Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.Comment: 11 pages, 8 figures, submitted for publicatio

Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

International audienceMixing phenomena in hyperspectral images depend on a variety of factors, such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that the mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed detect-then-unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images

A robust test for nonlinear mixture detection in hyperspectral images

International audienceThis paper studies a pixel by pixel nonlinearity detector for hyperspectral image analysis. The reflectances of linearly mixed pixels are assumed to be a linear combination of known pure spectral components (endmembers) contaminated by additive white Gaussian noise. Nonlinear mixing, however, is not restricted to any prescribed nonlinear mixing model. The mixing coefficients (abundances) satisfy the physically motivated sum-to-one and positivity constraints. The proposed detection strategy considers the distance between an observed pixel and the hyperplane spanned by the endmembers to decide whether that pixel satisfies the linear mixing model (null hypothesis) or results from a more general nonlinear mixture (alternative hypothesis). The distribution of this distance is derived under the two hypotheses. Closed-form expressions are then obtained for the probabilities of false alarm and detection as functions of the test threshold. The proposed detector is compared to another nonlinearity detector recently investigated in the literature through simulations using synthetic data. It is also applied to a real hyperspectral image

Chemotherapy or allogeneic transplantation in high-risk Philadelphia chromosome–negative adult lymphoblastic leukemia

The need for allogeneic hematopoietic stem cell transplantation (allo-HSCT) in adults with Philadelphia chromosome–negative (Ph−) acute lymphoblastic leukemia (ALL) with high-risk (HR) features and adequate measurable residual disease (MRD) clearance remains unclear. The aim of the ALL-HR-11 trial was to evaluate the outcomes of HR Ph− adult ALL patients following chemotherapy or allo-HSCT administered based on end-induction and consolidation MRD levels. Patients aged 15 to 60 years with HR-ALL in complete response (CR) and MRD levels (centrally assessed by 8-color flow cytometry) <0.1% after induction and <0.01% after early consolidation were assigned to receive delayed consolidation and maintenance therapy up to 2 years in CR. The remaining patients were allocated to allo-HSCT. CR was attained in 315/348 patients (91%), with MRD <0.1% after induction in 220/289 patients (76%). By intention-to-treat, 218 patients were assigned to chemotherapy and 106 to allo-HSCT. The 5-year (±95% confidence interval) cumulative incidence of relapse (CIR), overall survival (OS), and event-free survival probabilities for the whole series were 43% ± 7%, 49% ± 7%, and 40% ± 6%, respectively, with CIR and OS rates of 45% ± 8% and 59% ± 9% for patients assigned to chemotherapy and of 40% ± 12% and 38% ± 11% for those assigned to allo-HSCT, respectively. Our results show that avoiding allo-HSCT does not hamper the outcomes of HR Ph− adult ALL patients up to 60 years with adequate MRD response after induction and consolidation. Better postremission alternative therapies are especially needed for patients with poor MRD clearance

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to &lt;90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], &gt;300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of &lt;15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P&lt;0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P&lt;0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Azimuthal separation in nearly back-to-back jet topologies in inclusive 2-and 3-jet events in pp collisions at root s=13TeV

A measurement for inclusive 2- and 3-jet events of the azimuthal correlation between the two jets with the largest transverse momenta, Delta phi(12), is presented. The measurement considers events where the two leading jets are nearly collinear ("back-to-back") in the transverse plane and is performed for several ranges of the leading jet transverse momentum. Proton-proton collision data collected with the CMS experiment at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 35.9 fb(-1) are used. Predictions based on calculations using matrix elements at leading-order and next-to-leading-order accuracy in perturbative quantum chromodynamics supplemented with leading-log parton showers and hadronization are generally in agreement with themeasurements. Discrepancies between the measurement and theoretical predictions are as large as 15%, mainly in the region 177 degrees <Delta phi(12) <180 degrees. The 2- and 3-jet measurements are not simultaneously described by any of models.Peer reviewe

AFFINE PROJECTION ALGORITHM APPLIED TO NONLINEAR ADAPTIVE FILTERING

In this paper, we present a framework for nonlinear adaptive filtering. It employs the formalism of reproducing kernel Hilbert spaces to incorporate nonlinearity into the classical affine projection algorithm. A nonlinear normalized LMS (NLMS) algorithm with kernels is also derived as a particular case. We propose a sparsification strategy that employs a coherence parameter to control the model order increase typical of kernel-based methods. The resulting algorithms are suitable for real-time applications. Experimental results validate our approach. Index terms – Adaptive filters, nonlinear systems 1

Online prediction of time series data with kernels

Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods

Modélisation parcimonieuse non linéaire en ligne par une méthode à noyau reproduisant et un critère de cohérence

Cet article traite du problème d'identification de systèmes non linéaires et non stationnaires par des méthodes à noyau reproduisant. Les approches de ce type nécessitent un contrôle en ligne de l'ordre du modèle considéré. Notre approche exploite le critère de cohérence, issu des techniques de décomposition parcimonieuse. Elle permet le contrôle de l'ordre du modèle à noyau reproduisant avec un coût calculatoire linéaire par rapport à celui-ci, contrairement aux techniques existantes qui sont à complexité quadratique. On illustre cette approche par un algorithme de moindres carrés récursif, avec des simulations sur des modèles synthétiques et réels