Asymmetric Kernel Functions in Non-Parametric Regression Analysis and Prediction

Michels, Paul

doi:10.2307/2349008

Cited by 7 publications

(4 citation statements)

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“…Although a number of kernels exist, the most popular is the Epanechnikov kernel (Epanechnikov, 1969) designed to minimize the squared error of the fit for a fixed window 𝐼. In addition, the asymmetric kernel of Michels (1992) is considered (thereafter called the Michels kernel). Unlike the MA and the Epanechnikov kernels, the Michels kernel is asymmetric (i.e.…”

Section: Aggregation Of the Responsementioning

confidence: 99%

“…In past studies, only the moving average (Roberts, 2005;Sarmento et al, 2011) and Loess (Schwartz, 2000b) have been considered to aggregate the response. In the present paper, other aggregations are considered, in particular Nadaraya-Watson kernel smoothing (Nadaraya, 1964;Watson, 1964) with different kernels including the Epanechnikov kernel (Epanechnikov, 1969) and an asymmetric kernel proposed in Michels (1992).…”

Section: Introductionmentioning

confidence: 99%

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Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality

Masselot

Chebana

Bélanger

et al. 2018

Science of The Total Environment

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In environmental epidemiology studies, health response data (e.g. hospitalization or mortality) are often noisy because of hospital organization and other social factors. The noise in the data can hide the true signal related to the exposure. The signal can be unveiled by performing a temporal aggregation on health data and then using it as the response in regression analysis. From aggregated series, a general methodology is introduced to account for the particularities of an aggregated response in a regression setting. This methodology can be used with usually applied regression models in weather-related health studies, such as generalized additive models (GAM) and distributed lag nonlinear models (DLNM). In particular, the residuals are modelled using an autoregressive-moving average (ARMA) model to account for the temporal dependence. The proposed methodology is illustrated by modelling the influence of temperature on cardiovascular mortality in Canada. A comparison with classical DLNMs is provided and several aggregation methods are compared. Results show that there is an increase in the fit quality when the response is aggregated, and that the estimated relationship focuses more on the outcome over several days than the classical DLNM. More precisely, among various investigated aggregation schemes, it was found that an aggregation with an asymmetric Epanechnikov kernel is more suited for studying the temperature-mortality relationship.

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Section: Aggregation Of the Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality

Masselot

Chebana

Bélanger

et al. 2018

Science of The Total Environment

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“…The asymmetry of the proposed innovative multiscale kernel function is one salient feature that sets it apart from most of widely used kernel functions. Although the asymmetrical kernels have been found useful in nonlinear regression and object tracking [30]- [32], they were rarely studied and applied in the context of support vector learning [33]. It is well-known that only the Mercer kernel can be used for conventional quadratic programming support vector learning to ensure the positive definiteness of the Hessian matrix [1]- [6] for optimization.…”

Section: Multiscale Asymmetric Orthogonal Wavelet Kernel For Linear Pmentioning

confidence: 99%

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Sun

Butts

2014

IEEE Trans. Cybern.

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Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

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“…Asymmetric kernels have been used in the area of statistics for over a decade and have been shown to improve the density estimation [8]. This paper, however, does not use asymmetric kernels which have parametric profiles, due to their inability to represent the shape of the tracked objects.…”

Section: Introductionmentioning

confidence: 99%

Object Tracking by Asymmetric Kernel Mean Shift with Automatic Scale and Orientation Selection

Yilmaz

2007

2007 IEEE Conference on Computer Vision and Pattern Recognition

163

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Tracking objects using the mean shift method is performed by iteratively translating a kernel in the image space such that the past and current object observations are similar. Traditional mean shift method requires a symmetric kernel, such as a circle or an ellipse, and assumes constancy of the object scale and orientation during the course of tracking. In a tracking scenario, it is not uncommon to observe objects with complex shapes whose scale and orientation constantly change due to the camera and object motions. In this paper, we present an object tracking method based on the asymmetric kernel mean shift, in which the scale and orientation of the kernel adaptively change depending on the observations at each iteration. Proposed method extends the traditional mean shift tracking, which is performed in the image coordinates, by including the scale and orientation as additional dimensions and simultaneously estimates all the unknowns in a few number of mean shift iterations. The experimental results show that the proposed method is superior to the traditional mean shift tracking in the following aspects: 1) it provides consistent object tracking throughout the video; 2) it is not effected by the scale and orientation changes of the tracked objects; 3) it is less prone to the background clutter. 1 1-4244-1180-7/07/$25.00 ©2007 IEEE

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Asymmetric Kernel Functions in Non-Parametric Regression Analysis and Prediction

Cited by 7 publications

References 10 publications

Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality

Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Object Tracking by Asymmetric Kernel Mean Shift with Automatic Scale and Orientation Selection

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