Search results for "Kernel Density Estimation."
showing 10 items of 34 documents
An Introduction to Kernel Methods
2009
Machine learning has experienced a great advance in the eighties and nineties due to the active research in artificial neural networks and adaptive systems. These tools have demonstrated good results in many real applications, since neither a priori knowledge about the distribution of the available data nor the relationships among the independent variables should be necessarily assumed. Overfitting due to reduced training data sets is controlled by means of a regularized functional which minimizes the complexity of the machine. Working with high dimensional input spaces is no longer a problem thanks to the use of kernel methods. Such methods also provide us with new ways to interpret the cl…
Probabilistic Selection Approaches in Decomposition-based Evolutionary Algorithms for Offline Data-Driven Multiobjective Optimization
2022
In offline data-driven multiobjective optimization, no new data is available during the optimization process. Approximation models, also known as surrogates, are built using the provided offline data. A multiobjective evolutionary algorithm can be utilized to find solutions by using these surrogates. The accuracy of the approximated solutions depends on the surrogates and approximations typically involve uncertainties. In this paper, we propose probabilistic selection approaches that utilize the uncertainty information of the Kriging models (as surrogates) to improve the solution process in offline data-driven multiobjective optimization. These approaches are designed for decomposition-base…
Experimental approach for testing the uncoupling between cardiovascular variability series
2002
In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parame…
Multi-scale Modelling of Segmentation
2016
While listening to music, people often unwittingly break down musical pieces into constituent chunks such as verses and choruses. Music segmentation studies have suggested that some consensus regarding boundary perception exists, despite individual differences. However, neither the effects of experimental task (i.e., real-time vs. annotated segmentation), nor of musicianship on boundary perception are clear. Our study assesses musicianship effects and differences between segmentation tasks. We conducted a real-time experiment to collect segmentations by musicians and nonmusicians from nine musical pieces. In a second experiment on non-real-time segmentation, musicians indicated boundaries a…
Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel
2015
To assess the goodness-of-fit of a sample to a continuous random distribution, the most popular approach has been based on measuring, using either L∞ - or L2 -norms, the distance between the null hypothesis cumulative distribution function and the empirical cumulative distribution function. Indeed, as far as I know, almost all the tests currently available in R related to this issue (ks.test in package stats, ad.test in package ADGofTest, and ad.test, ad2.test, ks.test, v.test and w2.test in package truncgof) use one of these two distances on cumulative distribution functions. This paper (i) proposes dgeometric.test, a new implementation of the test that measures the discrepancy between a s…
Weighted samples, kernel density estimators and convergence
2003
This note extends the standard kernel density estimator to the case of weighted samples in several ways. In the first place I consider the obvious extension by substituting the simple sum in the definition of the estimator by a weighted sum, but I also consider other alternatives of introducing weights, based on adaptive kernel density estimators, and consider the weights as indicators of the informational content of the observations and in this sense as signals of the local density of the data. All these ideas are shown using the Penn World Table in the context of the macroeconomic convergence issue.
Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model
2020
International audience; We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain onRd. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidths are selected by a method inspired by the works of Goldenshluger and Lepski [(2011), 'Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality',The Annals of Statistics3: 1608-1632). Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty. Finally, we investigate the performance of the…
Gamma Kernel Intensity Estimation in Temporal Point Processes
2011
In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.
A semiparametric approach to estimate reference curves for biophysical properties of the skin
2006
Reference curves which take one covariable into account such as the age, are often required in medicine, but simple systematic and efficient statistical methods for constructing them are lacking. Classical methods are based on parametric fitting (polynomial curves). In this chapter, we describe a new methodology for the estimation of reference curves for data sets, based on nonparametric estimation of conditional quantiles. The derived method should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale. To avoid the curse of dimensionality when the covariate is multidimensional, a new semiparametric approach is proposed. Th…
Applications of Kernel Methods
2009
In this chapter, we give a survey of applications of the kernel methods introduced in the previous chapter. We focus on different application domains that are particularly active in both direct application of well-known kernel methods, and in new algorithmic developments suited to a particular problem. In particular, we consider the following application fields: biomedical engineering (comprising both biological signal processing and bioinformatics), communications, signal, speech and image processing.