Nonparametric Density Estimation by B-Spline Duality

Cui, Zhenyu; Kirkby, Justin; Nguyen, Duy

doi:10.1017/s0266466619000112

Cited by 15 publications

(22 citation statements)

References 83 publications

(124 reference statements)

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“…The discreteness of the indices limits the possibility of consistently comparing the impact of factors on the rate of growth in the cost of flows. The solution is to interpolate the flow dynamics with cubic splines (Cui et al, 2020;Edwards & Parry, 2018;Gao & Meng, 2018), followed by the use of flow velocity models (Figure 01). The c spline models allow for using the models of the rate of changes in export oil prices, the volume of oil production and the cost of oil exports.…”

Section: Resultsmentioning

confidence: 99%

The Cost Of Export Flows: Spline-Modeling And Factor Analysis

Ilyasov¹

2022

The European Proceedings of Social and Behavioural Sciences

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When examining the value of export flows, it is important to assess the impact of two key factors -export volumes and export prices. The subject of the study is a factor analysis of the value of export flows. The aim is to evaluate the effectiveness of spline modeling in the factor analysis of the cost of flows. The methods of factor analysis of export flows refer to economic indices. The discreteness of indices limits the effectiveness of the analysis of the cost of flows in case of strong fluctuations in export prices and (or) export volumes, which is characteristic of the dynamics of oil export flows. Modeling without smoothing the empirical dynamics retains information about velocity fluctuations; after that, differentiation can be used to change in the analysis and operational management of trends in the cost of flows. The required accuracy can be achieved by data processing in the Maple 17 computer mathematics system, which performs calculations without rounding errors. The method of factor analysis showed the possibility to study the dependence of trends in the cost of export flows on fluctuations in the speed of export prices and export volumes. The methods of spline modeling and factor analysis of flow cost trends are effective, determine the impact of factors at nodal points and at any arbitrary time within the interval under study.

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Section: Resultsmentioning

confidence: 99%

The Cost Of Export Flows: Spline-Modeling And Factor Analysis

Ilyasov¹

2022

The European Proceedings of Social and Behavioural Sciences

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“…Kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable [30], which is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval [31].…”

Section: Kernel Smoothing Density Estimationmentioning

confidence: 99%

Tool Wear Conditions Monitoring Based on Kernel Smoothing Density and Deep Learning

Bazi¹,

Benkedjouh²,

Habbouche³

et al. 2021

Preprint

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Life prediction and health assessment of cutting tools is a challenging problem in industrial manufacturing, and plays an important role for Prognostic activities. The degradation of this tool can cause significant economic losses and risks for machine users. However, due to the random nature of system degradation and the sensitivity of various features characterizing cutter degradation, may vary considerably under different operation conditions. This paper propose a new data driven approach for tool condition monitoring, based on kernel smoothing density to model the random phenomena of degradation progression. The health assessment is insured using one directional neural network to extract useful information’s. Deep learning allows relating between extracted features and health indicator progression, and estimate remaining useful life. This methodology is evaluated using regression metrics and compared with recent frameworks, based on an experimental dataset from PHM Data Challenge 2010. The obtained results shows that the proposed approach can effectively predict the tool wear and obtain higher prediction accuracy than other comparison models.

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“…Since B-spline basis functions possess the property of local support, local density estimators based on uniform B-splines have been discussed in [10][11][12][13]. In addition to the local support property, B-spline basis functions are also piecewise polynomials, which demonstrates their advantages where intensive numerical computations have been conducted after estimation [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Nonparametric Density Estimation with B-Spline Bases

Zhao

Zhang

et al. 2023

Mathematics

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Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can improve on the approximation capability of uniform B-splines. Based on this observation, we perform density estimation with nonuniform B-splines. By introducing the error indicator attached to each interval, we propose an adaptive strategy to generate the nonuniform knot vector. The error indicator is an approximation of the information entropy locally, which is closely related to the number of kernels when we construct the nonuniform estimator. The numerical experiments show that, compared with the uniform B-spline, the local density estimation with nonuniform B-splines not only achieves better estimation results but also effectively alleviates the overfitting phenomenon caused by the uniform B-splines. The comparison with the existing estimation procedures, including the state-of-the-art kernel estimators, demonstrates the accuracy of our new method.

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Nonparametric Density Estimation by B-Spline Duality

Cited by 15 publications

References 83 publications

The Cost Of Export Flows: Spline-Modeling And Factor Analysis

The Cost Of Export Flows: Spline-Modeling And Factor Analysis

Tool Wear Conditions Monitoring Based on Kernel Smoothing Density and Deep Learning

Adaptive Nonparametric Density Estimation with B-Spline Bases

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