Table 1.
Compression factors of PCA versus VAE
| Models | Populations | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Type | |z| | α | European (EUR) | East Asian (EAS) | Native American (AMR) | South Asian (SAS) | African (AFR) | Oceanian (OCE) | West Asian (WAS) |
| PCA | 2 | – | ×0.41 | ×0.38 | ×0.42 | ×0.39 | ×0.33 | ×0.36 | ×0.38 |
| VAE | 10−4 | ×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 | ||
| PCA | 4 | – | ×0.41 | ×0.37 | ×0.41 | ×0.38 | ×0.33 | ×0.36 | ×0.38 |
| VAE | 10−4 | ×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 | ||
| PCA | 8 | – | ×0.41 | ×0.37 | ×0.41 | ×0.38 | ×0.33 | ×0.36 | ×0.37 |
| VAE | 10−4 | ×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 | ||
| PCA | 16 | – | ×0.40 | ×0.36 | ×0.41 | ×0.38 | ×0.32 | ×0.35 | ×0.37 |
| VAE | 10−4 | ×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 | ||
| PCA | 32 | – | ×0.39 | ×0.36 | ×0.40 | ×0.37 | ×0.32 | ×0.34 | ×0.36 |
| VAE | 10−4 | ×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 | ||
| PCA | 64 | – | ×0.37 | ×0.34 | ×0.38 | ×0.35 | ×0.31 | ×0.33 | ×0.34 |
| VAE | 10−4 | ×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 | ||
| PCA | 128 | – | ×0.34 | ×0.32 | ×0.35 | ×0.32 | ×0.29 | ×0.30 | ×0.32 |
| VAE | 10−4 | ×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 | ||
| PCA | 256 | – | ×0.30 | ×0.28 | ×0.30 | ×0.28 | ×0.25 | ×0.27 | ×0.28 |
| VAE | 10−4 | ×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 | ||
| PCA | 512 | – | ×0.24 | ×0.23 | ×0.24 | ×0.23 | ×0.21 | ×0.22 | ×0.23 |
| VAE | 10−4 | ×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 | ||
-
The compression factors are computed as
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.
