Related papers: Finite-Sample Analysis of Fixed-k Nearest Neighbor…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…
We provide sufficient density condition for a set of nonuniform samples to give rise to a set of sampling for multivariate bandlimited functions when the measurements consist of pointwise evaluations of a function and its first $k$…
Recent works have demonstrated that the convergence rate of a nonparametric density estimator can be greatly improved by using a low-rank estimator when the target density is a convex combination of separable probability densities with…
The k-nearest-neighbour procedure is a well-known deterministic method used in supervised classification. This paper proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
Shape constrained densities are encountered in many nonparametric estimation problems. The classes of monotone or convex (and monotone) densities can be viewed as special cases of the classes of k-monotone densities. A density g is said to…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For…
We study the problem of adaptive variable selection in a Gaussian white noise model of intensity $\varepsilon$ under certain sparsity and regularity conditions on an unknown regression function $f$. The $d$-variate regression function $f$…
We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
In this paper, we study the local constant and the local linear estimators of the conditional density function with right-censored data which exhibit some type of dependence. It is assumed that the observations form a stationary…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density…
We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…