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1. Online proximal gradient for learning graphs from streaming signals

   https://doi.org/10.23919/Eusipco47968.2020.9287550  

   Shafipour, Rasoul; Mateos, Gonzalo (January 2021, 2020 28th European Signal Processing Conference (EUSIPCO))

   null (Ed.)

   We leverage proximal gradient iterations to develop an online graph learning algorithm from streaming network data. Our goal is to track the (possibly) time-varying network topology, and effect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations' covariance matrix and the so-called graph shift operator (GSO - a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a (e.g., sparse) GSO that is structurally admissible and approximately commutes with the observations' empirical covariance matrix. For streaming data said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Preliminary numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network. 

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2. Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

   https://doi.org/10.3390/a13090228  

   Shafipour, Rasoul; Mateos, Gonzalo (September 2020, Algorithms)

   null (Ed.)

   We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network. 

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3. Batch Updates of Distributed Streaming Graphs using Linear Algebra

   https://doi.org/10.1109/SCW63240.2024.00089  

   Hassani, Elaheh; Hussain, Md Taufique; Azad, Ariful (November 2024, IEEE)

   We develop a distributed-memory parallel algorithm for performing batch updates on streaming graphs, where vertices and edges are continuously added or removed. Our algorithm leverages distributed sparse matrices as the core data structures, utilizing equivalent sparse matrix operations to execute graph updates. By reducing unnecessary communication among processes and employing shared-memory parallelism, we accelerate updates of distributed graphs. Additionally, we maintain a balanced load in the output matrix by permuting the resultant matrix during the update process. We demonstrate that our streaming update algorithm is at least 25 times faster than alternative linear-algebraic methods and scales linearly up to 4,096 cores (32 nodes) on a Cray EX supercomputer. 

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4. Decentralized Learning Robust to Data Poisoning Attacks

   https://doi.org/10.1109/CDC51059.2022.9992702  

   Mao, Yanwen; Data, Deepesh; Diggavi, Suhas; Tabuada, Paulo (January 2022, IEEE Control and Decision Conference (CDC))

   This paper addresses the problem of decentralized learning in the presence of data poisoning attacks. In this problem, we consider a collection of nodes connected through a network, each equipped with a local function. The objective is to compute the global minimizer of the aggregated local functions, in a decentralized manner, i.e., each node can only use its local function and data exchanged with nodes it is connected to. Moreover, each node is to agree on the said minimizer despite an adversary that can arbitrarily change the local functions of a fraction of the nodes. This problem setting has applications in robust learning, where nodes in a network are collectively training a model that minimizes the empirical loss with possibly attacked local data sets. In this paper, we propose a novel decentralized learning algorithm that enables all nodes to reach consensus on the optimal model, in the absence of attacks, and approximate consensus in the presence of data poisoning attacks. 

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5. The Power of Abstract MAC Layer: A Fault-Tolerance Perspective

   https://doi.org/10.4230/LIPICS.DISC.2024.39  

   Zhang, Qinzi; Tseng, Lewis (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Alistarh, Dan (Ed.)

   This paper studies the power of the "abstract MAC layer" model in a single-hop asynchronous network. The model captures primitive properties of modern wireless MAC protocols. In this model, Newport [PODC '14] proves that it is impossible to achieve deterministic consensus when nodes may crash. Subsequently, Newport and Robinson [DISC '18] present randomized consensus algorithms that terminate with O(n³ log n) expected broadcasts in a system of n nodes. We are not aware of any results on other fault-tolerant distributed tasks in this model. We first study the computability aspect of the abstract MAC layer. We present a wait-free algorithm that implements an atomic register. Furthermore, we show that in general, k-set consensus is impossible. Second, we aim to minimize storage complexity. Existing algorithms require Ω(n log n) bits. We propose two wait-free approximate consensus and two wait-free randomized binary consensus algorithms that only need constant storage complexity (except for the phase index). One randomized algorithm terminates with O(n log n) expected broadcasts. All our algorithms are anonymous, meaning that at the algorithm level, nodes do not need to have a unique identifier. 

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