Related papers: On the computational complexity of the probabilist…
Modern key-value stores rely heavily on Log-Structured Merge (LSM) trees for write optimization, but this design introduces significant read amplification. Auxiliary structures like Bloom filters help, but impose memory costs that scale…
We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider…
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.…
Machine learning techniques are gaining prevalence in the production of a wide range of classifiers for complex real-world applications with nonuniform testing and misclassification costs. The increasing complexity of these applications…
The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $\pi$ from vertices of a graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|\pi(u) - \pi(v)|$. In that setting, vertices are often assumed to lie on a…
Multilevel programming is the standard framework for modeling hierarchical decision-making. In this paper, we characterize the computational complexity of deciding the existence of feasible and optimal solutions, as well as computing the…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic…
Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such…
Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this…
We introduce probabilistic language tries (PLTs), a unified representation that makes explicit the prefix structure implicitly defined by any generative model over sequences. By assigning to each outgoing edge the conditional probability of…
The problem considered is the following. Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified…
This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it…
Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…
Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the…
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…
In spite of their superior performance, neural probabilistic language models (NPLMs) remain far less widely used than n-gram models due to their notoriously long training times, which are measured in weeks even for moderately-sized…
The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…
We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from…
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…