Search results for "Kernel density estimation"
showing 10 items of 34 documents
Learning non-linear time-scales with kernel -filters
2009
A family of kernel methods, based on the @c-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) @c-filter [G. Camps-Valls, M. Martinez-Ramon, J.L. Rojo-Alvarez, E. Soria-Olivas, Robust @c-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493-499.], but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel @c-filters. The improved performance in several application examples suggest…
Proportional Small Sample Bias in Pricing Kernel Estimations
2014
Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In a first step, we analyze theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader of potential computational issues coupled with statistical techniques. In a second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kern…
Modelling and prediction of perceptual segmentation
2017
While listening to music, we somehow make sense of a multiplicity of auditory events; for example, in popular music we are often able to recognize whether the current section is a verse or a chorus, and to identify the boundaries between these segments. This organization occurs at multiple levels, since we can discern motifs, phrases, sections and other groupings. In this work, we understand segment boundaries as instants of significant change. Several studies on music perception and cognition have strived to understand what types of changes are associated with perceptual structure. However, effects of musical training, possible differences between real-time and non real-time segmentation, and…
Spectral density estimation for stationary stable random fields
1995
International audience
Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation
2017
International audience; The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , from a relatively small sample. We then show how this technique can be applied and implemented for a class of problems including the God-dard problem and the trajectory optimization of an Ariane 5-like launcher.
Computerized delimitation of odorant areas in gas-chromatography-olfactometry by kernel density estimation: Data processing on French white wines
2017
International audience; GC-O using the detection frequency method gives a list of odor events (OEs) where each OE is described by a linear retention index (LRI) and by the aromatic descriptor given by a human assessor. The aim of the experimenter is to gather OEs in a total olfactogram on which he tries to delimit odorant areas (OAs), then to compute each detection frequency. This paper proposes a computerized mathematical method based on kernel density estimation that makes up the total olfactogram as continuous and differentiable function from the OEs LRI only. The corresponding curve looks like a chromatogram, the peaks of which are potential OAs. The limits of an OA are the LRI of the t…
Observations of land use transformations during the Neolithic using exploratory spatial data analysis: contributions and limitations
2010
International audience; The settlement pattern analysis in archaeology implies some methodological questions. In this paper, we question some issues about the use of geostatistical methods for the observation of land use transformations during the Neolithic. We have developed two examples in Burgundy (France): the first one on a regional scale and the second one on a micro-regional scale. Using different ESDA approaches (Ripley’K function, Nearest Neighbour Distance, Kernel Density Estimation), we would like to underline what the methodological and archaeological contributions and their limits are. Both experiences point out that the results obtained depend not only on the analytical scale,…
Models and tools for territorial dynamic studies (chapter 1)
2012
As part of the ArchaeDyn project, a workgroup was formed to coordinate the development, implementation and application of methods and tools for spatial analysis. The workgroup's activities were directed at various problems. The first was to construct a grid common to all the workgroups and to homogenize the study areas used by the different workgroups in their databases. The 'confidence maps' method was suggested for assessing the quality and quantity of information inventoried in the databases. Confidence maps are produced from representation and reliability maps by simple map algebra and they can be considered as 'masks' for interpreting spatial analysis results. Finally, the research tea…
Spectral clustering with the probabilistic cluster kernel
2015
Abstract This letter introduces a probabilistic cluster kernel for data clustering. The proposed kernel is computed with the composition of dot products between the posterior probabilities obtained via GMM clustering. The kernel is directly learned from the data, is parameter-free, and captures the data manifold structure at different scales. The projections in the kernel space induced by this kernel are useful for general feature extraction purposes and are here exploited in spectral clustering with the canonical k-means. The kernel structure, informative content and optimality are studied. Analysis and performance are illustrated in several real datasets.
Semisupervised kernel orthonormalized partial least squares
2012
This paper presents a semisupervised kernel orthonormalized partial least squares (SS-KOPLS) algorithm for non-linear feature extraction. The proposed method finds projections that minimize the least squares regression error in Hilbert spaces and incorporates the wealth of unlabeled information to deal with small size labeled datasets. The method relies on combining a standard RBF kernel using labeled information, and a generative kernel learned by clustering all available data. The positive definiteness of the kernels is proven, and the structure and information content of the derived kernels is studied. The effectiveness of the proposed method is successfully illustrated in standard UCI d…