Related papers: H\"arpfer's Extended Indispensability Algorithm in…

Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…

In this paper we give a metric construction of a tree which correctly identifies connected components of superlevel sets of $\mathbb{R}$-valued continuous functions $f$ on $X$ and show that it is possible to retrieve the $H_0$-persistent…

Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems and has been widely reported in a variety of natural language processing applications. However, the emergence of natural language…

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…

This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…

In this paper, we consider classes of decision tables with many-valued decisions closed relative to removal of attributes (columns) and changing sets of decisions assigned to rows. For tables from an arbitrary closed class, we study a…

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates…

We reduce phrase-representation parsing to dependency parsing. Our reduction is grounded on a new intermediate representation, "head-ordered dependency trees", shown to be isomorphic to constituent trees. By encoding order information in…

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…

In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

Sentence embedding is an effective feature representation for most deep learning-based NLP tasks. One prevailing line of methods is using recursive latent tree-structured networks to embed sentences with task-specific structures. However,…

Most research into similarity search in metric spaces relies upon the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common…

We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) $x_1...x_n$ is the sum of terms over intervals $[i,j]$ where each term is non-zero only if the…

Let n be an integer greater than 1. A tree T is an n-ary tree provided that every node in T has at most n immediate successors. A forcing notion P has the n-localization property if every function from omega to omega in an extension via P…

Dealing with datasets of very high dimension is a major challenge in machine learning. In this paper, we consider the problem of feature selection in applications where the memory is not large enough to contain all features. In this…

In this article we propose a boosting algorithm for regression with functional explanatory variables and scalar responses. The algorithm uses decision trees constructed with multiple projections as the "base-learners", which we call…

We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant…

We study a spatial model of random permutations on trees with a time parameter $T>0$, a special case of which is the random stirring process. The model on trees was first analysed by Bj\"ornberg and Ueltschi[BU16], who established the…

We apply symbolic method to deduce functional equation which generating function of counting sequence of dependency trees must satisfy. Then we use Lagrange inversion theorem to obtain concrete expression of the counting sequence. We apply…