Multivariate Gaussianization for Data Processing

Intro Iterative Gaussianization Experiments ConclusionsPropertiesProperty 2: The iterative Gaussianization transform is differentiableThe Jacobian of the series of K iterations is the product of the Jacobians:∇ xG = ∏ Kk=1 R (k)∇ x (k)Ψ (k)Marg. Gauss. Ψ (k) is a dimension-wise transform with diagonal Jacobian:⎛⎞∂Ψ 1 (k)· · · 0∂x (k)1∇ x (k)Ψ (k) =⎜.⎝. ... ..⎟⎠0 · · ·Each element in ∇ x (k)Ψ (k) is:∂Ψ d (k)∂x (k)d∂Ψ i (k)∂x (k)i= ∂G∂u∂u∂x (k)i( ∂G−1=∂x i) −1p i (x (k)i) = g(Ψ i (k)(x (k)i)) −1 p i (x (k)i)Remark 1: rotation-independentThe differentiable nature of G is independent of the selected rotations R (k) .