Related papers: K$^2$IE: Kernel Method-based Kernel Intensity Esti…
In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…
We introduce a hull operator on Poisson point processes, the easiest example being the convex hull of the support of a point process in Euclidean space. Assuming that the intensity measure of the process is known on the set generated by the…
We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…
We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…
We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
We propose causal effect estimators based on empirical Fr\'{e}chet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
We introduce two types of estimators of the finite-dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and multi-step MLE. It is shown that the estimators…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…
The kinetic isotope effect (KIE) is essential in various chemical applications from reaction mechanism studies to tritium removal from water. Traditional KIE evaluation relies on experimental measurements or computational approaches like…
The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…
Imbalanced response variable distribution is a common occurrence in data science. In fields such as fraud detection, medical diagnostics, system intrusion detection and many others where abnormal behavior is rarely observed the data under…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
Recently, a method called the Mutual Information Neural Estimator (MINE) that uses neural networks has been proposed to estimate mutual information and more generally the Kullback-Leibler (KL) divergence between two distributions. The…