Related papers: A New Quartet Tree Heuristic for Hierarchical Clus…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…

In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…

We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that…

The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…

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…

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…

Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new…

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…

Planning can often be simpli ed by decomposing the task into smaller tasks arranged hierarchically. Charlin et al. [4] recently showed that the hierarchy discovery problem can be framed as a non-convex optimization problem. However, the…

We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…

Randomized experiments have been critical tools of decision making for decades. However, subjects can show significant heterogeneity in response to treatments in many important applications. Therefore it is not enough to simply know which…

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…

We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the…

Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…

We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…