We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear...We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selection of explanatory variables to build individual predictors. We define a measure of the importance of each variable in the score and an event risk measure by an odds-ratio. Moreover, we establish a property of linear discriminant analysis for mixed data. This methodology is applied to EPHESUS trial patients on whom biological, clinical and medical history variables were measured.展开更多
Selecting which explanatory variables to include in a given score is a common difficulty, as a balance must be found between statistical fit and practical application. This article presents a methodology for construct...Selecting which explanatory variables to include in a given score is a common difficulty, as a balance must be found between statistical fit and practical application. This article presents a methodology for constructing parsimonious event risk scores combining a stepwise selection of variables with ensemble scores obtained by aggregation of several scores, using several classifiers, bootstrap samples and various modalities of random selection of variables. Selection methods based on a probabilistic model can be used to achieve a stepwise selection for a given classifier such as logistic regression, but not directly for an ensemble classifier constructed by aggregation of several classifiers. Three selection methods are proposed in this framework, two involving a backward selection of the variables based on their coefficients in an ensemble score and the third involving a forward selection of the variables maximizing the AUC. The stepwise selection allows constructing a succession of scores, with the practitioner able to choose which score best fits his needs. These three methods are compared in an application to construct parsimonious short-term event risk scores in chronic HF patients, using as event the composite endpoint of death or hospitalization for worsening HF within 180 days of a visit. Focusing on the fastest method, four scores are constructed, yielding out-of-bag AUCs ranging from 0.81 (26 variables) to 0.76 (2 variables).展开更多
In this paper, we consider a vibrating system of Timoshenko-type in a onedimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the di...In this paper, we consider a vibrating system of Timoshenko-type in a onedimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initial data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.展开更多
In supervised learning the number of values of a response variable can be very high. Grouping these values in a few clusters can be useful to perform accurate supervised classification analyses. On the other hand sele...In supervised learning the number of values of a response variable can be very high. Grouping these values in a few clusters can be useful to perform accurate supervised classification analyses. On the other hand selecting relevant covariates is a crucial step to build robust and efficient prediction models. We propose in this paper an algorithm that simultaneously groups the values of a response variable into a limited number of clusters and selects stepwise the best covariates that discriminate this clustering. These objectives are achieved by alternate optimization of a user-defined model selection criterion. This process extends a former version of the algorithm to a more general framework. Moreover possible further developments are discussed in detail.展开更多
The present aim is to update, upon arrival of new learning data, the parameters of a score constructed with an ensemble method involving linear discriminant analysis and logistic regression in an online setting, witho...The present aim is to update, upon arrival of new learning data, the parameters of a score constructed with an ensemble method involving linear discriminant analysis and logistic regression in an online setting, without the need to store all of the previously obtained data. Poisson bootstrap and stochastic approximation processes were used with online standardized data to avoid numerical explosions, the convergence of which has been established theoretically. This empirical convergence of online ensemble scores to a reference “batch” score was studied on five different datasets from which data streams were simulated, comparing six different processes to construct the online scores. For each score, 50 replications using a total of 10N observations (N being the size of the dataset) were performed to assess the convergence and the stability of the method, computing the mean and standard deviation of a convergence criterion. A complementary study using 100N observations was also performed. All tested processes on all datasets converged after N iterations, except for one process on one dataset. The best processes were averaged processes using online standardized data and a piecewise constant step-size.展开更多
The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions ...The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization procedure.Then,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is stated.To accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional derivative.The resulting algorithm is highly efficient for long time simulations.Finally,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.展开更多
文摘We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selection of explanatory variables to build individual predictors. We define a measure of the importance of each variable in the score and an event risk measure by an odds-ratio. Moreover, we establish a property of linear discriminant analysis for mixed data. This methodology is applied to EPHESUS trial patients on whom biological, clinical and medical history variables were measured.
文摘Selecting which explanatory variables to include in a given score is a common difficulty, as a balance must be found between statistical fit and practical application. This article presents a methodology for constructing parsimonious event risk scores combining a stepwise selection of variables with ensemble scores obtained by aggregation of several scores, using several classifiers, bootstrap samples and various modalities of random selection of variables. Selection methods based on a probabilistic model can be used to achieve a stepwise selection for a given classifier such as logistic regression, but not directly for an ensemble classifier constructed by aggregation of several classifiers. Three selection methods are proposed in this framework, two involving a backward selection of the variables based on their coefficients in an ensemble score and the third involving a forward selection of the variables maximizing the AUC. The stepwise selection allows constructing a succession of scores, with the practitioner able to choose which score best fits his needs. These three methods are compared in an application to construct parsimonious short-term event risk scores in chronic HF patients, using as event the composite endpoint of death or hospitalization for worsening HF within 180 days of a visit. Focusing on the fastest method, four scores are constructed, yielding out-of-bag AUCs ranging from 0.81 (26 variables) to 0.76 (2 variables).
基金funded by KFUPM under the scientific project IN141015
文摘In this paper, we consider a vibrating system of Timoshenko-type in a onedimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initial data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.
文摘In supervised learning the number of values of a response variable can be very high. Grouping these values in a few clusters can be useful to perform accurate supervised classification analyses. On the other hand selecting relevant covariates is a crucial step to build robust and efficient prediction models. We propose in this paper an algorithm that simultaneously groups the values of a response variable into a limited number of clusters and selects stepwise the best covariates that discriminate this clustering. These objectives are achieved by alternate optimization of a user-defined model selection criterion. This process extends a former version of the algorithm to a more general framework. Moreover possible further developments are discussed in detail.
文摘The present aim is to update, upon arrival of new learning data, the parameters of a score constructed with an ensemble method involving linear discriminant analysis and logistic regression in an online setting, without the need to store all of the previously obtained data. Poisson bootstrap and stochastic approximation processes were used with online standardized data to avoid numerical explosions, the convergence of which has been established theoretically. This empirical convergence of online ensemble scores to a reference “batch” score was studied on five different datasets from which data streams were simulated, comparing six different processes to construct the online scores. For each score, 50 replications using a total of 10N observations (N being the size of the dataset) were performed to assess the convergence and the stability of the method, computing the mean and standard deviation of a convergence criterion. A complementary study using 100N observations was also performed. All tested processes on all datasets converged after N iterations, except for one process on one dataset. The best processes were averaged processes using online standardized data and a piecewise constant step-size.
基金supported by the NSFC under grants 11771035,91430216,U1530401supported by the NSFC under grants Nos.11571128,11771162support of the French ANR grant BOND(ANR-13-BS01-0009-01)and the LIASFMA(funding from the University of Lorraine).
文摘The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization procedure.Then,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is stated.To accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional derivative.The resulting algorithm is highly efficient for long time simulations.Finally,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.
