Correlation-Based ultrahigh-dimensional variable screening

Ahmed, Talal; Bajwa, Waheed U.

doi:10.1109/camsap.2017.8313129

Cited by 4 publications

(4 citation statements)

References 34 publications

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“…7.2), [14], here we rely on a priori knowledge about the presence (or absence) of a few edges; conceivably leading to simpler algorithmic updates and better recovery performance. We may learn about edge status via limited questionnaires and experiments, or, we could perform edge screening prior to topology inference [15]; see also the discussion in Section 4. The batch PG algorithm developed in Section 2.1.3 to recover the network topology is computationally more efficient than existing methods for this (and related) problem(s).…”

Section: Technical Approach and Paper Outlinementioning

confidence: 99%

“…7.3.4). Since (6) is a sparse linear regression problem, one could resort to so-termed variable screening techniques to drop edges prior to solving the optimization; see e.g., [15]. Either way, one ends up with extra constraints S ij = s ij , for a few vertex pairs (i, j) in the set Ω ⊂ N × N of observed edge weights s ij .…”

Section: Revisiting Stationarity For Graph Learningmentioning

confidence: 99%

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Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour

Mateos

2020

Algorithms

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We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

show abstract

Section: Technical Approach and Paper Outlinementioning

confidence: 99%

Section: Revisiting Stationarity For Graph Learningmentioning

confidence: 99%

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour

Mateos

2020

Algorithms

View full text Add to dashboard Cite

show abstract

“…7.2], [14], here we rely on a priori knowledge about the presence (or absence) of a few edges; conceivably leading to simpler algorithmic updates and better recovery performance. We may learn about edge status via limited questionnaires and experiments, or, we could perform edge screening prior to topology inference [15]. The batch PG algorithm developed in Section 2.3 to recover the network topology is computationally more efficient than existing methods for this (and related) problem(s).…”

Section: Technical Approach and Paper Outlinementioning

confidence: 99%

“…The key difference between the batch algorithm (11) and its online counterpart (15) is the variability of g t per iteration in the latter. Ideally, we would like Algorithm 2 to closely track the sequence of minimizers {S ⋆ t } for large enough t, something we corroborate numerically in Section 4.…”

Section: Convergence and Regret Analysismentioning

confidence: 99%

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour¹,

Mateos²

2020

Preprint

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We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and effect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations' covariance matrix and the so-called graph shift operator (GSO -a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations' empirical covariance matrix. For streaming data said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

show abstract

Online Network Topology Inference with Partial Connectivity Informatio

Shafipour

Mateos

2019

2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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Correlation-Based ultrahigh-dimensional variable screening

Cited by 4 publications

References 34 publications

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Online Network Topology Inference with Partial Connectivity Informatio

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