Related papers: Escaping the curse of dimensionality with a tree-b…

We prove minimax optimal learning rates for kernel ridge regression, resp.~support vector machines based on a data dependent partition of the input space, where the dependence of the dimension of the input space is replaced by the fractal…

This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…

This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models…

The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…

Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…

We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…

Rooted trees with probabilities are convenient to represent a class of random processes with memory. They allow to describe and analyze variable length codes for data compression and distribution matching. In this work, the Leaf-Average…

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…

In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…

Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is…

Pick a sequence of uniform points on the $d$-dimensional sphere. Then, link the $n$th point to its closest one that arrives in the past. This constructs a labelled tree called the nearest neighbour tree on the $d$-dimensional sphere. These…

In this work, we propose a novel dimensionality reduction technique, DiffRed, which first projects the data matrix, A, along first $k_1$ principal components and the residual matrix $A^{*}$ (left after subtracting its $k_1$-rank…

We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

The k-d tree was one of the first spatial data structures proposed for nearest neighbor search. Its efficacy is diminished in high-dimensional spaces, but several variants, with randomization and overlapping cells, have proved to be…

This article is motivated by the objective of providing a new analytically tractable and fully frequentist framework to characterize and implement regression trees while also allowing a multivariate (potentially high dimensional) response.…

Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we…

This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…

A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to…