Multivariate Gaussianization for Data Processing

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Intro Iterative Gaussianization Experiments ConclusionsExperiment 1: Density estimation toy examplesDensity estimation in high-dimensional problemsUnivariate density estimation is solved:Kernel estimatorsRadial basis function estimatesGaussian mixture modelsWavelet density estimates...High-dimensional density estimation is difficult!Parametric models: e.g. histogram-based→ Many samples needed, curse of dimensionalityNon-parametric models: e.g. Gaussian, GSM, etc.→ knowledge about the PDF
Intro Iterative Gaussianization Experiments ConclusionsExperiment 1: Density estimation toy examplesDensity estimation with RBIG1: Input: Given data x (0) = [x 1, . . . , x d ] ⊤ ∈ R d2: Learn the sequence of Gaussianization transforms, G, such that y = G(x)3: Compute its Jacobian, J G4: The p y(y) is a multivariate Gaussian:(1p y(y) = p y(G(x)) =( √ 2π|Σ|) exp − 1 )d 2 (G(x) − µ y) ⊤ Σ −1 (G(x) − µ y )5: Compute the probability in the input space with:p x(x) = p y(y) · |∇ xG|
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Multivariate Gaussianization for Data Processing

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