Related papers: Nonparametric, data-based kernel interpolation for…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random…
A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Finding a suitable density function is essential for density-based clustering algorithms such as DBSCAN and DPC. A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in these…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…
Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input.…
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…
Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base…
The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general…
In High Energy Physics, detailed and time-consuming simulations are used for particle interactions with detectors. To bypass these simulations with a generative model, the generation of large point clouds in a short time is required, while…
A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…
While particle trajectories encode information on their governing potentials, potentials can be challenging to robustly extract from trajectories. Measurement errors may corrupt a particle's position, and sparse sampling of the potential…