arXiv subjects

Maria Laura Battagliola

Publications and source records attributed to Maria Laura Battagliola.

12 recordsLinked to original sources

arXiv2026

Least-Variable Harmonic Matrix-Exponential Distributions

Concentrated matrix-exponential (CME) distributions are random clocks approximating a fixed time, with quality measured by the squared coefficient of variation (SCV); a well-known construction builds such clocks from products of cosine-squared terms under shared exponential damping, but the number of these terms, and hence the number of parameters to optimize, grows with the order. Since exhaustive search over the full parameter space becomes prohibitively expensive at high orders, previous work has relied on low-dimensional heuristic parametrizations rather than the true optimum. We introduce a strictly larger class of common-damping harmonic densities, built from an arbitrary nonnegative trigonometric polynomial rather than such a product. For each fixed pair of scalar parameters, coefficient optimization reduces to a single eigenvalue problem, leaving a two-dimensional nonlinear search independent of the order. The enlargement leaves the infimum unchanged from that of the classical cosine-squared construction. Applying this exact characterization at the orders where the three-parameter heuristic allows comparison gives smaller reported SCV values, with larger gains at higher orders. Separately, an explicit harmonic construction gives an $O(N^{-2})$ upper bound on the attainable SCV, where $N$ is the ME representation budget, compared with the Erlang distribution's linear rate $1/N$.

math.PR↗

arXiv2026

Least Variability in a Polynomial-Square Class of Rational Kernels

We solve an extremal problem for positive randomization kernels that concentrate a random time as tightly as possible around a deterministic target, within the class obtained by exponentially damping the square of a polynomial. The construction, borrowed from the concentrated matrix-exponential literature, automatically guarantees nonnegativity, gives the kernel a Laplace transform with a single repeated real pole, and contains the classical Erlang randomizer as the special case in which the polynomial is a pure power. The half-polynomial need not be real-rooted and so may have nonreal conjugate zeros, yet every optimizer is proved to be real-rooted. After normalizing the kernel to unit mean, the minimum variance at polynomial degree $m$ turns out to equal the smallest relative gap between adjacent zeros of the Laguerre polynomial $L_{m+2}$, with every optimizer obtained by deleting a pair attaining this minimum. This characterization yields the minimal variance, the normalized density, and every optimizer in closed form. The optimizer can be computed from the spectrum of a symmetric tridiagonal Jacobi matrix. In the large-order limit, the minimal variance decays quadratically in the order of the kernel, a marked improvement over the linear decay rate of the Erlang benchmark, and the deleted pair of zeros localizes at normalized location $2$, with limiting absolute separation $2π$.

math.PR↗

arXiv2026

Colored Markov-Modulated Brownian Motion for Preemptive Workload Stacks

We develop a colored Markov-modulated Brownian motion model for diffusion-scale systems in which newly created work preempts the active layer, occupies the top of an ordered stack, and must deplete before suspended work resumes. Such preemption arises whenever new work interrupts whatever is currently active, as in last-come, first-served queues and interrupt-driven scheduling, with diffusive dynamics appropriate when the processing rate itself fluctuates randomly. Colors encode stack position and priority, while a background phase, evolving through first-kind transitions that leave the active color unchanged, controls drift and volatility within each color. Second-kind transitions create higher colors at strictly positive random launch heights. A backward recursion summarizes higher-color excursions through return matrices and occupation-density kernels. We obtain stationary product-form representations under hold-and-jump and regulated-base boundary conventions, given explicitly through matrix-analytic formulae, and give matrix-transform formulas for illustrative launch-height families.

math.PR↗

arXiv2026

Local Second-Order Geometry Induced by Deformation Maps

Spatial deformations offer a flexible route to nonstationary dependence by warping the coordinates of a stationary random field. While the exact induced covariance depends on the deformation map in its entirety, we show that its behavior in a neighborhood is approximated accurately by linearization. This produces a tangent covariance whose discrepancy from the true covariance we bound explicitly, and its Fourier transform yields a local spectrum in closed form. Building on this spectral description, we introduce a simulation scheme that generates a deformed Gaussian field in a neighborhood accounting for the local spectrum, so that the simulated field reproduces the finite dimensional tangent covariance by construction. For repeated sampling across many reference points, a truncated singular value decomposition compresses the space and frequency weights into a reusable form. We further apply the summaries based on the local Jacobian as an exploratory device for deformations estimated from images, using cardiac magnetic resonance data from the Automated Cardiac Diagnosis Challenge together with optical flow. The resulting local geometry exhibits differences across diagnostic groups through directional and anisotropic features of myocardial deformation that go beyond simple measures of local expansion or compression.

stat.ME↗

arXiv2026

Optimization-Free Concentrated Matrix-Exponentials

Near-deterministic positive delays require highly concentrated distributions, but phase-type models are constrained by the Erlang variance limit. While matrix-exponential distributions can empirically bypass this barrier, prior low-variance constructions relied entirely on numerical optimization. We propose an explicit family of concentrated matrix-exponential densities for the unit delay, obtained by raising the trigonometric Fejér kernel to logarithmic power. With exact moments and closed-form parameters, this gives the first analytical proof of a matrix-exponential class that asymptotically surpasses the Erlang bound.

math.PR↗

arXiv2026

Extremile scalar-on-function regression

Extremiles provide a generalization of quantiles which are not only robust, but also have an intrinsic link with extreme value theory. This paper introduces an extremile regression model tailored for functional covariate spaces. The estimation procedure turns out to be a weighted version of local linear scalar-on-function regression, where now a double kernel approach plays a crucial role. Asymptotic expressions for the bias and variance are established, applicable to both decreasing bandwidth sequences and automatically selected bandwidths. The methodology is then investigated in detail through a simulation study. Furthermore, we illustrate the method's applicability with an analysis of the Berkeley Growth data, showcasing its performance in a real-world functional data setting.

stat.ME↗

arXiv2025

Modeling Spatio-Temporal Transport: From Rigid Advection to Realistic Dynamics

Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation over time. This work aims to bridge the gap between this simple framework and its physically realistic extensions. Our guiding principle is to introduce a spatial correlation structure that vanishes over time. To achieve this, we present two distinct approaches. The first constructs complex velocity structures, either through superpositions of advection components or by allowing the velocity to vary locally. The second is a spectral technique that replaces the singular spectrum of rigid advection with a more flexible form, introducing temporal decorrelation controlled by parameters. We accompany these models with efficient simulation algorithms and demonstrate their success in replicating complex dynamics, such as tropical cyclones and the solutions of partial differential equations. Finally, we illustrate the practical utility of the proposed framework by comparing its simulations to real-world precipitation data from Hurricane Florence.

stat.CO↗

arXiv2025

Functional Modeling of Learning and Memory Dynamics in Cognitive Disorders

Deficits in working memory, which includes both the ability to learn and to retain information short-term, are a hallmark of many cognitive disorders. Our study analyzes data from a neuroscience experiment on animal subjects, where performance on a working memory task was recorded as repeated binary success or failure data. We estimate continuous probability of success curves from this binary data in the context of functional data analysis, which is largely used in biological processes that are intrinsically continuous. We then register these curves to decompose each function into its amplitude, representing overall performance, and its phase, representing the speed of learning or response. Because we are able to separate speed from performance, we can address the crucial question of whether a cognitive disorder impacts not only how well subjects can learn and remember, but also how fast. This allows us to analyze the components jointly to uncover how speed and performance co-vary, and to compare them separately to pinpoint whether group differences stem from a deficit in peak performance or a change in speed.

stat.AP↗

arXiv2025

Estimating Velocity Vector Fields of Atmospheric Winds using Transport Gaussian Processes

Accurately estimating latent velocity vector fields of atmospheric winds is crucial for understanding weather phenomena. Direct measurement of atmospheric winds is costly, especially in the upper atmosphere, so researchers attempt to estimate atmospheric winds by observing the movement patterns of clouds and other features in satellite images of the atmosphere. These Derived Motion Winds use feature tracking algorithms to search for movement within small windows in space and time. Consequently, these algorithms cannot leverage information from broader-scale features and cannot ensure that the collection of wind vectors over space and time represents a physically realistic velocity field. In this work, we use spatial-temporal Gaussian processes to model the evolution of a scalar quantity transported over time by fluid flow. Our framework simultaneously estimates covariance parameters and latent velocities by maximizing the likelihood. Specifically, flows are represented using time-dependent residual neural networks, and velocities are subsequently derived through closed-form formulas. Performance evaluations using weather model data demonstrate our method's accuracy and efficiency. We apply our method to GOES-16 images, demonstrating computational efficiency and the ability to produce wind estimates where Derived Motion Winds fail.

stat.AP↗

arXiv2025

Localized Functional Principal Component Analysis Based on Covariance Structure

Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically have non-zero support across the entire domain. In applications, however, it is often desirable to analyze eigenfunctions that are non-zero only on specific portions of the original domain-and exhibit zero regions when little is contributed to a specific direction of variability-allowing for easier interpretability. Our method identifies sparse characteristics of the underlying stochastic process and derives localized eigenfunctions by mirroring these characteristics without explicitly enforcing sparsity. Specifically, we decompose the stochastic process into uncorrelated sub-processes, each supported on disjoint intervals. Applying FPCA to these sub-processes yields localized eigenfunctions that are naturally orthogonal. In contrast, approaches that enforce localization through penalization must additionally impose orthogonality. Moreover, these approaches can suffer from over-regularization, resulting in eigenfunctions and eigenvalues that deviate from the inherent structure of their population counterparts, potentially misrepresenting data characteristics. Our approach avoids these issues by preserving the inherent structure of the data. Moreover, since the sub-processes have disjoint supports, the eigenvalues associated to the localized eigenfunctions allow for assessing the importance of each sub-processes in terms of its contribution to the total explained variance. We illustrate the effectiveness of our method through simulations and real data applications. Supplementary material for this article is available online.

stat.ME↗

arXiv2023

Quantile regression for longitudinal functional data with application to feed intake of lactating sows

This article focuses on the study of lactating sows, where the main interest is the influence of temperature, measured throughout the day, on the lower quantiles of the daily feed intake. We outline a model framework and estimation methodology for quantile regression in scenarios with longitudinal data and functional covariates. The quantile regression model uses a time-varying regression coefficient function to quantify the association between covariates and the quantile level of interest, and it includes subject-specific intercepts to incorporate within-subject dependence. Estimation relies on spline representations of the unknown coefficient functions, and can be carried out with existing software. We introduce bootstrap procedures for bias adjustment and computation of standard errors. Analysis of the lactation data indicates, among others, that the influence of temperature increases during the lactation period.

stat.AP↗

arXiv2022

A bias-adjusted estimator in quantile regression for clustered data

The manuscript discusses how to incorporate random effects for quantile regression models for clustered data with focus on settings with many but small clusters. The paper has three contributions: (i) documenting that existing methods may lead to severely biased estimators for fixed effects parameters; (ii) proposing a new two-step estimation methodology where predictions of the random effects are first computed {by a pseudo likelihood approach (the LQMM method)} and then used as offsets in standard quantile regression; (iii) proposing a novel bootstrap sampling procedure in order to reduce bias of the two-step estimator and compute confidence intervals. The proposed estimation and associated inference is assessed numerically through rigorous simulation studies and applied to an AIDS Clinical Trial Group (ACTG) study.

stat.ME↗