arXiv subjects

Florence Forbes

Publications and source records attributed to Florence Forbes.

At least 37 records · Page 2Linked to original sources

arXiv2023

Brain subtle anomaly detection based on auto-encoders latent space analysis : application to de novo parkinson patients

Neural network-based anomaly detection remains challenging in clinical applications with little or no supervised information and subtle anomalies such as hardly visible brain lesions. Among unsupervised methods, patch-based auto-encoders with their efficient representation power provided by their latent space, have shown good results for visible lesion detection. However, the commonly used reconstruction error criterion may limit their performance when facing less obvious lesions. In this work, we design two alternative detection criteria. They are derived from multivariate analysis and can more directly capture information from latent space representations. Their performance compares favorably with two additional supervised learning methods, on a difficult de novo Parkinson Disease (PD) classification task.

eess.IV↗

arXiv2022

Improving Uncertainty-based Out-of-Distribution Detection for Medical Image Segmentation

Deep Learning models are easily disturbed by variations in the input images that were not seen during training, resulting in unpredictable behaviours. Such Out-of-Distribution (OOD) images represent a significant challenge in the context of medical image analysis, where the range of possible abnormalities is extremely wide, including artifacts, unseen pathologies, or different imaging protocols. In this work, we evaluate various uncertainty frameworks to detect OOD inputs in the context of Multiple Sclerosis lesions segmentation. By implementing a comprehensive evaluation scheme including 14 sources of OOD of various nature and strength, we show that methods relying on the predictive uncertainty of binary segmentation models often fails in detecting outlying inputs. On the contrary, learning to segment anatomical labels alongside lesions highly improves the ability to detect OOD inputs.

eess.IV↗

arXiv2022

Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis

The full acceptance of Deep Learning (DL) models in the clinical field is rather low with respect to the quantity of high-performing solutions reported in the literature. Particularly, end users are reluctant to rely on the rough predictions of DL models. Uncertainty quantification methods have been proposed in the literature as a potential response to reduce the rough decision provided by the DL black box and thus increase the interpretability and the acceptability of the result by the final user. In this review, we propose an overview of the existing methods to quantify uncertainty associated to DL predictions. We focus on applications to medical image analysis, which present specific challenges due to the high dimensionality of images and their quality variability, as well as constraints associated to real-life clinical routine. We then discuss the evaluation protocols to validate the relevance of uncertainty estimates. Finally, we highlight the open challenges of uncertainty quantification in the medical field.

eess.IV↗

arXiv2022

Beyond Voxel Prediction Uncertainty: Identifying brain lesions you can trust

Deep neural networks have become the gold-standard approach for the automated segmentation of 3D medical images. Their full acceptance by clinicians remains however hampered by the lack of intelligible uncertainty assessment of the provided results. Most approaches to quantify their uncertainty, such as the popular Monte Carlo dropout, restrict to some measure of uncertainty in prediction at the voxel level. In addition not to be clearly related to genuine medical uncertainty, this is not clinically satisfying as most objects of interest (e.g. brain lesions) are made of groups of voxels whose overall relevance may not simply reduce to the sum or mean of their individual uncertainties. In this work, we propose to go beyond voxel-wise assessment using an innovative Graph Neural Network approach, trained from the outputs of a Monte Carlo dropout model. This network allows the fusion of three estimators of voxel uncertainty: entropy, variance, and model's confidence; and can be applied to any lesion, regardless of its shape or size. We demonstrate the superiority of our approach for uncertainty estimate on a task of Multiple Sclerosis lesions segmentation.

eess.IV↗

arXiv2022

A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

math.ST↗

arXiv2021

Patch vs. Global Image-Based Unsupervised Anomaly Detection in MR Brain Scans of Early Parkinsonian Patients

Although neural networks have proven very successful in a number of medical image analysis applications, their use remains difficult when targeting subtle tasks such as the identification of barely visible brain lesions, especially given the lack of annotated datasets. Good candidate approaches are patch-based unsupervised pipelines which have both the advantage to increase the number of input data and to capture local and fine anomaly patterns distributed in the image, while potential inconveniences are the loss of global structural information. We illustrate this trade-off on Parkinson's disease (PD) anomaly detection comparing the performance of two anomaly detection models based on a spatial auto-encoder (AE) and an adaptation of a patch-fed siamese auto-encoder (SAE). On average, the SAE model performs better, showing that patches may indeed be advantageous.

eess.IV↗

arXiv2021

Non-asymptotic model selection in block-diagonal mixture of polynomial experts models

Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on introducing non-asymptotic criteria. We focus on the problem of modeling non-linear relationships in regression data with potential hidden graph-structured interactions between the high-dimensional predictors, within the mixture of experts modeling framework. In order to deal with such a complex situation, we investigate a block-diagonal localized mixture of polynomial experts (BLoMPE) regression model, which is constructed upon an inverse regression and block-diagonal structures of the Gaussian expert covariance matrices. We introduce a penalized maximum likelihood selection criterion to estimate the unknown conditional density of the regression model. This model selection criterion allows us to handle the challenging problem of inferring the number of mixture components, the degree of polynomial mean functions, and the hidden block-diagonal structures of the covariance matrices, which reduces the number of parameters to be estimated and leads to a trade-off between complexity and sparsity in the model. In particular, we provide a strong theoretical guarantee: a finite-sample oracle inequality satisfied by the penalized maximum likelihood estimator with a Jensen-Kullback-Leibler type loss, to support the introduced non-asymptotic model selection criterion. The penalty shape of this criterion depends on the complexity of the considered random subcollection of BLoMPE models, including the relevant graph structures, the degree of polynomial mean functions, and the number of mixture components.

math.ST↗

arXiv2021

Leveraging 3D Information in Unsupervised Brain MRI Segmentation

Automatic segmentation of brain abnormalities is challenging, as they vary considerably from one pathology to another. Current methods are supervised and require numerous annotated images for each pathology, a strenuous task. To tackle anatomical variability, Unsupervised Anomaly Detection (UAD) methods are proposed, detecting anomalies as outliers of a healthy model learned using a Variational Autoencoder (VAE). Previous work on UAD adopted a 2D approach, meaning that MRIs are processed as a collection of independent slices. Yet, it does not fully exploit the spatial information contained in MRI. Here, we propose to perform UAD in a 3D fashion and compare 2D and 3D VAEs. As a side contribution, we present a new loss function guarantying a robust training. Learning is performed using a multicentric dataset of healthy brain MRIs, and segmentation performances are estimated on White-Matter Hyperintensities and tumors lesions. Experiments demonstrate the interest of 3D methods which outperform their 2D counterparts.

eess.IV↗

arXiv2020

Rigid and Articulated Point Registration with Expectation Conditional Maximization

This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in terms of estimation of the registration parameters, and we propose an optimal method for estimating the rotational and translational parameters based on semi-definite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and we compare it both theoretically and experimentally with other robust methods for point registration.

cs.CV↗

arXiv2020

Conjugate Mixture Models for Clustering Multimodal Data

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or to compare them in some common space. A solution may consist in considering multiple clustering tasks independently for each modality. The main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent. In this paper we show that multimodal clustering can be addressed within a novel framework, namely conjugate mixture models. These models exploit the explicit transformations that are often available between an unobserved parameter space (objects) and each one of the observation spaces (sensors). We formulate the problem as a likelihood maximization task and we derive the associated conjugate expectation-maximization algorithm. The convergence properties of the proposed algorithm are thoroughly investigated. Several local/global optimization techniques are proposed in order to increase its convergence speed. Two initialization strategies are proposed and compared. A consistent model-selection criterion is proposed. The algorithm and its variants are tested and evaluated within the task of 3D localization of several speakers using both auditory and visual data.

stat.ML↗

arXiv2020

Approximate Bayesian computation via the energy statistic

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of summary statistics. Here we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the so-called two-sample energy statistic. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds, and prove that the rejection ABC algorithm, based on the energy statistic, generates pseudo-posterior distributions that achieves convergence to the correct limits, when implemented with rejection thresholds that converge to zero, in the finite sample setting. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate $g$-and-$k$ distribution. We find that our proposed method compares well with alternative discrepancy measures.

stat.ME↗

arXiv2019

Approximation results regarding the multiple-output mixture of linear experts model

Mixture of experts (MoE) models are a class of artificial neural networks that can be used for functional approximation and probabilistic modeling. An important class of MoE models is the class of mixture of linear experts (MoLE) models, where the expert functions map to real topological output spaces. There are a number of powerful approximation results regarding MoLE models, when the output space is univariate. These results guarantee the ability of MoLE mean functions to approximate arbitrary continuous functions, and MoLE models themselves to approximate arbitrary conditional probability density functions. We utilize and extend upon the univariate approximation results in order to prove a pair of useful results for situations where the output spaces are multivariate.

stat.ME↗

arXiv2016

Rectified binaural ratio: A complex T-distributed feature for robust sound localization

Most existing methods in binaural sound source localization rely on some kind of aggregation of phase-and level-difference cues in the time-frequency plane. While different ag-gregation schemes exist, they are often heuristic and suffer in adverse noise conditions. In this paper, we introduce the rectified binaural ratio as a new feature for sound source local-ization. We show that for Gaussian-process point source signals corrupted by stationary Gaussian noise, this ratio follows a complex t-distribution with explicit parameters. This new formulation provides a principled and statistically sound way to aggregate binaural features in the presence of noise. We subsequently derive two simple and efficient methods for robust relative transfer function and time-delay estimation. Experiments on heavily corrupted simulated and speech signals demonstrate the robustness of the proposed scheme.

cs.SD↗

arXiv2016

EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.

cs.CV↗

arXiv2015

Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies

Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between physical parameters and spectra has been established in a data-driven fashion, the learned relationship can be used to estimate physical parameters for new hyper-spectral observations. Within this framework, we propose a spatially-constrained and partially-latent regression method which maps high-dimensional inputs (hyper-spectral images) onto low-dimensional responses (physical parameters such as the local chemical composition of the soil). The proposed regression model comprises two key features. Firstly, it combines a Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent response model. While the former makes high-dimensional regression tractable, the latter enables to deal with physical parameters that cannot be observed or, more generally, with data contaminated by experimental artifacts that cannot be explained with noise models. Secondly, spatial constraints are introduced in the model through a Markov random field (MRF) prior which provides a spatial structure to the Gaussian-mixture hidden variables. Experiments conducted on a database composed of remotely sensed observations collected from the Mars planet by the Mars Express orbiter demonstrate the effectiveness of the proposed model.

stat.AP↗

arXiv2015

Physiologically Informed Bayesian Analysis of ASL fMRI Data

Arterial Spin Labelling (ASL) functional Magnetic Resonance Imaging (fMRI) data provides a quantitative measure of blood perfusion, that can be correlated to neuronal activation. In contrast to BOLD measure, it is a direct measure of cerebral blood flow. However, ASL data has a lower SNR and resolution so that the recovery of the perfusion response of interest suffers from the contamination by a stronger hemodynamic component in the ASL signal. In this work we consider a model of both hemodynamic and perfusion components within the ASL signal. A physiological link between these two components is analyzed and used for a more accurate estimation of the perfusion response function in particular in the usual ASL low SNR conditions.

stat.AP↗

arXiv2015

Hemodynamically informed parcellation of cerebral FMRI data

Standard detection of evoked brain activity in functional MRI (fMRI) relies on a fixed and known shape of the impulse response of the neurovascular coupling, namely the hemodynamic response function (HRF). To cope with this issue, the joint detection-estimation (JDE) framework has been proposed. This formalism enables to estimate a HRF per region but for doing so, it assumes a prior brain partition (or parcellation) regarding hemodynamic territories. This partition has to be accurate enough to recover accurate HRF shapes but has also to overcome the detection-estimation issue: the lack of hemodynamics information in the non-active positions. An hemodynamically-based parcellation method is proposed, consisting first of a feature extraction step, followed by a Gaussian Mixture-based parcellation, which considers the injection of the activation levels in the parcellation process, in order to overcome the detection-estimation issue and find the underlying hemodynamics.

stat.AP↗

arXiv2014

Clustering using skewed multivariate heavy tailed distributions with flexible tail behaviour

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. It nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic distribution. The Generalised Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian (NIG) whose practical relevance has been widely documented in the literature. In a multivariate setting, we propose to extend the standard location and scale mixture concept into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension of the variable space with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm with a particular focus on NIG distributions. Inference is then extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.

stat.ME↗