Related papers: Adaptive density estimation for directional data u…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and…
Directional wavelet dictionaries are hierarchical representations which efficiently capture and segment information across scale, location and orientation. Such representations demonstrate a particular affinity to physical signals, which…
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…
Compared with the traditional spherical harmonics, the spherical needlets are a new generation of spherical wavelets that possess several attractive properties. Their double localization in both spatial and frequency domains empowers them…
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we…
New bandwidth selectors for kernel density estimation with directional data are presented in this work. These selectors are based on asymptotic and exact error expressions for the kernel density estimator combined with mixtures of von Mises…
The problem of known signal detection in Additive White Gaussian Noise is considered. In this paper a new detection algorithm based on Discrete Wavelet Transform pre-processing and threshold comparison is introduced. Current approaches…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
Given an i.i.d. sample from a distribution $F$ on $\mathbb{R}$ with uniformly continuous density $p_0$, purely data-driven estimators are constructed that efficiently estimate $F$ in sup-norm loss and simultaneously estimate $p_0$ at the…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data.…
In this paper, we propose a new method for the construction of multi-dimensional, wavelet-like families of affine frames, commonly referred to as framelets, with specific directional characteristics, small and compact support in space,…
Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable…
This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…