Related papers: Engineering Top-Down Weight-Balanced Trees

Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \le k \le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, "Can $T$ be…

Hex-trees are identified as a particular instance of weighted unary-binary trees. The Horton-Strahler numbers of these objects are revisited, and, thanks to a substitution that is not immediately intuitive, explicit results are possible.…

Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…

The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring…

Markov chains based on spanning trees have been hugely influential in algorithms for assessing fairness in political redistricting. The input graph represents the geographic building blocks of a jurisdiction. The goal is to output a large…

Finite-horizon lookahead policies are abundantly used in Reinforcement Learning and demonstrate impressive empirical success. Usually, the lookahead policies are implemented with specific planning methods such as Monte Carlo Tree Search…

We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall…

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…

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

Efficient Neural Architecture Search methods based on weight sharing have shown good promise in democratizing Neural Architecture Search for computer vision models. There is, however, an ongoing debate whether these efficient methods are…

A new approach called NAF (the Neural Attention Forest) for solving regression and classification tasks under tabular training data is proposed. The main idea behind the proposed NAF model is to introduce the attention mechanism into the…

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…

Binary neural networks (BNNs) have received ever-increasing popularity for their great capability of reducing storage burden as well as quickening inference time. However, there is a severe performance drop compared with real-valued…

The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…

We present an unusual algorithm involving classification trees where two trees are grown in opposite directions so that they are matched at their leaves. This approach finds application in a new data mining task we formulate, called…

Weighting strategy prevails in machine learning. For example, a common approach in robust machine learning is to exert lower weights on samples which are likely to be noisy or quite hard. This study reveals another undiscovered strategy,…

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…

Because biological processes can make different loci have different evolutionary histories, species tree estimation requires multiple loci from across the genome. While many processes can result in discord between gene trees and species…

In observational causal inference, in order to emulate a randomized experiment, weights are used to render treatments independent of observed covariates. This property is known as balance; in its absence, estimated causal effects may be…

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…