forwardHiddenStateUpdate: Last hidden layer states update

In mgoulet847/tagi: Tractable Approximate Gaussian Inference in Neural Networks

Description

This function updates last hidden layer units using responses. It updates μ_{Z^{(0)}|y} and Σ_{Z^{(0)}|y} from the Z^{(0)}|y distribution.

Usage

forwardHiddenStateUpdate(mz, Sz, mzF, SzF, Cyz, y)

Arguments

mz	Mean vector of units for the last hidden layer μ_{X^{(0)}}
Sz	Covariance matrix of units for the last hidden layer Σ_{Z^{(0)}}
mzF	Mean vector of units for the output layer μ_{y}
SzF	Covariance matrix of tunits for the output layer Σ_{y}
Cyz	Covariance matrix between last hidden layer units and responses Σ_{YZ^{(0)}}
y	Response data

Details

f(\boldsymbol{z}^{(0)}|\boldsymbol{y}) = \mathcal{N}(\boldsymbol{z}^{(0)};\boldsymbol{μ_{Z^{(0)}|y}},\boldsymbol{Σ_{Z^{(0)}|y}}) where

\boldsymbol{μ_{{Z}^{(0)}|y}} = \boldsymbol{μ_{Z^{(0)}}} + \boldsymbol{Σ_{YZ^{(0)}}^{T}}\boldsymbol{Σ^{-1}_{Y}}(\boldsymbol{y} - \boldsymbol{μ_{Y}})

\boldsymbol{Σ_{{Z}^{(0)}|y}} = \boldsymbol{Σ_{Z^{(0)}}} - \boldsymbol{Σ_{YZ^{(0)}}^{T}}\boldsymbol{Σ^{-1}_{Y}}\boldsymbol{Σ_{YZ^{(0)}}}

Value

• Mean vector of last hidden layer units given y μ_{Z^{(0)}|y}

• Covariance matrix of last hidden layer units given y Σ_{Z^{(0)}|y}

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