Related papers: Density estimation using cellular binary trees and…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
The ratio of two densities provides a direct characterization of their differences. We consider the two-sample comparison problem by estimating this ratio given i.i.d. observations from two distributions. To this end, we propose additive…
Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in…
Binary density ratio estimation (DRE), the problem of estimating the ratio $p_1/p_2$ given their empirical samples, provides the foundation for many state-of-the-art machine learning algorithms such as contrastive representation learning…
We propose a simple recursive data-based partitioning scheme which produces piecewise-constant or piecewise-linear density estimates on intervals, and show how this scheme can determine the optimal $L_1$ minimax rate for some discrete…
This paper presents a brand new nonparametric density estimation strategy named the best-scored random forest density estimation whose effectiveness is supported by both solid theoretical analysis and significant experimental performance.…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
Density Estimation Trees (DETs) are decision trees trained on a multivariate dataset to estimate its probability density function. While not competitive with kernel techniques in terms of accuracy, they are incredibly fast, embarrassingly…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
It is widely believed that the prediction accuracy of decision tree models is invariant under any strictly monotone transformation of the individual predictor variables. However, this statement may be false when predicting new observations…
A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the…
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…
We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional P\'olya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.
We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…