Table 1.

Compression factors of PCA versus VAE

ModelsPopulations
Type|z|αEuropean (EUR)East Asian (EAS)Native American (AMR)South Asian (SAS)African (AFR)Oceanian (OCE)West Asian (WAS)
PCA2–×0.41×0.38×0.42×0.39×0.33×0.36×0.38
VAE10−4×0.68×0.64×0.76×0.62×0.53×0.50×0.67
10−5×0.65×0.61×0.73×0.60×0.52×0.49×0.63
PCA4–×0.41×0.37×0.41×0.38×0.33×0.36×0.38
VAE10−4×0.77×0.69×0.87×0.68×0.56×0.58×0.71
10−5×0.73×0.69×0.81×0.66×0.54×0.63×0.68
PCA8–×0.41×0.37×0.41×0.38×0.33×0.36×0.37
VAE10−4×1.00×0.93×1.17×0.88×0.63×0.68×0.89
10−5×0.96×0.90×1.08×0.88×0.63×0.74×0.88
PCA16–×0.40×0.36×0.41×0.38×0.32×0.35×0.37
VAE10−4×1.59×1.39×1.73×1.32×0.84×1.01×1.37
10−5×1.25×1.12×1.35×1.04×0.70×0.90×1.08
PCA32–×0.39×0.36×0.40×0.37×0.32×0.34×0.36
VAE10−4×2.00×1.75×2.33×1.69×1.03×1.27×1.72
10−5×1.67×1.45×1.85×1.39×1.85×1.23×1.28
PCA64–×0.37×0.34×0.38×0.35×0.31×0.33×0.34
VAE10−4×2.04×1.82×2.27×1.75×1.16×1.47×1.82
10−5×1.69×1.54×1.96×1.47×0.96×1.30×1.49
PCA128–×0.34×0.32×0.35×0.32×0.29×0.30×0.32
VAE10−4×1.54×1.45×1.61×1.41×1.06×1.25×1.43
10−5×1.47×1.37×1.56×1.35×0.97×1.20×1.37
PCA256–×0.30×0.28×0.30×0.28×0.25×0.27×0.28
VAE10−4×0.97×0.93×1.00×0.93×0.79×0.86×0.93
10−5×0.94×0.90×0.97×0.89×0.73×0.84×0.90
PCA512–×0.24×0.23×0.24×0.23×0.21×0.22×0.23
VAE10−4×0.54×0.53×0.55×0.53×0.48×0.50×0.53
10−5×0.53×0.52×0.54×0.51×0.45×0.49×0.52

[i] The compression factors are computed as ℓ(x)/(ℓ(z)+ℓ(A(r))) using test data. A compression ratio of 1 corresponds to the identity, and values <1 and >1 correspond to compression and expansion, respectively. VAEs with a bottleneck of 32, 64, and 128 latent factors are capable of lossless compression of all human populations. Successful compression is marked in bold. |z| is the number of latent factors and α stands for learning rate.