Our unifying Mixing Model Hierarchy begins with Linear Mixing Models (LMMs), a simple class of MOGP models typically characterised by low-rank covariance structure. An LMM decomposes a signal f (t) comprising p outputs into a fixed basis h 1 , . . . , h m ∈ R p whose coefficients x 1 (t), . . . , x m (t) are time-varying and modelled independently with Gaussian processes:
f (t) = h 1 x 1 (t) + . . . + h m x m (t) = h 1 · · · h m H x 1 (t) · · · x m (t) T x(t) = Hx(t).
The noisy signal y(t) is, then, generated by adding N (0, Λ)-distributed noise to f (t). Intuitively, this means that the p-dimensional **data** lives in a "pancake" around the m-dimensional column space of H, where typically m p.