Related papers: An Efficient Scheme for the Generation of Ordered …
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
A method is presented for constructing a Tunstall code that is linear time in the number of output items. This is an improvement on the state of the art for non-Bernoulli sources, including Markov sources, which require a (suboptimal)…
We propose a novel technique, termed compact shape trees, for computing correspondences of single-boundary 2-D shapes in O(n2) time. Together with zero or more features defined at each of n sample points on the shape's boundary, the compact…
The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
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…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
We develop algorithms, implemented in Maple, that study the number of vertices with a particular number of children in a random ordered tree where all vertices must have a number of children in some finite set. By calculating the mixed…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
An elimination tree for a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root $x$ and recursing on the connected components of $G-x$ to produce the subtrees of $x$. Elimination trees appear in many guises…
Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…