Related papers: Enumeration of Irredundant Forests
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…
Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing…
When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…
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…
RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
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…
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…
A tree ${\mathbb T} =\langle T\leq \rangle$ is reversible iff there is no order $\preccurlyeq \;\varsubsetneq \;\leq $ such that ${\mathbb T} \cong \langle T ,\preccurlyeq\rangle$. Using a characterization of reversibility via back and…
Reading comprehension models are based on recurrent neural networks that sequentially process the document tokens. As interest turns to answering more complex questions over longer documents, sequential reading of large portions of text…
We present a study of several generic tree search techniques applied to the Sequential Ordering Problem. This study enables us to propose a simple and competitive tree search algorithm. It consists of an iterative Beam Search algorithm that…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
Recent studies have shown that Dense Retrieval (DR) techniques can significantly improve the performance of first-stage retrieval in IR systems. Despite its empirical effectiveness, the application of DR is still limited. In contrast to…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…