calculations of the moments of truncated Gaussian distributions and on a suitably derived two-step procedure alternating graphical lasso with a novel block-coordinate multivariate lasso approach. We evaluate the performance of this approach on an extensive simulation study and on gene expression data generated by RT-qPCR technologies, where we are able to integrate network inference, differential expression detection and data normalization into one model.

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arXiv2018

L1-Penalized Censored Gaussian Graphical Model

Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this paper we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithms for inference. By an extensive simulation study, we evaluate the computational efficiency of the proposed algorithms and show that our proposal overcomes existing competitors when censored data are available. We apply the proposed method to gene expression data coming from microfluidic RT-qPCR technology in order to make inference on the regulatory mechanisms of blood development.

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