Régression des moindres carrés partiels

Résumé

La régression des moindres carrés partiels a été inventée en 1983 par Svante Wold et son père Herman Wold ; on utilise fréquemment l'abréviation anglaise régression PLS ( et/ou ). La régression PLS maximise la variance des prédicteurs (Xi) = X et maximise la corrélation entre X et la variable à expliquer Y. Cet algorithme emprunte sa démarche à la fois à l'analyse en composantes principales (ACP) et à la régression. Plus précisément, la régression PLS cherche des composantes, appelées variables latentes, liées à X et à Y, servant à exprimer la régression de Y sur ces variables et finalement de Y sur X. Historique En 1966, Herman Wold propose un algorithme nommé tout d'abord NILES (), puis NIPALS () pour l'analyse en composantes principales. En 1975 il présente l'approche PLS, pour analyser les données exprimées en J blocs de variables sur les mêmes individus. En 1983, Svante Wold (fils d'Herman Wold) et Harald Martens combinent NIPAL

Source officielle

https://fr.wikipedia.org/wiki/R%C3%A9gression_des_moindres_carr%C3%A9s_partiels

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Forecasting respiratory rate in sedated patients with partial least squares regression

Jérémie Guignard

Remifentanil, like the other sedative drugs used to achieve conscious sedation, has an impact on the efficiency of patient ventilation. Since the quality of breathing has an indirect effect on blood O2 and CO2 concentrations, keeping patients' blood homeostasis relies on anesthetists' and nurses' vigilence. The current state of patient monitoring during conscious sedation can detect unsuccessful respirations only after they have occurred. Hence, there is a clinical need for a signal classifier to predict potential respiration failure in sedated patients. Given that the physiological changes involved in this context are transitory, and that opioids affect the Central Nervous System, the hypothesis is that opioids' effect on a patient drive to breath will result in detectable changes in electrocardiogram and capnogram signals. The purpose of this project is to design a signal classiffier to predict respiratory rate (RR) based on the analysis of the ECG spectrum and capnogram shape. Using patient audit data, a modeling set was created. Power Spectral Density calculation on a sliding Hamming window was the feature extraction used on ECG. A custom filter was designed to extract values describing the shape of each breaths in terms of slope, curvature and integral of the capnographic trace. Both patient specific (single user) and robust (mulit-user) solution were investigated. PLS regression resulted in parsimonious patient specific models capable of predicting the respiratory rate with an average accuracy of 90%. The performance, however, dropped for low RR. The analysis of the weights showed that the frequencies under 7.5Hz contain the majority of the information. Several limitations are addressed in the building of a robust multi-user model. The results obtained suggest an existing patient-specific correlation between the frequency content of ECG and the upcoming RR. Further investigation is required to achieve clinically useful prediction

2009

Chargement

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We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the link between the discrete gradient and Haar-wavelet shrinkage with cycle spinning. The redundancy of the representation implies that some wavelet-domain estimates are inconsistent with the underlying signal model. However, by imposing additional constraints, our method finds wavelet-domain solutions that are mutually consistent. We confirm the MMSE performance of our method through statistical estimation of Levy processes that have sparse derivatives.

Ieee-Inst Electrical Electronics Engineers Inc2013

Chargement

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that achieves jointly the optimal prediction error rates for least-squares regression, both in terms of forgetting the initial conditions in O (1 / n(2)), and in terms of dependence on the noise and dimension d of the problem, as O (d / n). Our new algorithm is based on averaged accelerated regularized gradient descent, and may also be analyzed through finer assumptions on initial conditions and the Hessian matrix, leading to dimension-free quantities that may still be small in some distances while the "optimal" terms above are large. In order to characterize the tightness of these new bounds, we consider an application to non-parametric regression and use the known lower bounds on the statistical performance (without computational limits), which happen to match our bounds obtained from a single pass on the data and thus show optimality of our algorithm in a wide variety of particular trade-offs between bias and variance.

2017

Chargement

Forecasting respiratory rate in sedated patients with partial least squares regression

Jérémie Guignard

2009