Covariance Matrix Sample Clauses

Covariance Matrix. ‌ The general form of the covariance between two random variables x(m) and x(n) is expressed in Eq. 4.11, Cmn = C(x(m), x(n); θ) + δmnN (x(n); θ) (4.11) where θ refers to the hyperparameters and N is noise model which is varied for the case of input-dependent data noise and typically constant for the case of input-independent data noise [77]. The covariance can take different forms and the requirement for the covariance matrix constructed upon is that it should be positive definite. In practice, a covariance func- tional form reflecting the physical nature of the target machine-learning functional is preferable to enhance the prediction accuracy. For instance, for machine learning of periodic functions, the forms of sin x or cos x are usually adopted. Different covariance functions ever emerged historically and can be found in literature while new covariance form are also under research in the community [76–78]. Among them, one of the most commonly used covariance at I-dimensional database takes the following form, I Σ x(m) − x(n) 2  