Abstract
Covariance matrix is a generalization of covariance between two univariate random variables. It is composed of the pairwise covariance between components of a multivariate random variable. It underpins important stochastic processes such as Gaussian process, and in practice it provides key characterizations between multiple random factors.
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For a complete treatment of covariance matrix from a statistical perspective, see Casella and Berger (2002) and Mardia et al. (1979) provides details for the multivariate case. PCA is comprehensively discussed in Jolliffe (2002), and kernel methods are introduced in Schölkopf and Smola (2002). Williams and Rasmussen (2006) gives the state of the art on how Gaussian processes can be utilized for machine learning.
Recommended Reading
For a complete treatment of covariance matrix from a statistical perspective, see Casella and Berger (2002) and Mardia et al. (1979) provides details for the multivariate case. PCA is comprehensively discussed in Jolliffe (2002), and kernel methods are introduced in Schölkopf and Smola (2002). Williams and Rasmussen (2006) gives the state of the art on how Gaussian processes can be utilized for machine learning.
Casella G, Berger R 2002 Statistical inference, 2nd edn. Duxbury, Pacific Grove
Gretton A, Herbrich R, Smola A, Bousquet O, Schölkopf B (2005) Kernel methods for measuring independence. J Mach Learn Res 6:2075–2129
Jolliffe IT (2002) Principal component analysis. Springer series in statistics, 2nd edn. Springer, New York
Mardia KV, Kent JT, Bibby JM (1979) Multivariate analysis. Academic, London/New York
Schölkopf B, Smola A (2002) Learning with Kernels. MIT, Cambridge
Gaussian Processes for Machine Learning, Carl Edward Rasmussen and Chris Williams, the MIT Press, Cambridge, MA, 2006
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Zhang, X. (2016). Covariance Matrix. In: Sammut, C., Webb, G. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7502-7_57-1
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DOI: https://doi.org/10.1007/978-1-4899-7502-7_57-1
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