Table 4:

Training Timings per Epoch (in minutes) and Disentanglement Scores (Heusel et al., 2017) for Different Variants of RKM When Trained on the mini-3Dshapes Data Set.

St-RKM ($σ=0$)Gen-RKMAE-PCA
Training time  3.01 (0.71) 9.21 (0.54) 2.87 (0.33)
Disentanglement score Lasso 0.40 (0.02) 0.44 (0.01) 0.35 (0.01)
RF 0.27 (0.01) 0.31 (0.02) 0.22 (0.02)
Compliance score Lasso 0.64 (0.01) 0.51 (0.01) 0.42 (0.01)
RF 0.67 (0.02) 0.58 (0.01) 0.45 (0.02)
Information score Lasso 1.01 (0.02) 1.11 (0.02) 1.20 (0.01)
RF 0.98 (0.01) 1.09 (0.01) 1.17 (0.02)
St-RKM ($σ=0$)Gen-RKMAE-PCA
Training time  3.01 (0.71) 9.21 (0.54) 2.87 (0.33)
Disentanglement score Lasso 0.40 (0.02) 0.44 (0.01) 0.35 (0.01)
RF 0.27 (0.01) 0.31 (0.02) 0.22 (0.02)
Compliance score Lasso 0.64 (0.01) 0.51 (0.01) 0.42 (0.01)
RF 0.67 (0.02) 0.58 (0.01) 0.45 (0.02)
Information score Lasso 1.01 (0.02) 1.11 (0.02) 1.20 (0.01)
RF 0.98 (0.01) 1.09 (0.01) 1.17 (0.02)

Notes: Gen-RKM has the worst training time but gets the highest disentanglement scores. This is due to the exact eigendecomposition of the kernel matrix at every iteration. This computationally expensive step is approximated by the St-RKM model, which achieves significant speed-up and scalability to large data sets. Finally, the AE-PCA model has the fastest training time due to the absence of eigendecompositions in the training loop. However, using PCA in the postprocessing step alters the basis of the latent space. This basis is unknown to the decoder network, resulting in degraded disentanglement performance.

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