Classic machine learning methods

In this chapter, we present the main classic machine learning methods. A large part of the chapter is devoted to supervised learning techniques for classification and regression, including nearest-neighbor methods, linear and logistic regressions, support vector machines and tree-based algorithms. We also describe the problem of overfitting as well as strategies to overcome it. We finally provide a brief overview of unsupervised learning methods, namely for clustering and dimensionality reduction

Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines

Let a be a nonzero integer. If a is not congruent to 4 or 5 modulo 9 then there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x^3+y^3+z^3=a. In addition, there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x^3+y^3+2z^3=a.Comment: 24 pages; minor changes onl

Interpretable and reliable artificial intelligence systems for brain diseases

International audienceIn artificial intelligence for medicine, more interpretable and reliable systems are needed. Here, we report on recent advances toward these aims in the field of brain diseases

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a manifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances, and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

International audienceA common approach for analysis of anatomical variability relies on the stimation of a template representative of the population. The Large Deformation Diffeomorphic Metric Mapping is an attractive framework for that purpose. However, template estimation using LDDMM is computationally expensive, which is a limitation for the study of large datasets. This paper presents an iterative method which quickly provides a centroid of the population in the shape space. This centroid can be used as a rough template estimate or as initialization of a template estimation method. The approach is evaluated on datasets of real and synthetic hippocampi segmented from brain MRI. The results show that the centroid is correctly centered within the population and is stable for different orderings of subjects. When used as an initialization, the approach allows to substantially reduce the computation time of template estimation

Learning Myelin Content in Multiple Sclerosis from Multimodal MRI through Adversarial Training

Multiple sclerosis (MS) is a demyelinating disease of the central nervous system (CNS). A reliable measure of the tissue myelin content is therefore essential for the understanding of the physiopathology of MS, tracking progression and assessing treatment efficacy. Positron emission tomography (PET) with [^{11} \mbox{C}] \mbox{PIB} has been proposed as a promising biomarker for measuring myelin content changes in-vivo in MS. However, PET imaging is expensive and invasive due to the injection of a radioactive tracer. On the contrary, magnetic resonance imaging (MRI) is a non-invasive, widely available technique, but existing MRI sequences do not provide, to date, a reliable, specific, or direct marker of either demyelination or remyelination. In this work, we therefore propose Sketcher-Refiner Generative Adversarial Networks (GANs) with specifically designed adversarial loss functions to predict the PET-derived myelin content map from a combination of MRI modalities. The prediction problem is solved by a sketch-refinement process in which the sketcher generates the preliminary anatomical and physiological information and the refiner refines and generates images reflecting the tissue myelin content in the human brain. We evaluated the ability of our method to predict myelin content at both global and voxel-wise levels. The evaluation results show that the demyelination in lesion regions and myelin content in normal-appearing white matter (NAWM) can be well predicted by our method. The method has the potential to become a useful tool for clinical management of patients with MS.Comment: Accepted by MICCAI201

Machine learning for classification and prediction of brain diseases: recent advances and upcoming challenges

International audiencePurpose of review. Machine learning (ML) is an artificial intelligence technique that allows computers to perform a task without being explicitly programmed. ML can be used to assist diagnosis and prognosis of brain disorders. While the earliest papers date from more than ten years ago, research increases at a very fast pace. Recent findings. Recent works using ML for diagnosis have moved from classification of a given disease versus controls to differential diagnosis. Intense research has been devoted to the prediction of the future patient state. While a lot of earlier works focused on neuroimaging as data source, the current trend is on the integration of multimodal. In terms of targeted diseases, dementia remains dominant, but approaches have been developed for a wide variety of neurological and psychiatric diseases. Summary. ML is extremely promising for assisting diagnosis and prognosis in brain disorders. Nevertheless, we argue that key challenges remain to be addressed by the community for bringing these tools in clinical routine: good practices regarding validation and reproducible research need to be more widely adopted; extensive generalization studies are required; interpretable models are needed to overcome the limitations of black-box approaches

Learning spatio-temporal trajectories from manifold-valued longitudinal data

International audienceWe propose a Bayesian mixed-effects model to learn typical scenarios of changesfrom longitudinal manifold-valued data, namely repeated measurements of thesame objects or individuals at several points in time. The model allows to estimatea group-average trajectory in the space of measurements. Random variations ofthis trajectory result from spatiotemporal transformations, which allow changes inthe direction of the trajectory and in the pace at which trajectories are followed.The use of the tools of Riemannian geometry allows to derive a generic algorithmfor any kind of data with smooth constraints, which lie therefore on a Riemannianmanifold. Stochastic approximations of the Expectation-Maximization algorithmis used to estimate the model parameters in this highly non-linear setting. Themethod is used to estimate a data-driven model of the progressive impairments ofcognitive functions during the onset of Alzheimer’s disease. Experimental resultsshow that the model correctly put into correspondence the age at which each in-dividual was diagnosed with the disease, thus validating the fact that it effectivelyestimated a normative scenario of disease progression. Random effects provideunique insights into the variations in the ordering and timing of the succession ofcognitive impairments across different individuals