Many papers have addressed the problem of learning
the behavior (i.e., the local interaction function
at each node) of a networked system through
active queries, assuming that the network topology
is known. We address the problem of inferring
both the network topology and the behavior
of such a system through active queries. Our results
are for systems where the state of each node
is from {0, 1} and the local functions are Boolean.
We present inference algorithms under both batch
and adaptive query models for dynamical systems
with symmetric local functions. These algorithms
show that the structure and behavior of such dynamical
systems can be learnt using only a polynomial
number of queries. Further, we establish
a lower bound on the number of queries needed
to learn such dynamical systems. We also present
experimental results obtained by running our algorithms
on synthetic and real-world networks.
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This content will become publicly available on March 25, 2025
Learning the Topology and Behavior of Discrete Dynamical Systems
Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to certain classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known Natarajan dimension formalism. Our results provide a theoretical foundation for learning both the topology and behavior of discrete dynamical systems.
more » « less- PAR ID:
- 10567856
- Publisher / Repository:
- AAAI
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 38
- Issue:
- 13
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 14722 to 14730
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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