Kernel Smoothing Research Articles

Estimation on semi-functional linear errors-in-variables models

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method.

NLPAR: Non-local smoothing for enhanced EBSD pattern indexing

Due to continued advances in phosphor sensitivity and camera technology, electron backscattered diffraction (EBSD) within a scanning electron microscope (SEM) has become an increasingly popular method for determining crystal orientations within a given microstructure. Concurrent advances in computational processing have also made it possible to store each individual diffraction pattern as it is collected, which has allowed more complex algorithms to be deployed for post-processing and indexing patterns. This paper proposes a new post-processing technique for pattern enhancement that aids in re-indexing by leveraging a non-local smoothing kernel whose weights are based on the exponential decay of the Euclidean distance between patterns. The advantage of this approach is its ability to utilize very large smoothing kernels without losing integrity near interface boundaries and while still operating on timescales comparable to traditional indexing approaches. Using an Inconel 600 nickel alloy sample, the capabilities and performance of the proposed approach are compared to other indexing schemes, including neighbor pattern averaging with re-indexing (NPAR) and a dictionary-based approach. The results demonstrate that the proposed method consistently produces a higher index success rate (ISR) than NPAR and comparable ISRs to the dictionary-based approach, a method with orders-of-magnitude greater computational demands. Source code for the NLPAR algorithm is available at https://github.com/USNavalResearchLaboratory/NLPAR

Predicting pollution incidents through semiparametric quantile regression models

In this paper we present a method to forecast pollution episodes using measurements of the pollutant concentration along time. Specifically, we use a backfitting algorithm with local polynomial kernel smoothers to estimate a semiparametric additive quantile regression model. We also propose a statistical hypothesis test to determine critical values, i.e., the values of the concentration that are significant to forecast the pollution episodes. This test is based on a wild bootstrap approach modified to suit asymmetric loss functions, as occurs in quantile regression. The validity of the method was checked with both simulated and real data, the latter from $${\hbox {SO}}_{2}$$ emissions from a coal-fired power station located in Northern Spain.

Oracally efficient spline-backfitted kernel smoothing of additive partial linear measurement error model

We consider statistical inference for additive partial linear models when the linear covariate is measured with error. A bias-corrected spline-backfitted kernel smoothing method is proposed. Under mild assumptions, the proposed component function and parameter estimator are oracally efficient and fast to compute. The nonparametric function estimator’s pointwise distribution is asymptotically equivalent to an function estimator in partial linear model. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are applied to Boston house data set.

Several Aspects of Nonparametric Prediction of Nonlinear Time Series

Nonparametric regression is an alternative to the parametric approach, which consists of applying parametric models, i.e. models of the certain functional form with a fixed number of parameters. As opposed to the parametric approach, nonparametric models have a general form, which can be approximated increasingly precisely when the sample size grows. Hereby they do not impose such restricted assumptions about the form of the modelling dependencies and in consequence, they are more flexible and let the data speak for themselves. That is why they are a promising tool for forecasting, especially in case of nonlinear time series. One of the most popular nonparametric regression method is the Nadaraya- Watson kernel smoothing. Nowadays, there are a number of variations of this method, like the local-linear kernel estimator, which combines the local linear approximation and the kernel estimator. In the paper a Monte Carlo study is conducted in order to assess the usefulness of the kernel smoothers to nonlinear time series forecasting and to compare them with the other techniques of forecasting.

Generalized proximal smoothing (GPS) for phase retrieval.

In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and support constraint. We relax the support constraint by incorporating the Moreau-Yosida regularization and heat kernel smoothing, and derive the associated proximal mapping. We also relax the magnitude constraint into a least squares fidelity term, whose proximal mapping is available as well. GPS alternatively iterates between the two proximal mappings in primal and dual spaces, respectively. Using both numerical simulation and experimental data, we show that GPS algorithm consistently outperforms the classical phase retrieval algorithms such as hybrid input-output (HIO) and oversampling smoothness (OSS), in terms of the convergence speed, consistency of the phase retrieval, and robustness to noise.

Buckling loads of nano-beams in stress-driven nonlocal elasticity

Size-dependent buckling of compressed Bernoulli-Euler nano-beams is investigated by stress-driven nonlocal continuum mechanics. The nonlocal elastic strain is obtained by convoluting the stress field with a suitable smoothing kernel. Incremental equilibrium equations are established by a standard perturbation technique. Higher-order constitutive boundary conditions are naturally inferred by the stress-driven nonlocal integral convolution, equipped with the special bi-exponential kernel. Buckling loads of compressed nano-beams, with kinematic boundary constraints of applicative interest, are numerically calculated and compared with those obtained by the theory of strain gradient elasticity.

Identifying disaster-related tweets and their semantic, spatial and temporal context using deep learning, natural language processing and spatial analysis: a case study of Hurricane Irma

ABSTRACTWe introduce an analytical framework for analyzing tweets to (1) identify and categorize fine-grained details about a disaster such as affected individuals, damaged infrastructure and disrupted services; (2) distinguish impact areas and time periods, and relative prominence of each category of disaster-related information across space and time. We first identify disaster-related tweets by generating a human-labeled training dataset and experimenting a series of deep learning and machine learning methods for a binary classification of disaster-relatedness. We employ LSTM (Long Short-Term Memory) networks for the classification task because LSTM networks outperform other methods by considering the whole text structure using long-term semantic word and feature dependencies. Second, we employ an unsupervised multi-label classification of tweets using Latent Dirichlet Allocation (LDA), and identify latent categories of tweets such as affected individuals and disrupted services. Third, we employ spatially-adaptive kernel smoothing and density-based spatial clustering to identify the relative prominence and impact areas for each information category, respectively. Using Hurricane Irma as a case study, we analyze over 500 million keyword-based and geo-located collection of tweets before, during and after the disaster. Our results highlight potential areas with high density of affected individuals and infrastructure damage throughout the temporal progression of the disaster.

Spatial analysis and temporal trends of antimicrobial use in Danish pig herds following the introduction of the Yellow Card scheme

Spatial analysis and temporal trends of antimicrobial use in Danish pig herds following the introduction of the Yellow Card scheme

Nonparametric inference for continuous-time event counting and link-based dynamic network models

A flexible approach for modeling both dynamic event counting and dynamic link-based networks based on counting processes is proposed, and estimation in these models is studied. We consider nonparametric likelihood based estimation of parameter functions via kernel smoothing. The asymptotic behavior of these estimators is rigorously analyzed by allowing the number of nodes to tend to infinity. The finite sample performance of the estimators is illustrated through an empirical analysis of bike share data.

A Novel RLS-KS Method for Parameter Estimation in Particle Filtering-Based Fatigue Crack Growth Prognostics

The accurate prognosis of fatigue crack growth (FCG) is vital for securing structural safety and developing maintenance plans. With the development of structural health monitoring (SHM) technology, the particle filter (PF) has been considered a promising tool for online prognostics of FCG. Among the existing FCG models, the traditional Paris-Erdogan model is most commonly used in PF-based FCG prognostics. The parameters of the Paris-Erdogan model can be estimated together with the crack state in the PF framework. However, we find that there is a problem of “Coordinated Change” when the parameters priors are far from the true values. As a result, the filtering results appear as a correct remaining useful life (RUL) prognosis but an incorrect parameters estimation. To solve this problem, in this paper, a novel recursive least squares-kernel smoothing (RLS-KS) method is proposed for parameter estimation in PF-based FCG prognostics. The proposed method is validated through an experimental application; and then compared with the classic artificial evolution (AE) and kernel smoothing (KS) methods. The validation results show that the RLS-KS method can provide both correct RUL prognostics and parameter estimation. Moreover, this method provides better performance for FCG prognostics compared with classic methods.

Adaptive Partially Linear Regression Models by Mixing Different Estimates

This paper proposes adapting the semiparametric partial model (PLM) by mixing different estimation procedures defined under different conditions. Choosing an estimation method of PLM, from several estimation methods, is an important issue, which depends on the performance of the method and the properties of the resulting estimators. Practically, it is difficult to assign the conditions which give the best estimation procedure for the data at hand, so adaptive procedure is needed. Kernel smoothing, spline smoothing, and difference based methods are different estimation procedures used to estimate the partially linear model. Some of these methods will be used in adapting the PLM by mixing. The adapted proposed estimator is found to be a square root-consistent and has asymptotic normal distribution for the parametric component of the model. Simulation studies with different settings, and real data are used to evaluate the proposed adaptive estimator. Correlated and non-correlated regressors are used for the parametric components of the semiparametric partial model (PLM). Best results are obtained in the case of correlated regressors than in the non-correlated ones. The proposed adaptive estimator is compared to the candidate model estimators used in mixing. Best results are obtained in the form of less risk error and less convergence rate for the proposed adaptive partial linear model (PLM).

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

We develop theory of a novel fast bootstrap for dependent data. Our scheme deploys i.i.d. resampling of smoothed moment indicators. We characterize the class of parametric and semiparametric estimation problems for which the method is valid. We show the asymptotic re refinements of the new procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the advantages of our procedure for M-estimator, generalized method of moments, and generalized empirical likelihood estimation. In a Monte Carlo study, we consider an autoregressive conditional duration model and we compare our method with other extant, routinely-applied first- and higher-order correct methods. The results provide numerical evidence that the novel bootstrap yields higher-order accurate confidence intervals, while remaining computationally lighter than its higher-order correct competitors. A real-data example on dynamics of trading volume of US stocks illustrates the empirical relevance of our method.

B-spline Speckman Estimator of Partially Linear Model

The partially linear model (PLM) is one of semiparametric regression models; since it has both parametric (more than one) and nonparametric (only one) components in the same model, so this model is more flexible than the linear regression models containing only parametric components. In the literature, there are several estimators are proposed for this model; where the main difference between these estimators is the estimation method used to estimate the nonparametric component, since the parametric component is estimated by least squares method mostly. The Speckman estimator is one of the commonly used for estimating the parameters of the PLM, this estimator based on kernel smoothing approach to estimate nonparametric component in the model. According to the papers in nonparametric regression, in general, the spline smoothing approach is more efficient than kernel smoothing approach. Therefore, we suggested, in this paper, using the basis spline (B-spline) smoothing approach to estimate nonparametric component in the model instead of the kernel smoothing approach. To study the performance of the new estimator and compare it with other estimators, we conducted a Monte Carlo simulation study. The results of our simulation study confirmed that the proposed estimator was the best, because it has the lowest mean squared error.

Kernel density estimation from complex surveys in the presence of complete auxiliary information

Auxiliary information is widely used in survey sampling to enhance the precision of estimators of finite population parameters, such as the finite population mean, percentiles, and distribution function. In the context of complex surveys, we show how auxiliary information can be used effectively in kernel estimation of the superpopulation density function of a given study variable. We propose two classes of “model-assisted” kernel density estimators that make efficient use of auxiliary information. For one class we assume that the functional relationship between the study variable Y and the auxiliary variable X is known, while for the other class the relationship is assumed unknown and is estimated using kernel smoothing techniques. Under the first class, we show that if the functional relationship can be written as a simple linear regression model with constant error variance, the mean of the proposed density estimator will be identical to the well-known regression estimator of the finite population mean. If we drop the intercept from the linear model and allow the error variance to be proportional to the auxiliary variable, the mean of the proposed density estimator matches the ratio estimator of the finite population mean. The properties of the new density estimators are studied under a combined design-model-based inference framework, which accounts for the underlying superpopulation model as well as the randomization distribution induced by the sampling design. Moreover, the asymptotic normality of each estimator is derived under both design-based and combined inference frameworks when the sampling design is simple random sampling without replacement. For the practical implementation of these estimators, we discuss how data-driven bandwidth estimators can be obtained. The finite sample properties of the proposed estimators are addressed via simulations and an example that mimics a real survey. These simulations show that the new estimators perform very well compared to standard kernel estimators which do not utilize the auxiliary information.

Fingerprint Recognition Using Markov Chain and Kernel Smoothing Technique with Generalized Regression Neural Network and Adaptive Resonance Theory with Mapping

The necessity of fast and precise identification from fingerprints might be fulfilled via systems benefiting from intelligent elements such as Neural Networks. The process of recognition and classification have been performed according to beneficial points called core point, singularities, or minutiae. However, points always are sensitive to noise and distortion, thus inaccurate results. Hence, instead of extracting a point, two lines are defined to bring down the risk of finding a point. Plus, two approaches are proposed with the intention of extracting statistical features predicated upon Kernel and Markov chain. In fact, two sets of features are extracted from both horizontal and vertical Markov chain, derived from the ridges angle around the aforementioned lines. In addition, all features are trained and tested via two divergent neural networks, consisting Generalized Regression Neural Network (GRNN) and Adaptive Resonance Theory with mapping (ARTMAP). Fingerprint verification competition (FVC) database is used to analyze the system. The performances of networks with different sets of features are simulated and compared with MATLAB. The results coming from simulation are compared and 93.5% and 83.5% accuracy is achieved for GRNN and ARTMAP respectively. Furthermore, the system is tested by both networks with features coming from just vertical and horizontal features.

Large deviations for stochastic 3D Leray-<inline-formula><tex-math id="M1">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> model with fractional dissipation

In this paper we establish the Freidlin-Wentzell's large deviation principle for stochastic 3D Leray-$ \alpha $ model with general fractional dissipation and small multiplicative noise. This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of order $ \theta_1 $ in the nonlinear term and a $ \theta_2 $-fractional Laplacian. The main result generalizes the corresponding LDP result of the classical stochastic 3D Leray-$ \alpha $ model ($ \theta_1 = 1 $, $ \theta_2 = 1 $), and it is also applicable to the stochastic 3D hyperviscous Navier-Stokes equations ($ \theta_1 = 0 $, $ \theta_2\geq\frac{5}{4} $) and stochastic 3D critical Leray-$ \alpha $ model ($ \theta_1 = \frac{1}{4} $, $ \theta_2 = 1 $).

Inference on treatment effect modification by biomarker response in a three-phase sampling design.

An objective in randomized clinical trials is the evaluation of "principal surrogates," which consists of analyzing how the treatment effect on a clinical endpoint varies over principal strata subgroups defined by an intermediate response outcome under both or one of the treatment assignments. The latter effect modification estimand has been termed the marginal causal effect predictiveness (mCEP) curve. This objective was addressed in two randomized placebo-controlled Phase 3 dengue vaccine trials for an antibody response biomarker whose sampling design rendered previously developed inferential methods highly inefficient due to a three-phase sampling design. In this design, the biomarker was measured in a case-cohort sample and a key baseline auxiliary strongly associated with the biomarker (the "baseline surrogate measure") was only measured in a further sub-sample. We propose a novel approach to estimation of the mCEP curve in such three-phase sampling designs that avoids the restrictive "placebo structural risk" modeling assumption common to past methods and that further improves robustness by the use of non-parametric kernel smoothing for biomarker density estimation. Additionally, we develop bootstrap-based procedures for pointwise and simultaneous confidence intervals and testing of four relevant hypotheses about the mCEP curve. We investigate the finite-sample properties of the proposed methods and compare them to those of an alternative method making the placebo structural risk assumption. Finally, we apply the novel and alternative procedures to the two dengue vaccine trial data sets.

A kernel smoothing algorithm for ablation visualization in ultrasound elastography

Three-dimensional visualization of tumor ablation procedures have significant clinical value because the ability to accurately visualize ablated volumes can help clinicians gauge the extent of ablated tissue necrosis and plan future treatment steps. Better control over ablation volume can prevent recurrence of tumors treated using ablative procedures. This paper presents a kernel based smoothing algorithm called MatérnSmooth to reconstruct shear wave velocity maps from data acquired through ultrasound electrode vibration elastography. Shear wave velocity estimates are acquired on several intersecting imaging planes that share a common axis of intersection collinear with the ablation needle. An objective method of choosing smoothing parameters from underlying data is outlined through simulations. Experimental validation was performed on data acquired from a tissue mimicking phantom. Volume estimates were found to be within 20% of the true value.

Semi-parametric training of autoencoders with Gaussian kernel smoothed topology learning neural networks

Autoencoders are essential for training multi-hidden layer neural networks. Parametric autoencoder trainings often require user selections of hidden neuron numbers and kernel types. In this paper, a semi-parametric autoencoder training method based on self-organized learning and incremental learning is proposed. The cost function is constructed incrementally by nonparametric learning, and the model parameter is trained by parametric learning. First, a topology learning neural network such as growing neural gas or self-organizing incremental neural network is trained to obtain a discrete representation of the training data. Second, the correlations between different dimensions are modeled as a joint distribution by the neural network representation and kernel smoothers. Finally, the loss function is defined to be the regression prediction errors with each dimension as a response variable in density regression. The parameter of kernels is selected by gradient descent which minimizes the reconstruction error on a data subset. The proposed architecture has the advantage of high training space efficiency because of incremental training, and the advantage of automated selection of hidden neuron numbers. Experiments are carried out on 4 UCI datasets and an image interpolation task. Results show that the proposed methods outperform the perceptron architecture autoencoders and the restricted Boltzmann machine in the task of nonlinear feature learning.