H. Akaike. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19:716-723, 1974.
A. Aravkin, J. V. Burke, A. Chiuso, and G. Pillonetto. Convex vs non-convex estimators for regression and sparse estimation: the mean squared error properties of ard and glasso. Journal of Machine Learning Research, 15:217-252, 2014.
W.W. Barrett, C.R. Johnson, and M. Lundquist. Determinantal formulation for matrix completions associated with chordal graphs. Linear Algebra and its Applications, 121:265-289, 1989.
J. O. Berger. Statistical decision theory and Bayesian analysis. Springer Verlag, 1985.
F. P. Carli, T. Chen, A. Chiuso, L. Ljung, and G. Pillonetto. On the estimation of hyperparameters for bayesian system identification with exponentially decaying kernels. In Decision and Control (CDC), 2012 IEEE 51st Annual Conference on, pages 5260-5265. IEEE, 2012.
F. P. Carli, A. Chiuso, and G. Pillonetto. Efficient algorithms for large scale linear system identification using stable spline estimators. In Proceedings of the 16th IFAC symposium on system identification, SysId 2012, pages 119-124. IFAC, 2012.
F.P. Carli, A. Ferrante, M. Pavon, and G. Picci. A maximum entropy solution of the covariance extension problem for reciprocal processes. IEEE Transactions on Automatic Control, 56(9):1999-2012, 2011.
F.P. Carli, A. Ferrante, M. Pavon, and G. Picci. An efficient algorithm for maximum entropy extension of block-circulant covariance matrices. Linear Algebra and its Applications, 439(8):2309-2329, 2013.
F.P. Carli and T.T. Georgiou. On the covariance completion problem under a circulant structure. IEEE Transactions on Automatic Control, 56(4):918-922, 2011.
T. Chen and L. Ljung. Implementation of algorithms for tuning parameters in regularized least squares problems in system identification. Automatica, 49(7):2213-2220, 2013.
T. Chen, H. Ohlsson, G. C. Goodwin, and L. Ljung. Kernel selection in linear system identification part II: A classical perspective. In Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on, pages 4326-4331. IEEE, 2011.
T. Chen, H. Ohlsson, and L. Ljung. On the estimation of transfer functions, regularizations and Gaussian processes-revisited. Automatica, 48(8):1525-1535, 2012.
J. Dahl, L. Vanderberghe, and V. Roychowdhury. Covariance selection for non-chordal graphs via chordal embedding. Optimization Methods and Software, 23:501-520, 2008.
A. P. Dempster. Covariance selection. Biometrics, 28:157-175, 1972.
H. Dym and I. Gohberg. Extensions of band matrices with band inverses. Linear algebra and its applications, 36:1-24, 1981.
M. Fukuda, M. Kojima, K. Murota, and K. Nakata. Exploiting sparsity in semidefinite programming via matrix completion i: general framework. SIAM Journal on Optimization, 11:647-674, 2000.
I. Gohberg, S. Goldberg, and M. A. Kaashoek. Classes of Linear Operators, II,. Birkhaüser, Basel, 1993.
M. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
R. Grone, C.R. Johnson, E.M. Sa, and H. Wolkowicz. Positive definite completions of partial Hermitian matrices. Linear Algebra and Its Applications, 58:109-124, 1984.
T. Hastie, R. Tibshirani, and J. Friedman. The elements of statistical learning. Springer, 2008.
C.R. Johnson. Matrix completion problems: a survey. In Proceedings of Symposia in Applied Mathematics (1990), volume 40, pages 171-198.
L. Ljung. System Identification-Theory For the User. Prentice Hall, 1999.
J. S. Maritz and T. Lwin. Empirical Bayes methods. Chapman and Hall London, 1989.
K. Nakata, K. Fujitsawa, M. Fukuda, M. Kojima, and K. Murota. Exploiting sparsity in semidefinite programming via matrix completion ii: implementation and numerical details. Mathematical Programming Series B, 95:303-327, 2003.
G. Pillonetto, A. Chiuso, and G. De Nicolao. Prediction error identification of linear systems: A nonparametric Gaussian regression approach. Automatica, 47:291-305, 2011.
G. Pillonetto, A. Chiuso, and G. De Nicolao. Regularized estimation of sums of exponentials in spaces generated by stable spline kernels. In American Control Conference (ACC), 2010, pages 498-503. IEEE, 2010.
G. Pillonetto and G. De Nicolao. A new kernel-based approach for linear system identification. Automatica, 46:81-93, 2010.
G. Pillonetto and G. De Nicolao. Kernel selection in linear system identification Part I: A Gaussian process perspective. In Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on, pages 4318-4325. IEEE, 2011.
C. Rasmussen and C. Williams. Gaussian processes for machine learning. MIT press Cambridge, MA, 2006.
B. Scholkopf and A. J. Smola. Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT press, 2001.
G. Schwarz. Estimating the dimension of a model. The annals of statistics, 6(2):461-464, 1978.
J. Shawe-Taylor and N. Cristianini. Kernel methods for pattern analysis. Cambridge University Press, 2004.
T. Soderstrom and P. Stoica. System Identification. Prentice Hall, 1989.
