{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/anomaly-detection-via-graphical-lasso","title":"Anomaly Detection via Graphical Lasso","arxiv_id":"1811.04277","date":"2018-11-10","proceeding":null,"authors":["Haitao Liu","Randy C. Paffenroth","Jian Zou","Chong Zhou"],"abstract":"Anomalies and outliers are common in real-world data, and they can arise from\nmany sources, such as sensor faults. Accordingly, anomaly detection is\nimportant both for analyzing the anomalies themselves and for cleaning the data\nfor further analysis of its ambient structure. Nonetheless, a precise\ndefinition of anomalies is important for automated detection and herein we\napproach such problems from the perspective of detecting sparse latent effects\nembedded in large collections of noisy data. Standard Graphical Lasso-based\ntechniques can identify the conditional dependency structure of a collection of\nrandom variables based on their sample covariance matrix. However, classic\nGraphical Lasso is sensitive to outliers in the sample covariance matrix. In\nparticular, several outliers in a sample covariance matrix can destroy the\nsparsity of its inverse. Accordingly, we propose a novel optimization problem\nthat is similar in spirit to Robust Principal Component Analysis (RPCA) and\nsplits the sample covariance matrix $M$ into two parts, $M=F+S$, where $F$ is\nthe cleaned sample covariance whose inverse is sparse and computable by\nGraphical Lasso, and $S$ contains the outliers in $M$. We accomplish this\ndecomposition by adding an additional $ \\ell_1$ penalty to classic Graphical\nLasso, and name it \"Robust Graphical Lasso (Rglasso)\". Moreover, we propose an\nAlternating Direction Method of Multipliers (ADMM) solution to the optimization\nproblem which scales to large numbers of unknowns. We evaluate our algorithm on\nboth real and synthetic datasets, obtaining interpretable results and\noutperforming the standard robust Minimum Covariance Determinant (MCD) method\nand Robust Principal Component Analysis (RPCA) regarding both accuracy and\nspeed.","url_abs":"http://arxiv.org/abs/1811.04277v1","url_pdf":"http://arxiv.org/pdf/1811.04277v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"anomaly-detection-via-graphical-lasso","repo_url":"https://github.com/lht1949/AnomalyDetection","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"anomaly-detection","task_name":"Anomaly Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.04277","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}