arXiv subjects

Roberto Molinari

Publications and source records attributed to Roberto Molinari.

At least 19 recordsLinked to original sources

arXiv2026

Towards Open Science: Monitoring Crustal Deformations in North America

The study of the Earth's behavior has greatly benefited from the widespread deployment of Global Navigation Satellite Systems (GNSS), enabling large-scale monitoring of crustal deformation and long-term geophysical trends. In this work, we focus on the North American region, where complex tectonic activity, particularly along the western margin, requires methods capable of processing and analyzing large collections of GNSS time series distributed across extensive spatial domains. Analyzing the full GNSS network provides a coherent view of deformation across multiple scales, allowing detection of long-wavelength signals, subtle intraplate strain and regionally consistent velocity fields that are difficult to capture through local or subsampled analyses. Despite the availability of such data, existing methodologies remain computationally prohibitive for large-scale analyses across this region (or others). To address this limitation, we introduce a highly scalable framework (implemented in open-source software) that enables inference on crustal deformation across the full North American GNSS network using standard computational resources. The proposed method achieves substantial computational gains while maintaining inferential performance comparable to existing approaches and confirms existing tectonic trends, thereby supporting efficient large-scale monitoring and contributing to ongoing efforts toward "Open Science".

physics.geo-ph↗

arXiv2026

Large-Sample Bayesian Approximations for Privatized Data

The increased use of differential privacy (DP) has allowed the sharing of large amounts of data while reducing the risk of disclosure of sensitive information at the individual level. However, the noise introduced by DP methods makes performing statistical inference more challenging. While various methods have been proposed to address different inferential tasks, they often require strong parametric assumptions and/or do not scale well with sample sizes (e.g. U.S. Census products). In response to these limitations, we propose an approximate Bayesian method to analyze privatized data products, which uses a two-step approach of imputing the confidential data and then sampling from the non-private posterior, and which is inspired by the method of Guha and Reiter (2025). We prove that this approximate sampler is asymptotically valid under mild assumptions. While this approach is motivated by Bayesian theory, we show through simulations that it provides conservative frequentist properties as well. We demonstrate the utility of our method by applying it in simulated settings as well as for an analysis on the drivers of homeownership via the 2022 American Community Survey.

stat.ME↗

arXiv2026

Equivalence Testing Under Privacy Constraints

Protecting individual privacy is essential across research domains, from socio-economic surveys to big-tech user data. This need is particularly acute in healthcare, where analyses often involve sensitive patient information. A typical example is comparing treatment efficacy across hospitals or ensuring consistency in diagnostic laboratory calibrations, both requiring privacy-preserving statistical procedures. However, standard equivalence testing procedures for differences in proportions or means, commonly used to assess average equivalence, can inadvertently disclose sensitive information. To address this problem, we develop differentially private equivalence testing procedures that rely on simulation-based calibration, as the finite-sample distribution is analytically intractable. Our approach introduces a unified framework, termed DP-TOST, for conducting differentially private equivalence testing of both means and proportions. Through numerical simulations and real-world applications, we demonstrate that the proposed method maintains type-I error control at the nominal level and achieves power comparable to its non-private counterpart as the privacy budget and/or sample size increases, while ensuring strong privacy guarantees. These findings establish a reliable and practical framework for privacy-preserving equivalence testing in high-stakes fields such as healthcare, among others.

stat.AP↗

arXiv2026

Synthesizing the Counterfactual: A CTGAN-Augmented Causal Evaluation of Palliative Care on Spousal Depression

Spousal bereavement severely deteriorates mental health. While palliative care benefits dying patients, its "stress-buffering" effect on survivors' depression remains empirically elusive due to acute small-$N$ constraints in longitudinal dyadic data. This study evaluates the causal impact of palliative care on bereaved spouses while introducing Synthetic Data Generation (SDG) to resolve sample attrition in quasi-experimental designs. Using SHARE panel data, we augment the sparse treated cohort via a Conditional Tabular GAN, anchoring synthetic trajectories to empirical baseline constraints to preserve causal pathways. A Matched Difference-in-Differences estimator applied to the high-fidelity augmented dataset evaluates the treatment effect. Results reveal a non-linear psychological response. Palliative care initially exacerbates acute depressive symptoms at the time of loss ($\beta_0 = 0.218,\ p < 0.05$), reflecting the intense emotional confrontation of the intervention. However, a sustained stress-buffering effect emerges in subsequent periods ($\beta_2 = -0.763,\ p < 0.01$), indicating an accelerated long-term recovery compared to standard care. Estimates are highly robust to unobserved confounding (Oster's $\delta > 1$). Substantively, we advocate for reconceptualizing end-of-life care as a dyadic public health intervention. Methodologically, we establish SDG as a robust analytical tool capable of powering fragile quasi-experiments in longitudinal social surveys.

stat.AP↗

arXiv2025

Fiducial Matching: Differentially Private Inference for Categorical Data

The task of statistical inference, which includes the building of confidence intervals and tests for parameters and effects of interest to a researcher, is still an open area of investigation in a differentially private (DP) setting. Indeed, in addition to the randomness due to data sampling, DP delivers another source of randomness consisting of the noise added to protect an individual's data from being disclosed to a potential attacker. As a result of this convolution of noises, in many cases it is too complicated to determine the stochastic behavior of the statistics and parameters resulting from a DP procedure. In this work, we contribute to this line of investigation by employing a simulation-based matching approach, solved through tools from the fiducial framework, which aims to replicate the data generation pipeline (including the DP step) and retrieve an approximate distribution of the estimates resulting from this pipeline. For this purpose, we focus on the analysis of categorical (nominal) data that is common in national surveys, for which sensitivity is naturally defined, and on additive privacy mechanisms. We prove the validity of the proposed approach in terms of coverage and highlight its good computational and statistical performance for different inferential tasks in simulated and applied data settings.

stat.ME↗

arXiv2025

Differentially Private Conformal Prediction via Quantile Binary Search

Most Differentially Private (DP) approaches focus on limiting privacy leakage from learners based on the data that they are trained on, there are fewer approaches that consider leakage when procedures involve a calibration dataset which is common in uncertainty quantification methods such as Conformal Prediction (CP). Since there is a limited amount of approaches in this direction, in this work we deliver a general DP approach for CP that we call Private Conformity via Quantile Search (P-COQS). The proposed approach adapts an existing randomized binary search algorithm for computing DP quantiles in the calibration phase of CP thereby guaranteeing privacy of the consequent prediction sets. This however comes at a price of slightly under-covering with respect to the desired $(1 - \alpha)$-level when using finite-sample calibration sets (although broad empirical results show that the P-COQS generally targets the required level in the considered cases). Confirming properties of the adapted algorithm and quantifying the approximate coverage guarantees of the consequent CP, we conduct extensive experiments to examine the effects of privacy noise, sample size and significance level on the performance of our approach compared to existing alternatives. In addition, we empirically evaluate our approach on several benchmark datasets, including CIFAR-10, ImageNet and CoronaHack. Our results suggest that the proposed method is robust to privacy noise and performs favorably with respect to the current DP alternative in terms of empirical coverage, efficiency, and informativeness. Specifically, the results indicate that P-COQS produces smaller conformal prediction sets while simultaneously targeting the desired coverage and privacy guarantees in all these experimental settings.

stat.ME↗

arXiv2024

Inference for Large Scale Regression Models with Dependent Errors

The exponential growth in data sizes and storage costs has brought considerable challenges to the data science community, requiring solutions to run learning methods on such data. While machine learning has scaled to achieve predictive accuracy in big data settings, statistical inference and uncertainty quantification tools are still lagging. Priority scientific fields collect vast data to understand phenomena typically studied with statistical methods like regression. In this setting, regression parameter estimation can benefit from efficient computational procedures, but the main challenge lies in computing error process parameters with complex covariance structures. Identifying and estimating these structures is essential for inference and often used for uncertainty quantification in machine learning with Gaussian Processes. However, estimating these structures becomes burdensome as data scales, requiring approximations that compromise the reliability of outputs. These approximations are even more unreliable when complexities like long-range dependencies or missing data are present. This work defines and proves the statistical properties of the Generalized Method of Wavelet Moments with Exogenous variables (GMWMX), a highly scalable, stable, and statistically valid method for estimating and delivering inference for linear models using stochastic processes in the presence of data complexities like latent dependence structures and missing data. Applied examples from Earth Sciences and extensive simulations highlight the advantages of the GMWMX.

stat.ME↗

arXiv2024

Stellar Blend Image Classification Using Computationally Efficient Gaussian Processes

Stellar blends, where two or more stars appear blended in an image, pose a significant visualization challenge in astronomy. Traditionally, distinguishing these blends from single stars has been costly and resource-intensive, involving sophisticated equipment and extensive expert analysis. This is especially problematic for analyzing the vast data volumes from surveys, such as Legacy Survey of Space and Time (LSST), Sloan Digital Sky Survey (SDSS), Dark Energy Spectroscopic Instrument (DESI), Legacy Imaging Survey and the Zwicky Transient Facility (ZTF). To address these challenges, we apply different normalizations and data embeddings on low resolution images of single stars and stellar blends, which are passed as inputs into machine learning methods and to a computationally efficient Gaussian process model (MuyGPs). MuyGPs consistently outperforms the benchmarked models, particularly on limited training data. Moreover, MuyGPs with $r^\text{th}$ root local min-max normalization achieves 83.8% accuracy. Furthermore, MuyGPs' ability to produce confidence bands ensures that predictions with low confidence can be redirected to a specialist for efficient human-assisted labeling.

astro-ph.IM↗

arXiv2023

Accounting for Vibration Noise in Stochastic Measurement Errors

The measurement of data over time and/or space is of utmost importance in a wide range of domains from engineering to physics. Devices that perform these measurements therefore need to be extremely precise to obtain correct system diagnostics and accurate predictions, consequently requiring a rigorous calibration procedure which models their errors before being employed. While the deterministic components of these errors do not represent a major modelling challenge, most of the research over the past years has focused on delivering methods that can explain and estimate the complex stochastic components of these errors. This effort has allowed to greatly improve the precision and uncertainty quantification of measurement devices but has this far not accounted for a significant stochastic noise that arises for many of these devices: vibration noise. Indeed, having filtered out physical explanations for this noise, a residual stochastic component often carries over which can drastically affect measurement precision. This component can originate from different sources, including the internal mechanics of the measurement devices as well as the movement of these devices when placed on moving objects or vehicles. To remove this disturbance from signals, this work puts forward a modelling framework for this specific type of noise and adapts the Generalized Method of Wavelet Moments to estimate these models. We deliver the asymptotic properties of this method when applied to processes that include vibration noise and show the considerable practical advantages of this approach in simulation and applied case studies.

stat.ME↗

arXiv2021

Perturbed M-Estimation: A Further Investigation of Robust Statistics for Differential Privacy

Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP procedure should be similar in terms of their probability distribution. While DP mechanisms are provably effective in protecting privacy, they often negatively impact the utility of the query responses, statistics and/or analyses that come as outputs from these mechanisms. To address this problem, we use ideas from the area of robust statistics which aims at reducing the influence of outlying observations on statistical inference. Based on the preliminary known links between differential privacy and robust statistics, we modify the objective perturbation mechanism by making use of a new bounded function and define a bounded M-Estimator with adequate statistical properties. The resulting privacy mechanism, named "Perturbed M-Estimation", shows important potential in terms of improved statistical utility of its outputs as suggested by some preliminary results. These results consequently support the need to further investigate the use of robust statistical tools for differential privacy.

cs.CR↗

arXiv2021

Scale-wise Variance Minimization for Optimal Virtual Signals: An Approach for Redundant Gyroscopes

The increased use of low-cost gyroscopes within inertial sensors for navigation purposes, among others, has brought to the development of a considerable amount of research in improving their measurement precision. Aside from developing methods that allow to model and account for the deterministic and stochastic components that contribute to the measurement errors of these devices, an approach that has been put forward in recent years is to make use of arrays of such sensors in order to combine their measurements thereby reducing the impact of individual sensor noise. Nevertheless combining these measurements is not straightforward given the complex stochastic nature of these errors and, although some solutions have been suggested, these are limited to certain specific settings which do not allow to achieve solutions in more general and common circumstances. Hence, in this work we put forward a non-parametric method that makes use of the wavelet cross-covariance at different scales to combine the measurements coming from an array of gyroscopes in order to deliver an optimal measurement signal without needing any assumption on the processes underlying the individual error signals. We also study an appropriate non-parametric approach for the estimation of the asymptotic covariance matrix of the wavelet cross-covariance estimator which has important applications beyond the scope of this work. The theoretical properties of the proposed approach are studied and are supported by simulations and real applications, indicating that this method represents an appropriate and general tool for the construction of optimal virtual signals that are particularly relevant for arrays of gyroscopes. Moreover, our results can support the creation of optimal signals for other types of inertial sensors other than gyroscopes as well as for redundant measurements in other domains other than navigation.

stat.AP↗

arXiv2021

Multi-Signal Approaches for Repeated Sampling Schemes in Inertial Sensor Calibration

Inertial sensor calibration plays a progressively important role in many areas of research among which navigation engineering. By performing this task accurately, it is possible to significantly increase general navigation performance by correctly filtering out the deterministic and stochastic measurement errors that characterize such devices. While different techniques are available to model and remove the deterministic errors, there has been considerable research over the past years with respect to modelling the stochastic errors which have complex structures. In order to do the latter, different replicates of these error signals are collected and a model is identified and estimated based on one of these replicates. While this procedure has allowed to improve navigation performance, it has not yet taken advantage of the information coming from all the other replicates collected on the same sensor. However, it has been observed that there is often a change of error behaviour between replicates which can also be explained by different (constant) external conditions under which each replicate was taken. Whatever the reason for the difference between replicates, it appears that the model structure remains the same between replicates but the parameter values vary. In this work we therefore consider and study the properties of different approaches that allow to combine the information from all replicates considering this phenomenon, confirming their validity both in simulation settings and also when applied to real inertial sensor error signals. By taking into account parameter variation between replicates, this work highlights how these approaches can improve the average navigation precision as well as obtain reliable estimates of the uncertainty of the navigation solution.

eess.SP↗

arXiv2020

SWAG: A Wrapper Method for Sparse Learning

The majority of machine learning methods and algorithms give high priority to prediction performance which may not always correspond to the priority of the users. In many cases, practitioners and researchers in different fields, going from engineering to genetics, require interpretability and replicability of the results especially in settings where, for example, not all attributes may be available to them. As a consequence, there is the need to make the outputs of machine learning algorithms more interpretable and to deliver a library of "equivalent" learners (in terms of prediction performance) that users can select based on attribute availability in order to test and/or make use of these learners for predictive/diagnostic purposes. To address these needs, we propose to study a procedure that combines screening and wrapper approaches which, based on a user-specified learning method, greedily explores the attribute space to find a library of sparse learners with consequent low data collection and storage costs. This new method (i) delivers a low-dimensional network of attributes that can be easily interpreted and (ii) increases the potential replicability of results based on the diversity of attribute combinations defining strong learners with equivalent predictive power. We call this algorithm "Sparse Wrapper AlGorithm" (SWAG).

stat.ML↗

arXiv2020

Robust Two-Step Wavelet-Based Inference for Time Series Models

Complex time series models such as (the sum of) ARMA$(p,q)$ models with additional noise, random walks, rounding errors and/or drifts are increasingly used for data analysis in fields such as biology, ecology, engineering and economics where the length of the observed signals can be extremely large. Performing inference on and/or prediction from these models can be highly challenging for several reasons: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when models include more than just a few parameters and/or the time series are large; (iii) model building and/or selection adds another layer of (computational) complexity to the previous task; and (iv) solutions that address (i), (ii) and (iii) simultaneously do not exist in practice. For this reason, this paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. In this perspective, we first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator that are computed only once, we then develop the asymptotic properties of two-step robust estimators using the framework of the Generalized Method of Wavelet Moments (GMWM), hence defining the Robust GMWM (RGMWM) that we then use for robust model estimation and inference in a computationally efficient manner even for large time series. Simulation studies illustrate the good finite sample performance of the RGMWM estimator and applied examples highlight the practical relevance of the proposed approach.

stat.ME↗

arXiv2019

Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration

The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called "Allan variance slope method" which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing "automatic" approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the Allan variance or Wavelet Variance with their model-implied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This paper formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized Method of Wavelet Moments as an optimal choice.

stat.ME↗

arXiv2019

Multivariate Signal Modelling with Applications to Inertial Sensor Calibration

The common approach to inertial sensor calibration for navigation purposes has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different directions or arrayed in the same direction for redundancy. These signals usually have an extremely complex spectral structure that is often described using latent (or composite) models composed by a sum of underlying models. A large amount of research in this domain has been focused on the latter aspect through the proposal of various methods that have been able to improve the estimation of these models both from a computational and a statistical point of view. However, the separate calibration of the individual sensors is still unable to take into account the dependence between each of them which can have an important impact on the precision of the navigation systems. In this paper, we develop a new approach to simultaneously model both the individual signals and the dependence between them by studying the quantity called Wavelet Cross-Covariance and using it to extend the application of the Generalized Method of Wavelet Moments. This new method can be used in other settings for time series modeling, especially in cases where the dependence among signals may be hard to detect. Moreover, in the field of inertial sensor calibration, this approach can deliver important contributions among which the possibility to test dependence between sensors, integrate their dependence within the navigation filter and construct an optimal virtual sensor that can be used to simplify and improve navigation accuracy. The advantages of this method and its usefulness for inertial sensor calibration are highlighted through a simulation study and an applied example with a small array of XSens MTi-G IMUs.

stat.ME↗

arXiv2017

A Study of the Allan Variance for Constant-Mean Non-Stationary Processes

The Allan Variance (AV) is a widely used quantity in areas focusing on error measurement as well as in the general analysis of variance for autocorrelated processes in domains such as engineering and, more specifically, metrology. The form of this quantity is widely used to detect noise patterns and indications of stability within signals. However, the properties of this quantity are not known for commonly occurring processes whose covariance structure is non-stationary and, in these cases, an erroneous interpretation of the AV could lead to misleading conclusions. This paper generalizes the theoretical form of the AV to some non-stationary processes while at the same time being valid also for weakly stationary processes. Some simulation examples show how this new form can help to understand the processes for which the AV is able to distinguish these from the stationary cases and hence allow for a better interpretation of this quantity in applied cases.

math.ST↗

arXiv2016

Robust Inference for Time Series Models: a Wavelet-based Framework

We present a new framework for the robust estimation of latent time series models which is fairly general and, for example, covers models going from ARMA to state-space models. This approach provides estimators which are (i) consistent and asymptotically normally distributed, (ii) applicable to various classes of time series models, (iii) straightforward to implement and (iv) computationally efficient. The framework is based on the recently developed Generalized Method of Wavelet Moments (GMWM) and a new robust estimator of the wavelet variance. Compared to existing methods, the latter directly estimates the quantity of interest while performing better in finite samples and using milder conditions for its asymptotic properties to hold. Moreover, results are given showing the identifiability of the GMWM for various classes of time series models thereby allowing this method to consistently estimate many models (and combinations thereof) under mild conditions. Hence, not only does this paper provide an alternative estimator which allows to perform wavelet variance analysis when data are contaminated but also a general approach to robustly estimate the parameters of a variety of (latent) time series models. The simulation studies carried out confirm the better performance of the proposed estimators and the usefulness and broadness of the proposed methodology is shown using practical examples from the domains of economics and engineering with sample sizes up to 900,000.

stat.ME↗