@article {28392,
	title = {Sparse Online Learning with Kernels using Random Features for Estimating Nonlinear Dynamic Graphs},
	journal = {IEEE Transactions on Signal Processing},
	volume = {71},
	year = {2023},
	note = {This work is a joint collaboration between SimulaMet and University of Agder. This work was supported by the IKTPLUSS INDURB grant 270730/O70 and the SFI Offshore Mechatronics grant 237896/O30 from the Research Council of Norway.\&nbsp;},
	month = {06/2023},
	pages = {2027-2042},
	publisher = {IEEE},
	abstract = {Online topology estimation of graph-connected time series is challenging in practice, particularly because the dependencies between the time series in many real-world scenarios are nonlinear. To address this challenge, we introduce a novel kernel-based algorithm for online graph topology estimation. Our proposed algorithm also performs a Fourier-based random feature approximation to tackle the curse of dimensionality associated with kernel representations. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group-Lasso based optimization framework, which is solved using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. We provide theoretical guarantees for our algorithm and prove that it can achieve sublinear dynamic regret under certain reasonable assumptions. In experiments conducted on both real and synthetic data, our method outperforms existing state-of-the-art competitors.},
	issn = {1941-0476},
	doi = {10.1109/TSP.2023.3282068},
	url = {https://ieeexplore.ieee.org/document/10141675},
	author = {Money, Rohan and Krishnan, Joshin and Beferull-Lozano, Baltasar}
}
@article {42575,
	title = {Online Edge Flow Imputation on Networks},
	journal = {IEEE Signal Processing Letters},
	year = {2022},
	note = {This work is a joint collaboration between SimulaMet and University of Agder. This work was supported by the IKTPLUSS INDURB grant 270730/O70 and the SFI Offshore Mechatronics grant 237896/O30 from the Research Council of Norway.},
	publisher = {IEEE},
	abstract = {A novel online algorithm for missing data imputation for networks with signals defined on the edges is presented in this paper. Leveraging the prior knowledge intrinsic to most real-world networks, we propose a bi-level optimization scheme that includes (i) a sparse line graph identification strategy by solving a group-Lasso-based optimization framework via composite objective mirror descent to exploit the causal dependencies among the signals and (ii) a Kalman filtering-based signal reconstruction strategy developed using simplicial complex (SC) formulation to exploit the flow conservation. To the best of our knowledge, this is the first SC-based attempt for time-varying signal imputation, whose advantages have been demonstrated through numerical experiments conducted using EPANET models of both synthetic and real water distribution networks.},
	doi = {10.1109/LSP.2022.3221846},
	url = {https://ieeexplore.ieee.org/document/9947283},
	author = {Money, Rohan and Krishnan, Joshin and Beferull-Lozano, Baltasar and Isufi, Elvin}
}
@inproceedings {42572,
	title = {Online Joint Nonlinear Topology Identification and Missing Data Imputation over Dynamic Graphs},
	journal = {30th European Signal Processing Conference (EUSIPCO)},
	year = {2022},
	note = {This work is a joint collaboration between SimulaMet and University of Agder. This work was supported by the IKTPLUSS INDURB grant 270730/O70 and the SFI Offshore Mechatronics grant 237896/O30 from the Research Council of Norway.},
	publisher = { IEEE},
	abstract = {Extracting causal graph structures from multivariate time series, termed topology identification, is a fundamental problem in network science with several important applications. Topology identification is a challenging problem in real-world sensor networks, especially when the available time series are partially observed due to faulty communication links or sensor failures. The problem becomes even more challenging when the sensor dependencies are nonlinear and nonstationary. This paper proposes a kernel-based online framework using random feature approximation to jointly estimate nonlinear causal dependencies and missing data from partial observations of streaming graph-connected time series. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group lasso-based optimization framework for topology identification, which is solved online using alternating minimization techniques. The ability of the algorithm is illustrated using several numerical experiments conducted using both synthetic and real data.},
	doi = {10.23919/EUSIPCO55093.2022.9909681},
	url = {https://ieeexplore.ieee.org/document/9909681},
	author = {Money, Rohan and Krishnan, Joshin and Beferull-Lozano, Baltasar}
}
@inproceedings {28388,
	title = {Online Non-linear Topology Identification from Graph-connected Time Series},
	journal = {2021 IEEE Data Science and Learning Workshop (DSLW)2021 IEEE Data Science and Learning Workshop (DSLW)},
	year = {2021},
	note = {This work was carried out at University of Agder with the funding from the IKTPLUSS INDURB grant 270730/O70 and the SFI Offshore Mechatronics grant 237896/O30 from the Research Council of Norway.},
	month = {June/2021},
	publisher = {IEEE},
	address = {Toronto, ON, Canada},
	abstract = {Estimating the unknown causal dependencies among graph-connected time series plays an important role in many applications, such as sensor network analysis, signal processing over cyber-physical systems, and financial engineering. Inference of such causal dependencies, often known as topology identification, is not well studied for non-linear non-stationary systems, and most of the existing methods are batch-based which are not capable of handling streaming sensor signals. In this paper, we propose an online kernel-based algorithm for topology estimation of non-linear vector autoregressive time series by solving a sparse online optimization framework using the composite objective mirror descent method. Experiments conducted on real and synthetic data sets show that the proposed algorithm outperforms the state-of-the-art methods for topology estimation.},
	doi = {10.1109/DSLW51110.2021.9523399},
	url = {https://ieeexplore.ieee.org/document/9523399},
	author = {Money, Rohan and Krishnan, Joshin and Beferull-Lozano, Baltasar}
}
@inproceedings {28391,
	title = {Random Feature Approximation for Online Nonlinear Graph Topology Identification},
	journal = {2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP) 2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP)},
	year = {2021},
	note = {This work was carried out at University of Agder with the funding from the IKTPLUSS INDURB grant 270730/O70 and the SFI Offshore Mechatronics grant 237896/O30 from the Research Council of Norway.},
	month = {10/2021},
	publisher = {IEEE},
	address = {Gold Coast, Australia},
	abstract = {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 solved 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.},
	doi = {10.1109/MLSP52302.2021.9596512},
	url = {https://ieeexplore.ieee.org/document/9596512},
	author = {Money, Rohan and Krishnan, Joshin and Beferull-Lozano, Baltasar}
}
