Related papers: Hazard-free Decision Trees
We study a natural complexity measure of Boolean functions known as the rational degree. Denoted $\textrm{rdeg}(f)$, it is the minimal degree of a rational function that is equal to $f$ on the Boolean hypercube. For total functions $f$, it…
Decision trees have long been recognized as models of choice in sensitive applications where interpretability is of paramount importance. In this paper, we examine the computational ability of Boolean decision trees in deriving, minimizing,…
Decision tree learning has long been a central topic in theoretical computer science, driven by its practical importance. A fundamental and widely used method for decision tree construction is the top-down greedy heuristic, which…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
Outcomes of data-driven AI models cannot be assumed to be always correct. To estimate the uncertainty in these outcomes, the uncertainty wrapper framework has been proposed, which considers uncertainties related to model fit, input quality,…
This paper studies the hazard-free formula complexity of Boolean functions. Our first result shows that unate functions are the only Boolean functions for which the monotone formula complexity of the hazard-derivative equals the hazard-free…
We show tight upper and lower bounds for switching lemmas obtained by the action of random $p$-restrictions on boolean functions that can be expressed as decision trees in which every vertex is at a distance of at most $t$ from some leaf,…
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,…
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…
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…
The problem of constructing hazard-free Boolean circuits (those avoiding electronic glitches) dates back to the 1940s and is an important problem in circuit design and even in cybersecurity. We show that a DeMorgan circuit is hazard-free if…
We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting models are typically equivalent to networks whose nonzero weights are also $\pm 1$. The method…
Decision trees are a powerful prediction model with many applications in statistics, data mining, and machine learning. In some settings, the model and the data to be classified may contain sensitive information belonging to different…
Several real-world classification problems are example-dependent cost-sensitive in nature, where the costs due to misclassification vary between examples and not only within classes. However, standard classification methods do not take…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
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…
We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity…
The problem of inferring an inductive invariant for verifying program safety can be formulated in terms of binary classification. This is a standard problem in machine learning: given a sample of good and bad points, one is asked to find a…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
Decision trees are an extremely popular machine learning technique. Unfortunately, overfitting in decision trees still remains an open issue that sometimes prevents achieving good performance. In this work, we present a novel approach for…