Related papers: Spanning Trees and Redistricting: New Methods for …
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…
Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…
Besides serving as prediction models, classification trees are useful for finding important predictor variables and identifying interesting subgroups in the data. These functions can be compromised by weak split selection algorithms that…
A core step of every algorithm for learning regression trees is the selection of the best splitting variable from the available covariates and the corresponding split point. Early tree algorithms (e.g., AID, CART) employed greedy search…
We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is…
Recent advancements in pre-trained language models (PLMs) have demonstrated that these models possess some degree of syntactic awareness. To leverage this knowledge, we propose a novel chart-based method for extracting parse trees from…
Redistricting practitioners must balance many competing constraints and criteria when drawing district boundaries. To aid in this process, researchers have developed many methods for optimizing districting plans according to one or more…
We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
A new nonparametric approach, based on a decision tree algorithm, is proposed to calculate the overlap between two probability distributions. The devised framework is described analytically and numerically. The convergence of the estimated…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance).…
The space of connected graph partitions underlies statistical models used as evidence in court cases and reform efforts that analyze political districting plans. In response to the demands of redistricting applications, researchers have…
Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of…
Gerrymandering is a long-standing issue within the U.S. political system, and it has received scrutiny recently by the U.S. Supreme Court. In this note, we prove that deciding whether there exists a fair redistricting among legal maps is…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…