beta-VAE objective with an optional capacity target

L = E_q[log p(x|z)] - beta D_KL(q||p) with D_KL = 0.5 sum_j (mu_j^2 + sigma_j^2 - 1 - log sigma_j^2); the capacity variant uses gamma |D_KL - C| in place of beta D_KL.

Usage

Betavae(
  x,
  xhat,
  mu,
  logvar,
  beta = 4,
  capacity = NULL,
  gamma = NULL,
  noisevar = 1
)

Arguments

x

Observation.

xhat

Decoder mean.

mu

Posterior means.

logvar

Posterior log variances.

beta

Weight on the divergence.

capacity

Target C, or NULL.

gamma

Weight on |D_KL - C|; NULL reuses beta.

noisevar

Decoder variance, strictly positive.

Value

List with objective, recon, kl, klper, penalty, beta, J, d.

References

Higgins et al. (2017), ICLR; capacity form from Burgess et al. (2018), arXiv:1804.03599; Gaussian KL from Kingma and Welling (2014), Appendix B. Standard published form.

Examples

Betavae(x = c(1, 2, 3, 4, 5, 6, 7, 8), xhat = c(1, 2, 3, 4, 5, 6, 7, 8),
  mu = c(1, 2, 3, 4, 5, 6, 7, 8), logvar = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $objective
#> [1] -9755.8
#> 
#> $recon
#> [1] -7.351508
#> 
#> $kl
#> [1] 2437.112
#> 
#> $klper
#> [1]    0.8591409    4.1945280   12.5427685   32.7990750   83.7065796
#> [6]  216.2143967  568.8165792 1517.9789935
#> 
#> $penalty
#> [1] 9748.448
#> 
#> $beta
#> [1] 4
#> 
#> $J
#> [1] 8
#> 
#> $d
#> [1] 8
#> 
#> $method
#> [1] "beta-VAE objective (Higgins et al. 2017)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"