Related papers: Fully-Dynamic Decision Trees
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…
We consider the classic facility location problem in fully dynamic data streams, where elements can be both inserted and deleted. In this problem, one is interested in maintaining a stable and high quality solution throughout the data…
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)…
In this paper, we study learning and testing decision tree of size and depth that are significantly smaller than the number of attributes $n$. Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms with…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
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'…
There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…
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…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
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…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
We present a deterministic fully-dynamic data structure for maintaining information about the bridges in a graph. We support updates in $\tilde{O}((\log n)^2)$ amortized time, and can find a bridge in the component of any given vertex, or a…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
In this paper we describe a dynamic data structure that answers one-dimensional stabbing-max queries in optimal $O(\log n/\log\log n)$ time. Our data structure uses linear space and supports insertions and deletions in $O(\log n)$ and…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
We introduce an exact distributed algorithm to train Random Forest models as well as other decision forest models without relying on approximating best split search. We explain the proposed algorithm and compare it to related approaches for…
Maintaining maximal independent set in dynamic graph is a fundamental open problem in graph theory and the first sublinear time deterministic algorithm was came up by Assadi, Onak, Schieber and Solomon(STOC'18), which achieves $O(m^{3/4})$…