Related papers: Kernel Density Estimation under $C^{1,1}$ Regulari…
Empirical fixation densities, spatial distributions estimated from human eye-tracking data, are foundational to saliency benchmarking. They directly shape benchmark conclusions, leaderboard rankings, failure case analyses, and scientific…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
We show direct and conceptually simple reductions between the classical learning with errors (LWE) problem and its continuous analog, CLWE (Bruna, Regev, Song and Tang, STOC 2021). This allows us to bring to bear the powerful machinery of…
This paper introduces a novel density estimator supported on $d$-dimensional half-spaces. It stands out as the first asymmetric kernel density estimator for half-spaces in the literature. Using the multivariate inverse Gaussian (MIG)…
Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, this paper establishes Gaussian approximation results for high-dimensional fixed-order $U$-statistics whose kernels depend on the sample…
Accurate parameter estimation from cosmic microwave background data requires reliable likelihood modeling, particularly at large angular scales where angular power spectrum estimators exhibit non-Gaussian statistics. We present a novel…
We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we…
In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor…
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…
Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…
In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…
Approximate query processing (AQP) is an interesting alternative for exact query processing. It is a tool for dealing with the huge data volumes where response time is more important than perfect accuracy (this is typically the case during…
We theoretically investigate the many-body dynamics of a tight-binding chain with dephasing noise on the infinite interval. We obtain the exact solution of an average particle-density profile for the domain wall and the alternating initial…
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive…
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…
Aims: We examine the recoverability and completeness limits of the dense core mass functions (CMFs) derived for a molecular cloud using extinction data and a core identification scheme based on two-dimensional thresholding. Methods: We…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error…
We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…