Related papers: Reconstructing decision trees
Learning algorithms produce software models for realising critical classification tasks. Decision trees models are simpler than other models such as neural network and they are used in various critical domains such as the medical and the…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
A \emph{tree cut-sparsifier} $T$ of quality $\alpha$ of a graph $G$ is a single tree that preserves the capacities of all cuts in the graph up to a factor of $\alpha$. A \emph{tree flow-sparsifier} $T$ of quality $\alpha$ guarantees that…
We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to…
We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq 3$ and tree-minors in bounded-degree graphs. The complexity of these algorithms is related to the distance of the graph from being…
We show that top-down decision tree learning heuristics are amenable to highly efficient learnability estimation: for monotone target functions, the error of the decision tree hypothesis constructed by these heuristics can be estimated with…
Scaling inference compute enhances reasoning in large language models (LLMs), with long chains-of-thought (CoTs) enabling strategies like backtracking and error correction. Reinforcement learning (RL) has emerged as a crucial method for…
We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings. Given a string of length n over an alphabet of size $\sigma\leq n$, our method builds…
Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…
Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…
In this paper we study a polynomial time algorithms that for an input $A\subseteq {B_m}$ outputs a decision tree for $A$ of minimum depth. This problem has many applications that include, to name a few, computer vision, group testing, exact…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…
The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in $T$.…
The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold function (PTF) of degree $d$ and weight $W$ if there is a polynomial $p$ with integer coefficients of degree $d$ and with sum of absolute…