arXiv subjects

Marie-Hélène Descary

Publications and source records attributed to Marie-Hélène Descary.

7 recordsLinked to original sources

arXiv2026

Multivariate Planar Curves: A Statistical Framework for Shape Analysis in Images

Recent developments in computer vision have made segmented images widely available across many domains, such as medicine, where segmented radiographs play an important role in diagnosis. As prediction problems are common in image analysis, this work explores the use of the object contours highlighted by such images as predictors in a supervised classification context. To this end, we develop a new statistical learning framework that accounts for the joint shape of the multiple objects contained in an image. We introduce a formalism that extends the study of a single random planar curve to the joint analysis of several planar curves, referred to as a multivariate planar curve. Modeling the contours jointly, rather than separately, preserves the inter-component information, such as their relative position, scale, and orientation, which is often essential to the analysis. Based on this model, we propose a joint alignment procedure and we extend core inferential tools to multivariate shapes: shape dissimilarity, Fréchet mean estimation, and tangent-space representation. These tangent coordinates are then used as predictors in standard functional classification models. A simulation study shows accurate recovery of deformation parameters over increasing noise levels. Then, through a cardiomegaly detection problem on segmented chest X-rays, we show that jointly modeling the contours is robust to misalignment and improves classification accuracy over both a contour-wise univariate analysis and a naive approach based on the raw curves.

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arXiv2026

A Functional Approach to Curve Alignment and Shape Analysis

In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization. Previous studies in statistical shape analysis have mainly focused on analyzing contours and shapes through discrete observations. While this approach might offer computational advantages, it overlooks the continuous nature of these objects and their underlying geometric structure. It also ignores potential dependencies between the deformation variables and their effect on the shape, which may result in a loss of statistical information and reduced interpretability. In this paper, we introduce a novel framework for analyzing shapes within the context of Functional Data Analysis (FDA). Basis expansion techniques are employed to derive analytic solutions for the estimation of deformation variables, namely scaling, translation, rotation, and reparametrization, thereby achieving curve alignment. A generative model for random contours is then developed using principal component analysis techniques. Numerical experiments on simulated data and the \textit{MPEG-7} database demonstrate that our method successfully identifies deformation parameters and captures the underlying distribution of random contours in settings where traditional FDA methods fail.

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arXiv2026

Simulation of warping processes with applications to temperature data

Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that properly account for phase variability in functional data. In this paper, we focus on the simulation of continuous warping processes with a prescribed expectation and a controllable variance. We study and compare three procedures, including two existing methods and a new algorithm based on randomized empirical cumulative distribution functions. For each approach, we provide an operational description and establish theoretical results for the first two moments of the simulated processes. A numerical study illustrates the theoretical findings and highlights the respective merits of the three methods. Finally, we present an application to the analysis of temperature distributions in Montreal based on simulated realizations from a warping process estimated from temperature quantile functions.

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arXiv2024

Constructing Ancestral Recombination Graphs through Reinforcement Learning

Over the years, many approaches have been proposed to build ancestral recombination graphs (ARGs), graphs used to represent the genetic relationship between individuals. Among these methods, many rely on the assumption that the most likely graph is among the shortest ones. In this paper, we propose a new approach to build short ARGs: Reinforcement Learning (RL). We exploit the similarities between finding the shortest path between a set of genetic sequences and their most recent common ancestor and finding the shortest path between the entrance and exit of a maze, a classic RL problem. In the maze problem, the learner, called the agent, must learn the directions to take in order to escape as quickly as possible, whereas in our problem, the agent must learn the actions to take between coalescence, mutation, and recombination in order to reach the most recent common ancestor as quickly as possible. Our results show that RL can be used to build ARGs as short as those built with a heuristic algorithm optimized to build short ARGs, and sometimes even shorter. Moreover, our method allows to build a distribution of short ARGs for a given sample, and can also generalize learning to new samples not used during the learning process.

cs.LG↗

arXiv2021

A convolution type model for the intensity of spatial point processes applied to eye-movement data

Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we introduce a convolution type model where the log-intensity is modelled as the convolution of a function $β(\cdot)$, to be estimated, and a single spatial covariate (the image an individual is looking at for eye-movement data). Based on a Fourier series expansion, we show that the proposed model \rev{can be viewed as a} log-linear model with an infinite number of coefficients, which correspond to the spectral decomposition of $β(\cdot)$. After truncation, we estimate these coefficients through a penalized Poisson likelihood. We illustrate the efficiency of the proposed methodology on simulated data and on eye-movement data.

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arXiv2018

Recovering Covariance from Functional Fragments

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is only observed on a subinterval of length $δ<1$, one has no statistical information on the unknown covariance outside a $δ$-band around the diagonal. The problem seems unidentifiable without parametric assumptions, but we show that nonparametric estimation is feasible under suitable smoothness and rank conditions on the unknown covariance. This remains true even when observation is discrete, and we give precise deterministic conditions on how fine the observation grid needs to be relative to the rank and fragment length for identifiability to hold true. We show that our conditions translate the estimation problem to a low-rank matrix completion problem, construct a nonparametric estimator in this vein, and study its asymptotic properties. We illustrate the numerical performance of our method on real and simulated data.

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arXiv2018

Functional Data Analysis by Matrix Completion

Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony and interpretability of the analysis. The goal of this paper is to investigate how both smooth and rough variations can be recovered on the basis of discretely observed functional data. Assuming that a functional datum arises as the sum of two uncorrelated components, one smooth and one rough, we develop identifiability conditions for the recovery of the two corresponding covariance operators. The key insight is that they should possess complementary forms of parsimony: one smooth and finite rank (large scale), and the other banded and potentially infinite rank (small scale). Our conditions elucidate the precise interplay between rank, bandwidth, and grid resolution. Under these conditions, we show that the recovery problem is equivalent to rank-constrained matrix completion, and exploit this to construct estimators of the two covariances, without assuming knowledge of the true bandwidth or rank; we study their asymptotic behaviour, and then use them to recover the smooth and rough components of each functional datum by best linear prediction. As a result, we effectively produce separate functional PCAs for smooth and rough variation.

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