Summary of Interacting Particle Systems on Networks: Joint Inference Of the Network and the Interaction Kernel, by Quanjun Lang et al.
Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel
by Quanjun Lang, Xiong Wang, Fei Lu, Mauro Maggioni
First submitted to arxiv on: 13 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Dynamical Systems (math.DS); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary In this paper, researchers develop a novel approach to modeling multi-agent systems on networks by jointly inferring the weight matrix of the network and the interaction kernel from multiple trajectories. The proposed estimator leads to a non-convex optimization problem, which is tackled using two algorithms: alternating least squares (ALS) and operator regression with ALS (ORALS). Both methods are scalable to large datasets and provide guarantees for identifiability and well-posedness. While ALS appears statistically efficient in small data regimes, ORALS is consistent and asymptotically normal under certain conditions. The paper demonstrates the effectiveness of these algorithms through numerical experiments on various systems, including Kuramoto particle dynamics and opinion models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how complex systems work by learning from many examples of agents interacting with each other. Researchers develop a new way to figure out which agents interact and what rules they follow based only on the paths these agents take. They test two different methods to solve this problem, one called ALS (alternating least squares) and another called ORALS (operator regression with alternating least squares). Both methods work well for large datasets, but ORALS is more reliable. The researchers show how their approach works by applying it to different scenarios, like a game where particles follow each other or a model of how opinions spread. |
Keywords
* Artificial intelligence * Optimization * Regression
