arXiv subjects

Tullia Padellini

Publications and source records attributed to Tullia Padellini.

6 recordsLinked to original sources

arXiv2023

Energy Trees: Regression and Classification With Structured and Mixed-Type Covariates

The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex data objects in their original form, these tools are typically limited to single-type variables. In this work, we propose energy trees as a regression and classification model capable of accommodating structured covariates of various types. Energy trees leverage energy statistics to extend the capabilities of conditional inference trees, from which they inherit sound statistical foundations, interpretability, scale invariance, and freedom from distributional assumptions. We specifically focus on functional and graph-structured covariates, while also highlighting the model's flexibility in integrating other variable types. Extensive simulation studies demonstrate the model's competitive performance in terms of variable selection and robustness to overfitting. Finally, we assess the model's predictive ability through two empirical analyses involving human biological data. Energy trees are implemented in the R package etree.

stat.ME↗

arXiv2021

A Bayesian hierarchical small-area population model accounting for data source specific methodologies from American Community Survey, Population Estimates Program, and Decennial Census data

Small area estimates of population are necessary for many epidemiological studies, yet their quality and accuracy are often not assessed. In the United States, small area estimates of population counts are published by the United States Census Bureau (USCB) in the form of the Decennial census counts, Intercensal population projections (PEP), and American Community Survey (ACS) estimates. Although there are significant relationships between these data sources, there are important contrasts in data collection and processing methodologies, such that each set of estimates may be subject to different sources and magnitudes of error. Additionally, these data sources do not report identical small area population counts due to post-survey adjustments specific to each data source. Resulting small area disease/mortality rates may differ depending on which data source is used for population counts (denominator data). To accurately capture annual small area population counts, and associated uncertainties, we present a Bayesian population model (B-Pop), which fuses information from all three USCB sources, accounting for data source specific methodologies and associated errors. The main features of our framework are: 1) a single model integrating multiple data sources, 2) accounting for data source specific data generating mechanisms, and specifically accounting for data source specific errors, and 3) prediction of estimates for years without USCB reported data. We focus our study on the 159 counties of Georgia, and produce estimates for years 2005-2021.

stat.ME↗

arXiv2021

Interoperability of statistical models in pandemic preparedness: principles and reality

We present "interoperability" as a guiding framework for statistical modelling to assist policy makers asking multiple questions using diverse datasets in the face of an evolving pandemic response. Interoperability provides an important set of principles for future pandemic preparedness, through the joint design and deployment of adaptable systems of statistical models for disease surveillance using probabilistic reasoning. We illustrate this through case studies for inferring spatial-temporal coronavirus disease 2019 (COVID-19) prevalence and reproduction numbers in England.

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arXiv2019

Model-aware Quantile Regression for Discrete Data

Quantile regression relates the quantile of the response to a linear predictor. For a discrete response distributions, like the Poission, Binomial and the negative Binomial, this approach is not feasible as the quantile function is not bijective. We argue to use a continuous model-aware interpolation of the quantile function, allowing for proper quantile inference while retaining model interpretation. This approach allows for proper uncertainty quantification and mitigates the issue of quantile crossing. Our reanalysis of hospitalisation data considered in Congdon (2017) shows the advantages of our proposal as well as introducing a novel method to exploit quantile regression in the context of disease mapping.

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arXiv2017

Persistence Flamelets: multiscale Persistent Homology for kernel density exploration

In recent years there has been noticeable interest in the study of the "shape of data". Among the many ways a "shape" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure: connected components (topological features of dimension 0), cycles (features of dimension 1) and so on. There is a growing number of techniques, generally denoted as Topological Data Analysis, aimed at estimating topological invariants of a fixed object; when we allow this object to change, however, little has been done to investigate the evolution in its topology. In this work we define the Persistence Flamelets, a multiscale version of one of the most popular tool in TDA, the Persistence Landscape. We examine its theoretical properties and we show how it could be used to gain insights on KDEs bandwidth parameter.

stat.ML↗

arXiv2017

Supervised Learning with Indefinite Topological Kernels

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in complex spaces, we adopt a kernel approach to translate them into more familiar vector spaces. We define a topological exponential kernel, we characterize it, and we show that, despite not being positive semi-definite, it can be successfully used in regression and classification tasks.

stat.ML↗