backwardParameterUpdate: Backward parameters update

Description Usage Arguments Details Value

View source: R/tagi.R

Description

This function updates parameters from responses to input data. It updates μ_{θ|y} and Σ_{θ|y} from the θ|y distribution for a given layer.

Usage

1
backwardParameterUpdate(mp, Sp, mzF, SzF, SzB, Czp, mzB, idx)

Arguments

mp

Mean vector of parameters for the current layer μ_{θ}

Sp

Covariance matrix of parameters for the current layer Σ_{θ}

mzF

Mean vector of units for the next layer μ_{Z^{+}}

SzF

Covariance matrix of units for the next layer Σ_{Z^{+}}

SzB

Covariance matrix of units for the next layer given y Σ_{Z^{+}|y}

Czp

Covariance matrix between units and parameters for the current layer Σ_{θ Z^{+}}

mzB

Mean vector of units for the next layer given y μ_{Z^{+}|y}

idx

Indices for the parameter update step of the current layer

Details

f(\boldsymbol{θ}|\boldsymbol{y}) = \mathcal{N}(\boldsymbol{θ};\boldsymbol{μ_{θ|y}},\boldsymbol{Σ_{θ|y}}) where

\boldsymbol{μ_{θ|y}} =\boldsymbol{μ_{θ}} + \boldsymbol{J_{θ}}(\boldsymbol{μ_{Z^{+}|y}} - \boldsymbol{μ_{Z^{+}}})

\boldsymbol{Σ_{θ|y}} = \boldsymbol{Σ_{θ}} + \boldsymbol{J_{θ}}(\boldsymbol{Σ_{Z^{+}|y}} - \boldsymbol{Σ_{Z^{+}}})\boldsymbol{J_{θ}^{T}}

\boldsymbol{J_{θ}} = \boldsymbol{Σ_{θ Z^{+}}}\boldsymbol{Σ^{-1}_{Z^{+}}}

Value


mgoulet847/tagi documentation built on Dec. 21, 2021, 5:10 p.m.