arXiv subjects

Pierpaolo Brutti

Publications and source records attributed to Pierpaolo Brutti.

14 recordsLinked to original sources

arXiv2026

Spectral Diffusion Models on the Sphere

Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. However, extension of spectral diffusion approaches to spherical data raises nontrivial geometric and stochastic issues that are absent in the Euclidean setting. In this work, we develop a diffusion modeling framework defined directly on finite-dimensional spherical harmonic representations of real-valued functions on the sphere. We show that the spherical discrete Fourier transform maps spatial Brownian motion to a constrained Gaussian process in the frequency domain with deterministic, generally non-isotropic covariance. This induces modified forward- and reverse-time stochastic differential equations in the spectral domain. As a consequence, spatial and spectral score matching objectives are generally no longer equivalent, even in the band-limited setting. We establish a quantitative relationship between the two objectives, showing that the geometry-induced covariance of the spectral noise gives rise to a distinct, geometry-dependent inductive bias. We also derive the corresponding forward and reverse diffusion equations and characterize the induced noise covariance.

math.PR↗

arXiv2026

Statistical Foundations of DIME: Risk Estimation for Practical Index Selection

High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify informative components of embeddings. DIME relies on a costly grid search to select a priori a dimensionality for all the query corpus's embeddings. Our work provides a statistically grounded criterion that directly identifies the optimal set of dimensions for each query at inference time. Experiments confirm achieving parity of effectiveness and reduces embedding size by an average of $\sim50\%$ across different models and datasets at inference time.

cs.IR↗

arXiv2025

Change Point Detection for Functional Autoregressive Processes on the Sphere

We introduce a novel framework for change point detection in spherical functional autoregressive (SPHAR) processes, enabling the identification of structural breaks in spatio-temporal random fields on the sphere. Our LASSO-regularized estimator, based on penalized dynamic programming in the harmonic domain, operates without knowledge of the number or locations of change points and offers non-asymptotic theoretical guarantees. This approach provides a new tool for analyzing nonstationary phenomena on the sphere, relevant to climate science, cosmology, and beyond.

stat.ME↗

arXiv2024

Federated GNNs for EEG-Based Stroke Assessment

Machine learning (ML) has the potential to become an essential tool in supporting clinical decision-making processes, offering enhanced diagnostic capabilities and personalized treatment plans. However, outsourcing medical records to train ML models using patient data raises legal, privacy, and security concerns. Federated learning has emerged as a promising paradigm for collaborative ML, meeting healthcare institutions' requirements for robust models without sharing sensitive data and compromising patient privacy. This study proposes a novel method that combines federated learning (FL) and Graph Neural Networks (GNNs) to predict stroke severity using electroencephalography (EEG) signals across multiple medical institutions. Our approach enables multiple hospitals to jointly train a shared GNN model on their local EEG data without exchanging patient information. Specifically, we address a regression problem by predicting the National Institutes of Health Stroke Scale (NIHSS), a key indicator of stroke severity. The proposed model leverages a masked self-attention mechanism to capture salient brain connectivity patterns and employs EdgeSHAP to provide post-hoc explanations of the neurological states after a stroke. We evaluated our method on EEG recordings from four institutions, achieving a mean absolute error (MAE) of 3.23 in predicting NIHSS, close to the average error made by human experts (MAE $\approx$ 3.0). This demonstrates the method's effectiveness in providing accurate and explainable predictions while maintaining data privacy.

cs.LG↗

arXiv2024

Feasibility Analysis of Federated Neural Networks for Explainable Detection of Atrial Fibrillation

Early detection of atrial fibrillation (AFib) is challenging due to its asymptomatic and paroxysmal nature. However, advances in deep learning algorithms and the vast collection of electrocardiogram (ECG) data from devices such as the Internet of Things (IoT) hold great potential for the development of an effective solution. This study assesses the feasibility of training a neural network on a Federated Learning (FL) platform to detect AFib using raw ECG data. The performance of an advanced neural network is evaluated in centralized, local, and federated settings. The effects of different aggregation methods on model performance are investigated, and various normalization strategies are explored to address issues related to neural network federation. The results demonstrate that federated learning can significantly improve the accuracy of detection over local training. The best performing federated model achieved an F1 score of 77\%, improving performance by 15\% compared to the average performance of individually trained clients. This study emphasizes the promise of FL in medical diagnostics, offering a privacy-preserving and interpretable solution for large-scale healthcare applications.

eess.SP↗

arXiv2024

Towards Explainable Graph Neural Networks for Neurological Evaluation on EEG Signals

After an acute stroke, accurately estimating stroke severity is crucial for healthcare professionals to effectively manage patient's treatment. Graph theory methods have shown that brain connectivity undergoes frequency-dependent reorganization post-stroke, adapting to new conditions. Traditional methods often rely on handcrafted features that may not capture the complexities of clinical phenomena. In this study, we propose a novel approach using Graph Neural Networks (GNNs) to predict stroke severity, as measured by the NIH Stroke Scale (NIHSS). We analyzed electroencephalography (EEG) recordings from 71 patients at the time of hospitalization. For each patient, we generated five graphs weighted by Lagged Linear Coherence (LLC) between signals from distinct Brodmann Areas, covering $δ$ (2-4 Hz), $θ$ (4-8 Hz), $α_1$ (8-10.5 Hz), $α_2$ (10.5-13 Hz), and $β_1$ (13-20 Hz) frequency bands. To emphasize key neurological connections and maintain sparsity, we applied a sparsification process based on structural and functional brain network properties. We then trained a graph attention model to predict the NIHSS. By examining its attention coefficients, our model reveals insights into brain reconfiguration, providing clinicians with a valuable tool for diagnosis, personalized treatment, and early intervention in neurorehabilitation.

eess.SP↗

arXiv2024

A Distributed Approach for Persistent Homology Computation on a Large Scale

Persistent homology (PH) is a powerful mathematical method to automatically extract relevant insights from images, such as those obtained by high-resolution imaging devices like electron microscopes or new-generation telescopes. However, the application of this method comes at a very high computational cost, that is bound to explode more because new imaging devices generate an ever-growing amount of data. In this paper we present PixHomology, a novel algorithm for efficiently computing $0$-dimensional PH on 2D images, optimizing memory and processing time. By leveraging the Apache Spark framework, we also present a distributed version of our algorithm with several optimized variants, able to concurrently process large batches of astronomical images. Finally, we present the results of an experimental analysis showing that our algorithm and its distributed version are efficient in terms of required memory, execution time, and scalability, consistently outperforming existing state-of-the-art PH computation tools when used to process large datasets.

cs.DC↗

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↗

arXiv2022

Reprogramming FairGANs with Variational Auto-Encoders: A New Transfer Learning Model

Fairness-aware GANs (FairGANs) exploit the mechanisms of Generative Adversarial Networks (GANs) to impose fairness on the generated data, freeing them from both disparate impact and disparate treatment. Given the model's advantages and performance, we introduce a novel learning framework to transfer a pre-trained FairGAN to other tasks. This reprogramming process has the goal of maintaining the FairGAN's main targets of data utility, classification utility, and data fairness, while widening its applicability and ease of use. In this paper we present the technical extensions required to adapt the original architecture to this new framework (and in particular the use of Variational Auto-Encoders), and discuss the benefits, trade-offs, and limitations of the new model.

cs.LG↗

arXiv2021

Towards global monitoring: equating the Food Insecurity Experience Scale (FIES) and food insecurity scales in Latin America

In order to face food insecurity as a global phenomenon, it is essential to rely on measurement tools that guarantee comparability across countries. Although the official indicators adopted by the United Nations in the context of the Sustainable Development Goals (SDGs) and based on the Food Insecurity Experience Scale (FIES) already embeds cross-country comparability, other experiential scales of food insecurity currently employ national thresholds and issues of comparability thus arise. In this work we address comparability of food insecurity experience-based scales by presenting two different studies. The first one involves the FIES and three national scales (ELCSA, EMSA and EBIA) currently included in national surveys in Guatemala, Ecuador, Mexico and Brazil. The second study concerns the adult and children versions of these national scales. Different methods from the equating practice of the educational testing field are explored: classical and based on the Item Response Theory (IRT).

stat.AP↗

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↗

arXiv2015

A note on an Adaptive Goodness-of-Fit test with Finite Sample Validity for Random Design Regression Models

Given an i.i.d. sample $\{(X_i,Y_i)\}_{i \in \{1 \ldots n\}}$ from the random design regression model $Y = f(X) + ε$ with $(X,Y) \in [0,1] \times [-M,M]$, in this paper we consider the problem of testing the (simple) null hypothesis $f = f_0$, against the alternative $f \neq f_0$ for a fixed $f_0 \in L^2([0,1],G_X)$, where $G_X(\cdot)$ denotes the marginal distribution of the design variable $X$. The procedure proposed is an adaptation to the regression setting of a multiple testing technique introduced by Fromont and Laurent (2005), and it amounts to consider a suitable collection of unbiased estimators of the $L^2$--distance $d_2(f,f_0) = \int {[f(x) - f_0 (x)]^2 d\,G_X (x)}$, rejecting the null hypothesis when at least one of them is greater than its $(1-u_α)$ quantile, with $u_α$ calibrated to obtain a level--$α$ test. To build these estimators, we will use the warped wavelet basis introduced by Picard and Kerkyacharian (2004). We do not assume that the errors are normally distributed, and we do not assume that $X$ and $ε$ are independent but, mainly for technical reasons, we will assume, as in most part of the current literature in learning theory, that $|f(x) - y|$ is uniformly bounded (almost everywhere). We show that our test is adaptive over a particular collection of approximation spaces linked to the classical Besov spaces.

math.ST↗

arXiv2008

Warped Wavelet and Vertical Thresholding

Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+ε$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of $L^2([0,1],G_X)$ norm where $G_X(\cdot)$ denotes the (known) marginal distribution of the design variable $X$. Recently much work has been devoted to the construction of estimators that adapts in this setting (see, for example, [5,24,25,32]), but only a few of them come along with a easy--to--implement computational scheme. Here we propose a family of estimators based on the warped wavelet basis recently introduced by Picard and Kerkyacharian [36] and a tree-like thresholding rule that takes into account the hierarchical (across-scale) structure of the wavelet coefficients. We show that, if the regression function belongs to a certain class of approximation spaces defined in terms of $G_X(\cdot)$, then our procedure is adaptive and converge to the true regression function with an optimal rate. The results are stated in terms of excess probabilities as in [19].

math.ST↗