ACTIVE LEARNING BASED STRUCTURAL INFERENCE

Abstract

In this paper, we propose an active-learning based framework, Active Learning based Structural Inference (ALaSI), to infer the existence of directed connections from observed agents' states over a time period in a dynamical system. With the help of deep active learning, ALaSI is competent in learning the representation of connections with relatively small pool of prior knowledge. Moreover, based on information theory, we propose inter-and out-of-scope message learning pipelines, which are remarkably beneficial to the structural inference for large dynamical systems. We evaluate ALaSI on various large datasets including simulated systems and real-world networks, to demonstrate that ALaSI is able to precisely infer the existence of connections in these systems under either supervised learning or unsupervised learning, with better performance than baseline methods.

1. INTRODUCTION

Dynamical systems are commonly observed in real-world, including physical systems (Kwapień & Drożdż, 2012; Ha & Jeong, 2021) , biological systems (Tsubaki et al., 2019; Pratapa et al., 2020) , and multi-agent systems (Brasó & Leal-Taixé, 2020; Li et al., 2022) . A dynamical system can be described as a set of three core elements: (a) the state of the system in a time period, including state of the individual agents; (b) the state-space of the system; and (c) the state-transition function (Irwin & Wang, 2017) . Knowing these core elements, we can describe and predict how a dynamical system behaves. Yet the three elements are not independent of each other, for example, the evolution of the state is affected by the state-transition function, which suggests that we may predict the future state based on its current state and the entities which affect the agents (i.e. connectivity). Moreover, the state-transition function is often deterministic (Katok & Hasselblatt, 1995) , which simplifies the derivation of the future state as a Markovian transition function. However, in most cases, we hardly have access to the connectivity within a given system, or only have limited knowledge about the connectivity. Is it possible to infer the connectivity from observed states of the agents over a time period? We formulate it as the problem of structural inference, and several machine learning frameworks have been proposed to address it (Kipf et al., 2018; Webb et al., 2019; Alet et al., 2019; Chen et al., 2021; Löwe et al., 2022; Wang & Pang, 2022) . Although these frameworks can accurately infer the connectivity, as they perform representation learning on a fully connected graph, these methods can only work for small systems (up to dozens of agents), and cannot scale well to real-world dynamical systems, for example, with hundreds of agents. Besides that, as we show in the experiment and appendix sections in this work, the integration of prior knowledge about partial connectivity of the system is quite problematic among these methods. On the other hand, deep active learning (DeepAL) is an emerging branch of research that is used to reduce the cost of annotation while retaining the powerful learning capabilities of deep learning (Ren et al., 2022) . This motivates us to explore DeepAL to solve the problem of structural inference. In order to perform structural inference on large dynamical systems, instead of building pools based on batches, we build pools based on agents, and expect the learning framework can consequently infer the existence of directed connections with a little prior knowledge of the connections. Therefore, in this work, based on DeepAL, we propose a novel structural inference framework, namely, Active Learning based Structural Inference (ALaSI), which is designed for the structural inference of large dynamical systems, and is suitable for the integration of prior knowledge. ALaSI leverages query strategy with dynamics for agent-wise selection to update the pool with the most informative partial system, which encourages ALaSI to infer the connections efficiently and

