Joint Statistical Mask Learning and Distributed Estimation Without Support Priors

This paper addresses the problem of distributed estimation under partial observability, where nodes mustcollaboratively process masked or incomplete measurements to infer a global target vector. Such masking arises from sensing limitations, communication constraints, or privacy requirements. We propose a novel framework for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed masked information learning</i>, extending the Diffusion Least Mean Squares (DLMS) algorithm to operate under node-specific observation masks. To enable effective cooperation, we develop a signal-flow-inspired combination strategy and a thresholding-based algorithm for support inference. This allows each node to identify observable components of the target signal and adaptively control the diffusion of local estimates. We analyze the convergence of the proposed method in terms of mean and energy, and derive conditions for optimal threshold selection based on mask estimation error. Simulation results across both time- and transform-domain sparsity scenarios show that our method achieves a 30-40 dB improvement in mean square deviation over standard DLMS, matching the performance of fully observable settings under realistic observability ratios. These results underscore the potential of mask-aware adaptation for robust and scalable signal processing over networks.