Related papers: A sharp oracle inequality for Graph-Slope
A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important…
Graph Neural Networks (GNNs) have emerged as the de facto standard for representation learning on graphs, owing to their ability to effectively integrate graph topology and node attributes. However, the inherent suboptimal nature of node…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
We present an effective heuristic for the Steiner Problem in Graphs. Its main elements are a multistart algorithm coupled with aggressive combination of elite solutions, both leveraging recently-proposed fast local searches. We also propose…
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is…
Autonomous navigation requires an accurate model or map of the environment. While dramatic progress in the prior two decades has enabled large-scale SLAM, the majority of existing methods rely on non-linear optimization techniques to find…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and $\ell_2$ estimation rate $(s/n)\log (p/s)$ in high-dimensional…
In a semi-supervised learning scenario, (possibly noisy) partially observed labels are used as input to train a classifier, in order to assign labels to unclassified samples. In this paper, we study this classifier learning problem from a…
One of many impediments to applying graph neural networks (GNNs) to large-scale real-world graph data is the challenge of centralized training, which requires aggregating data from different organizations, raising privacy concerns.…
We develop universal gradient methods for Stochastic Convex Optimization (SCO). Our algorithms automatically adapt not only to the oracle's noise but also to the H\"older smoothness of the objective function without a priori knowledge of…
We tackle the problem of forecasting network-signal snapshots using past signal measurements acquired by a subset of network nodes. This task can be seen as a combination of multivariate time-series prediction and graph-signal…
In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
The objective of pose SLAM or pose-graph optimization (PGO) is to estimate the trajectory of a robot given odometric and loop closing constraints. State-of-the-art iterative approaches typically involve the linearization of a non-convex…
We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
This paper proposes a deep recurrent Rotation Averaging Graph Optimizer (RAGO) for Multiple Rotation Averaging (MRA). Conventional optimization-based methods usually fail to produce accurate results due to corrupted and noisy relative…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the…