Related papers: High-Dimensional Non-Parametric Density Estimation…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…
In this paper, we show that the approximation of high-dimensional functions, which are effectively low-dimensional, does not suffer from the curse of dimensionality. This is shown first in a general reproducing kernel Hilbert space set-up…
Hyperbolic space is increasingly used for hierarchical, tree-like, and network-structured data, but likelihood-based density modeling on hyperbolic space remains relatively limited. This paper develops finite mixture modeling with isotropic…
Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…
Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good…
High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…
Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
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…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well…
Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic…
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…