Asymmetric Kernel Function Research Articles

A Robust Asymmetric Kernel Function for Bayesian Optimization, With Application to Image Defect Detection in Manufacturing Systems

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive to evaluate. To tackle this challenge, Bayesian optimization (BO), which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process (GP) surrogate model to be sporadic. In this article, we propose a robust kernel function, asymmetric elastic net radial basis function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared with the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding BO with GPs. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms the existing benchmark kernel functions. Note to Practitioners—Some industrial systems cannot be accurately represented by physical models. In this situation, data-driven black-box optimization is necessary for advancing the system automation and intelligence. BO is one of the widely used strategies for learning the global optimum of black-box functions. BO has been applied to robotics, anomaly detection, automatic learning algorithm configuration, reinforcement learning, and deep learning. This article proposes one new kernel function, named after AEN-RBF. The new kernel function will make BO with GPs more robust to outliers and lower the data quality barrier of model training. This article was motivated by the hyperparameter tuning problem of deep learning models for image defect detection in advanced manufacturing, but the method can be easily extended to other applications where kernel functions are needed. Our proposed method is verified by synthetic and real-world optimization problems.

Local linear smoothers using inverse Gaussian regression

Local linear fitting has been widely used for estimating the univariate regression function, it has numerous fantastic properties like minimax efficiency and boundary correction. The asymmetric kernel functions match the support of the explanatory variables, and we discover the inverse Gaussian (IG) kernel function is identical to the normal kernel with variable bandwidth. Based on these, this paper proposes a new local linear estimation procedure with the IG kernel when the covariates are supported on \((0,\infty )\). Asymptotic theories of the proposed estimator are systematically studied, including the conditional mean squared error, the asymptotic normality and the uniform almost sure convergence. A simulation study and a data example indicate that the proposed estimator works efficiently.

A nonparametric approach to the estimation of jump-diffusion models with asymmetric kernels

This paper presents the nonparametric estimation of first and second infinitesimal moments of the underlying jump-diffusion model with asymmetric kernel functions. In particular, we use asymmetric kernel estimators characterized by the gamma distribution. This approach allows to conciliate the idea of using the asymmetric kernel with jump-diffusion models. We show that the proposed estimators are consistent and asymptotically follow normal distribution under the conditions of recurrence and stationarity.

适于机载环境对地目标跟踪的粒子滤波设计

To improve the robustness while tracking a ground target with strong mobility in the cabin environment, a particle filter was taken as tracking framework, and its dynamic model and observation model were investigated. According to the two-stage dynamic model proposed by Kristan et al, a two-stage acceleration (TSA) dynamic model was proposed for the characteristics of cabin environment and the strong mobility of the tracking target. According to the idea of asymmetric kernel function proposed by Yilmaz et al., a method was proposed by using Snake algorithm to extract the object contour and to construct an asymmetric kernel function based on contour information to solve the real-time moving target problem. Finally, the TSA-AK particle filter tracking algorithm was proposed based on above methods. The proposed algorithm was tested on the video tracking ground target in cabin environment. The results show that the proposed algorithm can stably track target moving in a wide range of velocity. The targeting accuracy is 98%, and the computing frame rate is 26 frame/s when the object scale is 25 pixel30 pixel.

Non Parametric Estimation of Second-Order Diffusion Equation by Using Asymmetric Kernels

In this paper, we study the non parametric estimation of drift coefficient and diffusion coefficient in the second-order diffusion equation by using the asymmetric kernel functions, based on the difference of discrete time observations. The basic idea relies upon replacing the symmetric kernel by asymmetric kernel and provides a new way of obtaining the non parametric estimation for second-order diffusion equation. Under the appropriate assumptions, we prove that the proposed estimators of second-order diffusion equation are consistent and asymptotically follow normal distribution.

Asymmetric kernel regression.

Kernel regression is one model that has been applied to explain or design radial-basis neural networks. Practical application of the kernel regression method has shown that bias errors caused by the boundaries of the data can seriously effect the accuracy of this type of regression. This paper investigates the correction of boundary error by substituting an asymmetric kernel function for the symmetric kernel function at data points close to the boundary. The asymmetric kernel function allows a much closer approach to the boundary to be achieved without adversely effecting the noise-filtering properties of the kernel regression.

Asymmetric Kernel Functions in Non-Parametric Regression Analysis and Prediction

Non-parametric kernel and nearest neighbour estimates represent flexible alternatives to parametric modelling. For non-constant densities of the explanatory variables, kernel estimates are usually biased for finite samples, even in the case of linear regression functions. This can be seen by looking at the asymptotic expression of the bias of kernel regression estimates derived under certain mixing conditions. In this paper bias reduction techniques using asymmetric kernel functions are suggested. In contrast to well-designed experiments, in environmental data analysis the positions of the design points are not under control, and therefore the measurements of the explanatory variables are arbitrarily scattered over the factor space in an unbalanced way. In this case the asymmetric kernel techniques outperform the usual symmetric kernel methods as demonstrated by an application of both methods to the relationship between the oxygen concentration and the temperature of river water. Furthermore the new methods lead to better predictions in an autoregressive time series model for air pollution measurements such as nitrogen dioxide and sulphur dioxide concentrations.