Related papers: Power of Decision Trees with Monotone Queries

Given a classical query algorithm as a decision tree, when does there exist a quantum query algorithm with a speed-up over the classical one? We provide a general construction based on the structure of the underlying decision tree, and…

Recent papers have used machine learning architecture to fit low-order functional ANOVA models with main effects and second-order interactions. These GAMI (GAM + Interaction) models are directly interpretable as the functional main effects…

In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of…

The minimum number of NOT gates in a Boolean circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that…

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…

We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…

Herein, we investigate the zero-error randomized complexity, which is the least cost against the worst input, of AND-OR tree computation by imposing various restrictions on the algorithm to find the Boolean value of the root of that tree…

We study the power of negation in the Boolean and algebraic settings and show the following results. * We construct a family of polynomials $P_n$ in $n$ variables, all of whose monomials have positive coefficients, such that $P_n$ can be…

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…

We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their…

The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…

We give strengthened provable guarantees on the performance of widely employed and empirically successful {\sl top-down decision tree learning heuristics}. While prior works have focused on the realizable setting, we consider the more…

This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the disagreement coefficient for…

This work demonstrates a methodology for using deep learning to discover simple, practical criteria for classifying matrices based on abstract algebraic properties. By combining a high-performance neural network with explainable AI (XAI)…

A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc. Here we consider an additional parameter associated with each arc, a measure such as the time required to select the arc. MPTs are often…

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to…

Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…

Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through…

We prove a new lower bound on the parity decision tree complexity $\mathsf{D}_{\oplus}(f)$ of a Boolean function $f$. Namely, granularity of the Boolean function $f$ is the smallest $k$ such that all Fourier coefficients of $f$ are integer…

Deep Reinforcement Learning (DRL) has recently achieved significant advances in various domains. However, explaining the policy of RL agents still remains an open problem due to several factors, one being the complexity of explaining neural…