Related papers: Universal Tree Source Coding Using Grammar-Based C…
Zero-error single-channel source coding has been studied extensively over the past decades. Its natural multi-channel generalization is however not well investigated. While the special case with multiple symmetric-alphabet channels was…
A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources.…
We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
We describe a new Pr\"ufer code which works also for infinite trees.
Tree kernels have been proposed to be used in many areas as the automatic learning of natural language applications. In this paper, we propose a new linear time algorithm based on the concept of weighted tree automata for SubTree kernel…
Statistical language models are powerful tools which have been used for many tasks within natural language processing. Recently, they have been used for other sequential data such as source code.(Ray et al., 2015) showed that it is possible…
This article studies the limit of binary search trees drawn from Mallows permutations under various topologies. The main result, pertaining to the standard local topology for graphs, requires the introduction of a generalization of binary…
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, "end of minimal chain" and "parent of maximum leaf" a true Tree Calculus is being developed to solve a partial difference equation system and…
The Poisson-sampling technique eliminates dependencies among symbol appearances in a random sequence. It has been used to simplify the analysis and strengthen the performance guarantees of randomized algorithms. Applying this method to…
The order of letters is not always relevant in a communication task. This paper discusses the implications of order irrelevance on source coding, presenting results in several major branches of source coding theory: lossless coding,…
Tree-controlled grammars are context-free grammars where the derivation process is controlled in such a way that every word on a level of the derivation tree must belong to a certain control language. We investigate the generative capacity…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
We reveal an algorithm for determining the complete prefix code irreducibility (CPC-irreducibility) of dyadic trees labeled by a finite alphabet. By introducing an extended directed graph representation of tree shift of finite type (TSFT),…
We introduce a tree-based formulation for the minimum-cost multi-commodity flow problem that addresses large-scale instances. The method decomposes the source-based model by representing flows as convex combinations of trees rooted at…
Probabilistic distributions over spanning trees in directed graphs are a fundamental model of dependency structure in natural language processing, syntactic dependency trees. In NLP, dependency trees often have an additional root…
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable…