Related papers: Abstract Huffman Coding and PIFO Tree Embeddings
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…
We use reinforcement learning to learn tree-structured neural networks for computing representations of natural language sentences. In contrast with prior work on tree-structured models in which the trees are either provided as input or…
We extend the results we obtained in an earlier work. The cocommutative case of rooted ladder trees is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the…
In this paper, we consider the problem of distributed inference in tree based networks. In the framework considered in this paper, distributed nodes make a 1-bit local decision regarding a phenomenon before sending it to the fusion center…
In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most…
We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a…
We present a new algorithm for dynamic prefix-free coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We…
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…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
Building trees to represent or to fit distances is a critical component of phylogenetic analysis, metric embeddings, approximation algorithms, geometric graph neural nets, and the analysis of hierarchical data. Much of the previous…
Adaptive (variable-length) codes associate variable-length codewords to symbols being encoded depending on the previous symbols in the input data string. This class of codes has been presented in [Dragos Trinca, cs.DS/0505007] as a new…
In this work we introduce a new linear time compression algorithm, called "Re-pair for Trees", which compresses ranked ordered trees using linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free…
Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such…
We introduce a novel incremental decision tree learning algorithm, Hoeffding Anytime Tree, that is statistically more efficient than the current state-of-the-art, Hoeffding Tree. We demonstrate that an implementation of Hoeffding Anytime…
We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…
Bojanczyk and Pilipczuk showed in their celebrated article "Definability equals recognizability for graphs of bounded treewidth" (LICS 2016) that monadic second-order logic can define tree-decompositions in graphs of bounded treewidth. This…
We study a family of tree-type diagrams that arise in studies of the cumulant expansion in discrete Erd\H os-R\'enyi random matrix models. Using a version of the Pr\" ufer code, we obtain an explicit expression for the number of tree-type…
Vine copulas are pair-copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine copula is the selection of a suitable tree structure. For this the prevalent…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…