Related papers: Time and space complexity of deterministic and non…
The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2)…
Decision trees partition the feature space using hard binary thresholds, assigning identical confidence to instances far from a decision boundary and to those directly on it. We introduce ternary decision trees, which augment each split…
Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. \citet{zhou2019deep} further propose a deep forest algorithm with multi-layer forests,…
Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…
Different sources of information might tell different stories about the evolutionary history of a given set of species. This leads to (rooted) phylogenetic trees that "disagree" on triples of species, which we call "conflict triples". An…
We study the problem of set discovery where given a few example tuples of a desired set, we want to find the set in a collection of sets. A challenge is that the example tuples may not uniquely identify a set, and a large number of…
Problem definition. In retailing, discrete choice models (DCMs) are commonly used to capture the choice behavior of customers when offered an assortment of products. When estimating DCMs using transaction data, flexible models (such as…
Decision trees are one of the most fundamental computational models for computing Boolean functions $f : \{0, 1\}^n \mapsto \{0, 1\}$. It is well-known that the depth and size of decision trees are closely related to time and number of…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research…
We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…
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…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
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…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…
In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a…
The adoption of the distributed paradigm has allowed applications to increase their scalability, robustness and fault tolerance, but it has also complicated their structure, leading to an exponential growth of the applications'…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…