Related papers: Biased Range Trees
Decision trees are simple, yet powerful, classification models used to classify categorical and numerical data, and, despite their simplicity, they are commonly used in operations research and management, as well as in knowledge mining.…
We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a…
Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive…
Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
This paper studies the "explanation problem" for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A whose…
A consensus tree is a phylogenetic tree that captures the similarity between a set of conflicting phylogenetic trees. The problem of computing a consensus tree is a major step in phylogenetic tree reconstruction. It also finds applications…
Tree-based machine learning techniques, such as Decision Trees and Random Forests, are top performers in several domains as they do well with limited training datasets and offer improved interpretability compared to Deep Neural Networks…
When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We show how to use a balanced wavelet tree as a data structure that stores a list of numbers and supports efficient {\em range quantile queries}. A range quantile query takes a rank and the endpoints of a sublist and returns the number with…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…
Tree-based data structures are ubiquitous across applications. Therefore, a multitude of different tree implementations exist. However, while these implementations are diverse, they share a tree structure as the underlying data structure.…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Scaling regression to large datasets is a common problem in many application areas. We propose a two step approach to scaling regression to large datasets. Using a regression tree (CART) to segment the large dataset constitutes the first…
In concurrent data structures, the efficiency of set operations can vary significantly depending on the workload characteristics. Numerous concurrent set implementations are optimized and fine-tuned to excel in scenarios characterized by…
The field of machine learning is subject to an increasing interest in models that are not only accurate but also interpretable and robust, thus allowing their end users to understand and trust AI systems. This paper presents a novel method…
The degree distribution of an ordered tree $T$ with $n$ nodes is $\vec{n} = (n_0,\ldots,n_{n-1})$, where $n_i$ is the number of nodes in $T$ with $i$ children. Let $\mathcal{N}(\vec{n})$ be the number of trees with degree distribution…