Variable Kernel Density Estimation

Terrell, George R.; Scott, David W.

doi:10.1214/aos/1176348768

Cited by 685 publications

(439 citation statements)

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“…The quantities p W (w exp r ; x, δ X ) are estimated using the independent realizations of W calculated with the stochastic computational model (using the Monte Carlo method) and the multivariate Gaussian kernel density estimation method (see for instance [139,140]). …”

Section: Estimation Of the Parameters Of The Prior Stochastic Model Omentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

139

106

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To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

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Section: Estimation Of the Parameters Of The Prior Stochastic Model Omentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

139

106

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“…General non-parametric pdf estimators from samples can be written as a sum of kernels K with (possibly varying) bandwidth h (see [29] for a review):…”

Section: Non-parametric Estimation Of the Similarity Measurementioning

confidence: 99%

“…We use a balloon estimator with a binary kernel and a bandwidth computed in the k-th nearest neighbor (kNN) framework [29]. This is a dual approach to the fixed size kernel methods and was firstly proposed in [30]: the bandwidth adapts to the local sample density by letting the kernel contain exactly k neighbors of x among a given sample set:…”

Section: Non-parametric Estimation Of the Similarity Measurementioning

confidence: 99%

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Sparse Multiscale Patches for Image Processing

Piro

Anthoine

Debreuve

et al. 2009

Emerging Trends in Visual Computing

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Abstract. This paper presents a framework to define an objective measure of the similarity (or dissimilarity) between two images for image processing. The problem is twofold: 1) define a set of features that capture the information contained in the image relevant for the given task and 2) define a similarity measure in this feature space. In this paper, we propose a feature space as well as a statistical measure on this space. Our feature space is based on a global descriptor of the image in a multiscale transformed domain. After decomposition into a Laplacian pyramid, the coefficients are arranged in intrascale/interscale/interchannel patches which reflect the dependencies of neighboring coefficients in presence of specific structures or textures. At each scale, the probability density function (pdf) of these patches is used as a descriptor of the relevant information. Because of the sparsity of the multiscale transform, the most significant patches, called Sparse Multiscale Patches (SMP), describe efficiently these pdfs. We propose a statistical measure (the Kullback-Leibler divergence) based on the comparison of these probability density functions. Interestingly, this measure is estimated via the nonparametric, k-th nearest neighbor framework without explicitly building the pdfs. This framework is applied to a query-by-example image retrieval method. Experiments on two publicly available databases showed the potential of our SMP approach for this task. In particular, it performed comparably to a SIFT -based retrieval method and two versions of a fuzzy segmentation-based method (the UFM and CLUE methods), and it exhibited some robustness to different geometric and radiometric deformations of the images.

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“…Considerable research has been carried out on the question of how one should select K in order to optimize the properties of f h (see e.g., [5,8,10,16], and [4]). In the case of d ≥ 1, the most often choice is a density function, symmetric about zero, and such that…”

Section: Introductionmentioning

confidence: 99%