相关论文: Geodesic Property of Greedy Algorithms for Optimiz…

An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a…

Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the…

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…

We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…

We introduce a new geometric spanner, $\delta$-Greedy, whose construction is based on a generalization of the known Path-Greedy and Gap-Greedy spanners. The $\delta$-Greedy spanner combines the most desirable properties of geometric…

In this paper we prove the efficacy of a simple greedy algorithm for a finite horizon online resource allocation/matching problem, when the corresponding static planning linear program (SPP) exhibits a non-degeneracy condition called the…

Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…

Many dynamic programming algorithms for discrete 0-1 optimizationproblems are "pure" in that their recursion equations only use min/max and addition operations, and do not depend on actual input weights. The well-known greedy algorithm of…

Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…

The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for…

We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…

We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems. Using the algorithm, we obtain the set of all possible greedy solutions and…

We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…

We propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers…

Orthogonal greedy learning (OGL) is a stepwise learning scheme that adds a new atom from a dictionary via the steepest gradient descent and build the estimator via orthogonal projecting the target function to the space spanned by the…

We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…

We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…

With the rising importance of large-scale network control, the problem of actuator placement has received increasing attention. Our goal in this paper is to find a set of actuators minimizing the metric that measures the average energy…

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

This paper is devoted to the development and convergence analysis of greedy reconstruction algorithms based on the strategy presented in [Y. Maday and J. Salomon, Joint Proceedings of the 48th IEEE Conference on Decision and Control and the…