Related papers: Superpolynomial Lower Bounds for Decision Tree Lea…

In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…

Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we investigate the problem of finding a spanning tree of $G$ that satisfies the constraints imposed by $D$. The restrictions to add an edge in the tree depend on its…

We present a simple deterministic reduction which, assuming the Exponential Time Hypothesis ($\mathsf{ETH}$), yields tight lower bounds for approximating the parameterized Maximum Likelihood Decoding problem ($\mathsf{MLD}$) and the…

We approximate the d complex zeros of a univariate polynomial p(x) of a degree d or those zeros that lie in a fixed region of interest on the complex plane such as a disc or a square. Our divide and conquer algorithm of STOC 1995 supports…

The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…

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…

Let $({\bf U},{\bf S},d)$ be an instance of Set Cover Problem, where ${\bf U}=\{u_1,...,u_n\}$ is a $n$ element ground set, ${\bf S}=\{S_1,...,S_m\}$ is a set of $m$ subsets of ${\bf U}$ satisfying $\bigcup_{i=1}^m S_i={\bf U}$ and $d$ is a…

Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…

Given a boolean predicate $\Pi$ on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for $\Pi$ is a distributed algorithm that can start from any initial configuration of the network (i.e., every…

We study the sample complexity of differentially private optimization of quasi-concave functions. For a fixed input domain $\mathcal{X}$, Cohen et al. (STOC 2023) proved that any generic private optimizer for low sensitive quasi-concave…

Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…

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…

Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…

The $\epsilon$-approximate degree of a Boolean function $f: \{-1, 1\}^n \to \{-1, 1\}$ is the minimum degree of a real polynomial that approximates $f$ to within $\epsilon$ in the $\ell_\infty$ norm. We prove several lower bounds on this…

Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…

We introduce techniques for proving superlinear conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not decidable in…

Submodular and fractionally subadditive (or equivalently XOS) functions play a fundamental role in combinatorial optimization, algorithmic game theory and machine learning. Motivated by learnability of these classes of functions from random…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…

We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large…