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Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
In epidemiological studies, it is common to analyze disease risk by categorizing continuous variables, such as calorie and nutrient intake, for interpretability. When the original continuous variable is contaminated with measurement errors,…
Wearable devices permit the continuous monitoring of biological processes, such as blood glucose metabolism, and behavior, such as sleep quality and physical activity. The continuous monitoring often occurs in epochs of 60 seconds over…
Change detection in remote sensing imagery plays a vital role in various engineering applications, such as natural disaster monitoring, urban expansion tracking, and infrastructure management. Despite the remarkable progress of deep…
Measuring stress fields in fluids and soft materials is crucial in various fields such as mechanical engineering, medicine, and bioengineering. However, conventional methods that calculate stress fields from velocity fields struggle to…
In standard hospital blood tests, the traditional process requires doctors to manually isolate leukocytes from microscopic images of patients' blood using microscopes. These isolated leukocytes are then categorized via automatic leukocyte…
A self-consistent 1-D model was developed to study the effect of the electron energy distribution function (EEDF) on power deposition and plasma density profiles in a planar inductively coupled plasma (ICP) in the non-local regime (pressure…
In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…
Nonlinear stochastic differential equation models with unobservable variables are now widely used in the analysis of PK/PD data. The unobservable variables are often estimated with extended Kalman filter (EKF), and the unknown…
This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…
Public health researchers often estimate health effects of exposures (e.g., pollution, diet, lifestyle) that cannot be directly measured for study subjects. A common strategy in environmental epidemiology is to use a first-stage (exposure)…
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phenomena are prevalent in fluid dynamics and materials science,…
Delocalization errors, such as charge-transfer and some self-interaction errors, plague computationally-efficient and otherwise-accurate density functional approximations (DFAs). Evaluating a semi-local DFA non-self-consistently on the…
The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability…
In neutral meson mixing, a certain class of convolution integrals is required whose solution involves the error function $\mathrm{erf}(z)$ of a complex argument $z$. We show the the general shape of the analytic solution of these integrals,…
No unmeasured confounding is often assumed in estimating treatment effects in observational data when using approaches such as propensity scores and inverse probability weighting. However, in many such studies due to the limitation of the…
HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations. Density-corrected DFT (DC-DFT) is a general theoretical framework for identifying…