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Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…
This paper studies selecting a subset of the system's output to minimize the state estimation mean square error (MSE). This results in the maximization problem of a set function defined on possible sensor selections subject to a cardinality…
Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…
With input sizes becoming massive, coresets -- small yet representative summary of the input -- are relevant more than ever. A weighted set $C_w$ that is a subset of the input is an $\varepsilon$-coreset if the cost of any feasible solution…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of the…
Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…
We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global…
Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
A vector-measurement-sensor problem for the least squares estimation is considered, by extending a previous novel approach in this paper. An extension of the vector-measurement-sensor selection of the greedy algorithm is proposed and is…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
The use of Bayesian methods in large-scale data settings is attractive because of the rich hierarchical models, uncertainty quantification, and prior specification they provide. Standard Bayesian inference algorithms are computationally…