Reparameterization trick (Geron Ch 17, morie.fn grrep)

z = mu + exp(0.5 logvar) eps; the 0.5 is load-bearing. The LCG normal stream here CLAMPS u1 at 1e-12 before the log, unlike the grhei / grgrp / grdpmf streams, and always fills whole Box-Muller pairs.

Usage

morie_geron_reparameterization_trick(mu, logvar, eps = NULL, seed = 42)

Arguments

mu, logvar

Same-shaped numeric objects.

eps

Optional noise; otherwise LCG normals.

seed

LCG seed.

Value

List with z, sigma, eps, dz_dmu, dz_dlogvar, sample_mean, sample_variance.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_geron_reparameterization_trick(V, V)
#> $z
#> [1]  3.327226  4.372061  3.806142 11.630776 21.826247 10.512573 37.898967
#> [8] 54.920096
#> 
#> $sigma
#> [1]  1.648721  2.718282  4.481689  7.389056 12.182494 20.085537 33.115452
#> [8] 54.598150
#> 
#> $eps
#> [1] 1.4115336 0.8726326 0.1798745 1.0327133 1.3811824 0.2246678 0.9330679
#> [8] 0.8593715
#> 
#> $dz_dmu
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $dz_dlogvar
#> [1]  1.1636128  1.1860306  0.4030708  3.8153882  8.4131234  2.2562866 15.4494834
#> [8] 23.4600478
#> 
#> $sample_mean
#> [1] 0.8618805
#> 
#> $sample_variance
#> [1] 0.1846673
#> 
#> $estimate
#> [1]  3.327226  4.372061  3.806142 11.630776 21.826247 10.512573 37.898967
#> [8] 54.920096
#> 
#> $n
#> [1] 8
#>