Related papers: Density estimates of 1-avoiding sets via higher or…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…
Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…
An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols.…
The ``extended Overhauser model'' [Overhauser, Can. J. Phys. 1995, 73, 683] for the calculation of the spherically and system-averaged pair density (APD) has been recently combined with the Kohn-Sham equations to yield realistic APD and…
We study density estimation in Kullback-Leibler divergence: given an i.i.d. sample from an unknown density $p^\star$, the goal is to construct an estimator $\widehat{p}$ such that $\mathrm{KL}(p^\star,\widehat{p})$ is small with high…
We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric…
We focus on training machine learning regression models in scenarios where the availability of labeled training data is limited due to computational constraints or high labeling costs. Thus, selecting suitable training sets from unlabeled…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new…
While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to…
Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
We consider density estimation for Besov spaces when each sample is quantized to only a limited number of bits. We provide a noninteractive adaptive estimator that exploits the sparsity of wavelet bases, along with a simulate-and-infer…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due…
This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…