This section illustrates how basic probabilistic rules may be reformulated as (multi)linear algebraic operations in the kernel embedding framework and is primarily based on the work of Song et al [REF].
In practice, all embeddings are empirically estimated from data \{(x_1,y_1),\dots, (x_n, y_n)\} and it assumed that a set of samples \{\widetilde{y}_1, \dots, \widetilde{y}_{\widetilde{n}} \} may be used to estimate the kernel embedding of the prior distribution \pi(Y) .