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Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…

We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…

We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…

We study notions of hyperuniformity for invariant locally square-integrable point processes in regular trees. We show that such point processes are never geometrically hyperuniform, and if the diffraction measure has support in the…

We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric…

This paper studies the concentration properties of random codes. Specifically, we show that, for discrete memoryless channels, the error exponent of a randomly generated code with pairwise-independent codewords converges in probability to…

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…

SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance).…

Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find…

Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…

The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks…

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little…

We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle.…

The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…

Asymptotic behaviour of maximum sizes of induced trees and forests has been studied extensively in last decades, though the overall picture is far from being complete. In this paper, we close several significant gaps: 1) We prove $2$-point…

This paper presents an efficient algorithm for retrieving from a database of trees, all trees that match a given query tree approximately, that is, within a certain error tolerance. It has natural language processing applications in…

We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a half-translation surface endowed with a flat unitary vector bundle. By doing so, over the discretizations, we relate the…

We study the effectiveness of non-uniform randomized feature selection in decision tree classification. We experimentally evaluate two feature selection methodologies, based on information extracted from the provided dataset: $(i)$…