{"doi":"10.1109/tsipn.2025.3583488","title":"Learning Networks From Wide-Sense Stationary Stochastic Processes","abstract":"Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_{t} = {L^{\\ast }}Y_{t}$, where $X_{t}, Y_{t} \\in \\mathbb {R}^{p}$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \\times p$ Laplacian $L^{\\ast }$ encodes the edge structure. Assuming $X_{t}$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\\ast }$ from temporally correlated samples of $Y_{t}$ via an $\\ell _{1}$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\\ast }$. We provide recovery guarantees for $L^\\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (","journal":"IEEE Transactions on Signal and Information Processing over Networks","year":2025,"id":545053,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9458,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2025-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1171629,"name":"Jiajun Cheng","orcid":"0000-0002-6995-430X","position":1,"is_corresponding":false},{"id":751287,"name":"Rajasekhar Anguluri","orcid":"0000-0003-2537-2778","position":2,"is_corresponding":false},{"id":1358437,"name":"Deepjyoti Deka","orcid":"0000-0003-3928-3936","position":3,"is_corresponding":false},{"id":618264,"name":"Gautam Dasarathy","orcid":"0000-0003-2252-2988","position":4,"is_corresponding":false},{"id":1171861,"name":"Anirudh Rayas","orcid":null,"position":0,"is_corresponding":true}],"reference_count":98,"raw_metadata":null,"created_at":"2026-07-19T02:53:17.418915Z","pmid":"41180157","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}