Related papers: Using Kernel-Based Statistical Distance to Study t…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
In the first part of the paper a generalized theoretical approach towards beam coupling impedances and stretched-wire measurements is introduced. Applied to a circular symmetric setup, this approach allows to estimate the systematic…
This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…
Measuring the quasar distance through joint analysis of spectroastrometry (SA) and reverberation mapping (RM) observations is a new method for driving the development of cosmology. In this paper, we carry out detailed simulation and…
High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…
Acceleration processes that occur in astrophysical plasmas produce cosmic rays that are observed on Earth. To study particle acceleration, fully-kinetic particle-in-cell (PIC) simulations are often used as they can unveil the microphysics…
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
A geometrical method is used for the analysis of stochastic processes in plasma turbulence. Distances between thermodynamic states can be computed according the thermodynamic length methodology which allows the use of a Riemannian metric on…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
Control applications are increasingly sampled non-equidistantly in time, including in motion control, networked control, resource-aware control, and event-triggered control. Some of these applications use measurement devices that sample…