6533b837fe1ef96bd12a1dc5

RESEARCH PRODUCT

Random Feature Approximation for Online Nonlinear Graph Topology Identification

Baltasar Beferull-lozanoJoshin P. KrishnanRohan Money

subject

Signal Processing (eess.SP)FOS: Computer and information sciencesComputer Science - Machine LearningComputational complexity theoryComputer scienceApproximation algorithmTopology (electrical circuits)Network topologyMachine Learning (cs.LG)Kernel (statistics)FOS: Electrical engineering electronic engineering information engineeringTopological graph theoryElectrical Engineering and Systems Science - Signal ProcessingOnline algorithmAlgorithmCurse of dimensionality

description

Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation. The algorithm uses a Fourier-based Random feature approximation to tackle the curse of dimensionality associated with the kernel representations. Exploiting the fact that the real-world networks often exhibit sparse topologies, we propose a group lasso based optimization framework, which is solve using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. The experiments conducted on real and synthetic data show that the proposed method outperforms its competitors.

https://dx.doi.org/10.48550/arxiv.2110.09935