20.07.2015 Views

Multivariate Gaussianization for Data Processing

Multivariate Gaussianization for Data Processing

Multivariate Gaussianization for Data Processing

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

Intro Iterative <strong>Gaussianization</strong> Experiments ConclusionsPropertiesProperty 2: The iterative <strong>Gaussianization</strong> trans<strong>for</strong>m 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 trans<strong>for</strong>m 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)

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!