{"id":406,"date":"2024-12-06T07:00:37","date_gmt":"2024-12-06T07:00:37","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2024\/12\/06\/2412-03768\/"},"modified":"2024-12-06T07:00:37","modified_gmt":"2024-12-06T07:00:37","slug":"2412-03768","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2024\/12\/06\/2412-03768\/","title":{"rendered":"Learning Networks from Wide-Sense Stationary Stochastic Processes"},"content":{"rendered":"

Learning Networks from Wide-Sense Stationary Stochastic Processes
\n \t

\n
<\/BR>
\n
\n \t

\n
<\/BR><\/p>\n

arXiv:2412.03768v1 Announce Type: new
\nAbstract: 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 $n$.
\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 (such as the human brain).<\/div>\n

\t

\n
<\/BR>
\n Anirudh Rayas, Jiajun Cheng, Rajasekhar Anguluri, Deepjyoti Deka, Gautam Dasarathy
\n \t

\n
<\/BR>
\nGo to original source<\/a>
\n \t

\n
<\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"

Learning Networks from Wide-Sense Stationary Stochastic Processes arXiv:2412.03768v1 Announce Type: new 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: $X_t = {L^{ast}}Y_{t}$, […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,382,112],"tags":[490,491,492],"class_list":["post-406","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-eess-sp","category-stat-ml","tag-ast","tag-networks","tag-systems"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/406"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=406"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/406\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}