Related papers: Precedence-Constrained Decision Trees and Covering…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
Large-scale subset selection asks for a small useful set of examples, features, sensors, seed users, or context passages from an enormous ground set. Submodular maximization is a canonical model for such diminishing-returns problems, but…
We give the first algorithm that maintains an approximate decision tree over an arbitrary sequence of insertions and deletions of labeled examples, with strong guarantees on the worst-case running time per update request. For instance, we…
It is well-known that an algorithm exists which approximates the NP-complete problem of Set Cover within a factor of ln(n), and it was recently proven that this approximation ratio is optimal unless P = NP. This optimality result is the…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART,…
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…
A plethora of problems in AI, engineering and the sciences are naturally formalized as inference in discrete probabilistic models. Exact inference is often prohibitively expensive, as it may require evaluating the (unnormalized) target…
Model selection consists in comparing several candidate models according to a metric to be optimized. The process often involves a grid search, or such, and cross-validation, which can be time consuming, as well as not providing much…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
This paper studies the important problem of finding all $k$-nearest neighbors to points of a query set $Q$ in another reference set $R$ within any metric space. Our previous work defined compressed cover trees and corrected the key…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…
Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in…
Structural properties of optimal preemptive schedules have been studied in a number of recent papers with a primary focus on two structural parameters: the minimum number of preemptions necessary, and a tight lower bound on `shifts', i.e.,…