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📄 Abstract
Abstract: This paper tackles the challenging problem of jointly inferring time-varying
network topologies and imputing missing data from partially observed graph
signals. We propose a unified non-convex optimization framework to
simultaneously recover a sequence of graph Laplacian matrices while
reconstructing the unobserved signal entries. Unlike conventional decoupled
methods, our integrated approach facilitates a bidirectional flow of
information between the graph and signal domains, yielding superior robustness,
particularly in high missing-data regimes. To capture realistic network
dynamics, we introduce a fused-lasso type regularizer on the sequence of
Laplacians. This penalty promotes temporal smoothness by penalizing large
successive changes, thereby preventing spurious variations induced by noise
while still permitting gradual topological evolution. For solving the joint
optimization problem, we develop an efficient Alternating Direction Method of
Multipliers (ADMM) algorithm, which leverages the problem's structure to yield
closed-form solutions for both the graph and signal subproblems. This design
ensures scalability to large-scale networks and long time horizons. On the
theoretical front, despite the inherent non-convexity, we establish a
convergence guarantee, proving that the proposed ADMM scheme converges to a
stationary point. Furthermore, we derive non-asymptotic statistical guarantees,
providing high-probability error bounds for the graph estimator as a function
of sample size, signal smoothness, and the intrinsic temporal variability of
the graph. Extensive numerical experiments validate the approach, demonstrating
that it significantly outperforms state-of-the-art baselines in both
convergence speed and the joint accuracy of graph learning and signal recovery.
Authors (2)
Chuansen Peng
Xiaojing Shen
Submitted
October 19, 2025
Key Contributions
This paper proposes a unified non-convex optimization framework for jointly inferring time-varying network topologies and imputing missing graph signals. By integrating graph and signal recovery, it achieves superior robustness, especially with high missing data, and introduces a fused-lasso regularizer for temporal smoothness in network dynamics.
Business Value
Enables more accurate analysis and prediction in dynamic networks where data is often incomplete, such as in real-time sensor networks or evolving social graphs, leading to better decision-making.