FDP control in multivariate linear models using the bootstrap

In this article we develop a method for performing post hoc inference of the False Discovery Proportion (FDP) over multiple contrasts of interest in the multivariate linear model. To do so we use the bootstrap to simulate from the distribution of the null contrasts. We combine the bootstrap with the post hoc inference bounds of Blanchard (2020) and prove that doing so provides simultaneous asymptotic control of the FDP over all subsets of hypotheses. This requires us to demonstrate consistency of the multivariate bootstrap in the linear model, which we do via the Lindeberg Central Limit Theorem, providing a simpler proof of this result than that of Eck (2018). We demonstrate, via simulations, that our approach provides simultaneous control of the FDP over all subsets and is typically more powerful than existing, state of the art, parametric methods. We illustrate our approach on functional Magnetic Resonance Imaging data from the Human Connectome project and on a transcriptomic dataset of chronic obstructive pulmonary disease

Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

International audienceThis paper deals with the minimal polyadic decomposition (also known as canonical decomposition or Parafac) of a 3-way array, assuming each entry is positive. In this case, the low-rank approximation problem becomes well-posed. The suggested approach consists of taking into account the nonnegative nature of the loading matrices directly in the problem parameterization. Then, the three gradient components are derived allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, we focus on the conjugate gradient algorithm, well matched to large problems. The good behaviour of the proposed approach is illustrated through computer simulations in the context of data analysis and compared to other existing approaches

Computing the polyadic decomposition of nonnegative third order tensors

International audienceComputing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the Enhanced Line Search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors

Computing the nonnegative 3-way tensor factorization using Tikhonov regularization

International audienceThis paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with matrix exponentials. Gradient components are then derived, allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, Alternating Least Squares (ALS) and conjugate gradient algorithms are studied and compared with another existing algorithm, thanks to computer simulations performed in the context of data analysis

Joint T1 and brain fiber diffeomorphic registration using the demons

International audienceImage registration is undoubtedly one of the most active areas of research in medical imaging. Within inter-individual comparison, registration should align images as well as cortical and external structures such as sulcal lines and fibers. While using image-based registration[1], neural fibers appear uniformly white giving no information to the registration. Tensor-based registration was recently proposed to improve white-matter alignment[2,3], however misregistration may also persist in regions where the tensor field appears uniform[4]. We propose an hybrid approach by extending the Diffeomorphic Demons(D)[5] registration to incorporate geometric constrains. Combining the deformation field induce by the image and the geometry, we define a mathematically sound framework to jointly register images and geometric descriptors such as fibers or sulcal lines

Error Analysis of Low-rank Three-Way Tensor Factorization Approach to Blind Source Separation

International audienceIn tensor factorization approaches to blind separation of multidimensional sources, two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the will to better figure this out, we present error analyses in source tensor estimation performed by low-rank factorization of three-way tensors. To that aim, computer simulations as well as the analytical calculation of the theoretical error are carried out. The conclusions drawn from these numerical and analytical error analyses are supported by the results obtained thanks to tensor-based blind decomposition of an experimental multispectral image of a skin tumor

Shared Independent Component Analysis for Multi-Subject Neuroimaging

Peer reviewe

Measuring fish activities as additional environmental data during a hydrographic survey with a multi-beam echo sounder

International audienceThe modern multi-beam echo sounders (MBES) are advanced instrumentation for active underwater acoustic surveys that can be boarded on oceanic vessels as well on light crafts. Although their versatility allows scientists to perform various environmental studies, their potential is seldom fully exploited. A single data acquisition cruise is not only able to display the seabed backscatter, but also provide an estimation of the fish activities from an underwater site thanks to water column imagery. This work is aiming at developing some (automatic) signal processing techniques to detect, analyse and classify objects observed in the water column with a focus on fish activities to provide fish accumulation and classification but also some comparative analyses along with the seafloor classification

Clinical and radiological results with a 36-mm Cobalt-Chrome prosthetic head, cross-linked Durasul liners associated with Allofit cups: A more than 10-year follow-up period.

peer reviewedHighly cross-linked polyethylene is currently a common articulation surface used for THA. The aim of the present study is in-vivo assessment of highly cross-linked Durasul® polyethylene linear and volumetric wear when associated with a 36-mm prosthetic femoral head. We retrospectively reviewed clinical and radiographic data of 78 patients (81 hips) having primary THAs using Durasul® liner combined with a 36-mm CoCr prosthetic head. All of them were followed for more than 10 years. Patient outcome was assessed with the Harris Hip Score (HHS) preoperatively and at last follow-up. Two-dimensional prosthetic head penetration into polyethylene, three-dimensional wear rates and cup migration were evaluated. the preoperative and last follow-up HHS were 50.43 +/- 10.42 and 97.44 +/- 5.51 respectively. The annual penetration of the prosthetic head into Durasul® liner was 0.029 +/- 0.003 mm. The annual linear penetration and volumetric wear extrapolation rates using Charnley and Ilchmann formulas were 37.84% and 57.76% respectively of that seen with conventional polyethylene liner. At last follow-up, the total loss of material in Durasul® represents only 0.15% of the initial polyethylene mass. We did not observed any significant cup migration in the study group. Results are promising and we believe that these data authorize the continued use of highly cross-linked polyethylene liner associated with a 36-mm prosthetic head for total hip arthroplasties in older patients. More long-term follow-up studies are mandatory before we feel comfortable with the project of using cross-linked polyethylene in young and active patients instead of ceramic-on-ceramic bearings