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We introduce an optimization-based reconstruction attack capable of completely or near-completely reconstructing a dataset utilized for training a random forest. Notably, our approach relies solely on information readily available in…

Machine Learning · Computer Science 2024-08-16 Julien Ferry , Ricardo Fukasawa , Timothée Pascal , Thibaut Vidal

We show that the union of two or more independent uniform spanning forests (USF) on $\mathbb{Z}^d$ with $d\geq 3$ almost surely forms a connected transient graph. In fact, this also holds when taking the union of a deterministic everywhere…

Probability · Mathematics 2023-11-16 Eleanor Archer , Asaf Nachmias , Matan Shalev , Pengfei Tang

Given a class of (undirected) graphs $\mathcal{C}$, we say that a Feedback Arc Set (FAS for short) $F$ is a $\mathcal{C}$-FAS if the graph induced by the edges of $F$ (forgetting their orientations) belongs to $\mathcal{C}$. We show that…

Combinatorics · Mathematics 2026-01-26 Pierre Aboulker , Guillaume Aubian , Raul Lopes

Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indexes, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial…

Data Structures and Algorithms · Computer Science 2016-12-16 Ferdinando Cicalese , Balázs Keszegh , Bernard Lidický , Dömötör Pálvölgyi , Tomáš Valla

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph $D$ has an upward planar embedding into a point set $S$. We show that any switch tree admits an upward planar…

Data Structures and Algorithms · Computer Science 2015-05-20 Markus Geyer , Michael Kaufmann , Tamara Mchedlidze , Antonios Symvonis

We provide a new approach for proving the indistinguishability of connected components of random one-or-two-ended oriented forests on unimodular random graphs. In particular, this approach leads to a new and simpler proof for the wired…

Probability · Mathematics 2026-05-18 Francois Baccelli , Ali Khezeli

The last decade has shed some light on theoretical properties such as their consistency for regression tasks. In the current paper, we propose a new class of very simple learners based on so-called naive trees. These naive trees partition…

Statistics Theory · Mathematics 2024-12-18 Nico Föge , Markus Pauly , Lena Schmid , Marc Ditzhaus

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…

Physics and Society · Physics 2022-03-14 C. Tyler Diggans , Erik M. Bollt , Daniel ben-Avraham

Uniform spanning trees are a statistical model obtained by taking the set of all spanning trees on a given graph (such as a portion of a cubic lattice in d dimensions), with equal probability for each distinct tree. Some properties of such…

Statistical Mechanics · Physics 2009-11-10 N. Read

In this note we show that pattern matching in permutations is polynomial time reducible to pattern matching in set partitions. In particular, pattern matching in set partitions is NP-Complete.

Combinatorics · Mathematics 2020-09-02 Thomas Grubb

A string-like compact data structure for unlabelled rooted trees is given using 2n bits.

Data Structures and Algorithms · Computer Science 2015-03-20 Julius D'souza

Interpreting three-leaf binary trees or {\em rooted triples} as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to…

Data Structures and Algorithms · Computer Science 2018-07-03 Matthew P. Johnson

This paper outlines a method to determine whether two label-regular directed trees, are isomorphic and when they are almost isomorphic. The approach involves reinterpreting label-regular directed trees as universal covers of rooted graphs.…

Combinatorics · Mathematics 2023-03-13 Roman Gorazd

Random forests on the one hand, and neural networks on the other hand, have met great success in the machine learning community for their predictive performance. Combinations of both have been proposed in the literature, notably leading to…

Machine Learning · Computer Science 2021-10-15 Ludovic Arnould , Claire Boyer , Erwan Scornet , Sorbonne Lpsm

Increasingly, biologists are constructing evolutionary trees on large numbers of overlapping sets of taxa, and then combining them into a `supertree' that classifies all the taxa. In this paper, we ask how much coverage of the total set of…

Populations and Evolution · Quantitative Biology 2009-06-29 Mike Steel , Michael J. Sanderson

This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…

Statistics Theory · Mathematics 2024-02-22 Ricardo Blum , Munir Hiabu , Enno Mammen , Joseph T. Meyer

Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…

Populations and Evolution · Quantitative Biology 2017-02-15 Andreas Gunawan

This paper investigates the connections between two state of the art classifiers: decision forests (DFs, including decision jungles) and convolutional neural networks (CNNs). Decision forests are computationally efficient thanks to their…

Computer Vision and Pattern Recognition · Computer Science 2016-03-04 Yani Ioannou , Duncan Robertson , Darko Zikic , Peter Kontschieder , Jamie Shotton , Matthew Brown , Antonio Criminisi

We address unsupervised discontinuous constituency parsing, where we observe a high variance in the performance of the only previous model in the literature. We propose to build an ensemble of different runs of the existing discontinuous…

Computation and Language · Computer Science 2024-11-07 Behzad Shayegh , Yuqiao Wen , Lili Mou

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

Combinatorics · Mathematics 2017-02-08 Song Guo , Victor J. W. Guo