QUIC swMATH ID: 11795 Software Authors: Hsieh, Cho-Jui; Sustik, M'aty'as A.; Dhillon, Inderjit S.; Ravikumar, Pradeep Description: QUIC: quadratic approximation for sparse inverse covariance estimation. The ℓ 1 -regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to recent state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton’s method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and present experimental results using synthetic and real-world application data that demonstrate the considerable improvements in performance of our method when compared to previous methods. Homepage: http://cran.r-project.org/web/packages/QUIC/index.html Source Code: https://github.com/cran/QUIC Dependencies: R Keywords: graphical model; regularization; optimization; Gaussian Markov random field Related Software: glasso; huge; R; Saga; FASTCLIME; GMRFLib; LIBLINEAR; FRK; igraph; bnstruct; bnlearn; L-BFGS; FPC_AS; Adam; AdaGrad; LIBSVM; TFOCS; SDPT3; spcov; HdBCS Cited in: 35 Publications all top 5 Cited by 116 Authors 3 Sejnowski, Terrence J. 2 Cash, Sydney S. 2 Das, Anup 2 Lainscsek, Claudia S. M. 2 Toh, Kim Chuan 1 Ağraz, Melih 1 Avron, Haim 1 Aybat, Necdet Serhat 1 Bazhenov, Maxim 1 Becker, Stephen R. 1 Bertsimas, Dimitris John 1 Bian, Fengmiao 1 Bollhöfer, Matthias 1 Bottou, Léon 1 Boutsidis, Christos 1 Bukhari, Qasim 1 Cai, Tony Tony 1 Chen, Luonan 1 Chen, Yusi 1 Choi, Young-Geun 1 Curtis, Frank E. 1 Dauwels, Justin 1 Davanloo Tajbakhsh, Sam 1 Del Castillo, Enrique 1 Deshpande, Sameer K. 1 Devijver, Emilie 1 Dhillon, Inderjit S. 1 Doyle, John C. 1 Drineas, Petros 1 Eftekhari, Aryan 1 Fukuda, Mituhiro 1 Gallopin, Mélina 1 Genton, Marc G. 1 George, Edward I. 1 Ghose, Amur 1 Halgren, Eric 1 Han, Insu 1 Hsieh, Cho-Jui 1 Hu, Guyu 1 Huynh-Thu, Vân Anh 1 Jaini, Priyank 1 Jiang, Binyan 1 Kambadur, Prabhanjan 1 Keyes, David Elliot 1 Kim, Sunyoung 1 Kleiber, William 1 Kontopoulou, Eugenia-Maria 1 Krishnan, Giri P. 1 Krock, Mitchell 1 Kuhn, Daniel 1 Lamperski, Jourdain B. 1 Lee, Seunghwan 1 Levina, Elizaveta 1 Li, Tianxi 1 Li, Tiejun 1 Li, Zhen 1 Liang, Jingwei 1 Liang, Ling 1 Lim, Johan 1 Lin, Tiger W. 1 Lin, Wutu 1 Litvinenko, Alexander 1 Liu, Xiaoping 1 Malioutov, Dmitry M. 1 Menickelly, Matt 1 Milzarek, Andre 1 Mohajerin Esfahani, Peyman 1 Molstad, Aaron J. 1 Muller, Lyle E. 1 Müller, Samuel 1 Nakagaki, Takashi 1 Nocedal, Jorge 1 Pan, Zhisong 1 Park, Seongoh 1 Pauphilet, Jean 1 Phan, Dzung T. 1 Poupart, Pascal 1 Purutçuoğlu, Vilda 1 Qian, Cheng 1 Ravikumar, Pradeep 1 Ren, Zhao 1 Ročková, Veronika 1 Sampson, Aaron L. 1 Sanguinetti, Guido 1 Scheidegger, Simon 1 Schenk, Olaf 1 Sexton, Daniel 1 Shin, Jinwoo 1 Sun, Defeng 1 Sun, Wei 1 Sun, Ying 1 Sustik, Mátyás A. 1 Tarr, Garth 1 Tran Dinh Quoc 1 Treister, Eran 1 Turek, Javier S. 1 Wang, Cheng 1 Wang, Xinlei 1 Weber, Neville C. 1 Wen, Zaiwen ...and 16 more Authors all top 5 Cited in 22 Serials 4 Journal of Machine Learning Research (JMLR) 3 Neural Computation 3 Computational Statistics and Data Analysis 3 SIAM Journal on Scientific Computing 3 Electronic Journal of Statistics 2 Mathematical Programming. Series A. Series B 2 Journal of Computational and Graphical Statistics 1 Inverse Problems 1 Journal of the American Statistical Association 1 Mathematics of Operations Research 1 Operations Research 1 International Journal of Approximate Reasoning 1 Computational Statistics 1 Journal of Statistical Computation and Simulation 1 Linear Algebra and its Applications 1 SIAM Review 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 INFORMS Journal on Computing 1 Mathematical Problems in Engineering 1 The Annals of Applied Statistics 1 Methods in Molecular Biology all top 5 Cited in 8 Fields 19 Statistics (62-XX) 11 Operations research, mathematical programming (90-XX) 7 Numerical analysis (65-XX) 6 Computer science (68-XX) 6 Biology and other natural sciences (92-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Probability theory and stochastic processes (60-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Citations by Year