Research map / Probabilistic and scientific modeling / Variational and generative sampling
Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| include metric-space scale factor (Gx = a_x I) when estimating data probability from VAE objective (ablation) | VAE probability estimation on toy dataset · Toy dataset (downward-convex loss) | correlation with p(x): 0.771 -> around 0.91 | Helped |
| use VAE objective exp(-L_x/beta) instead of prior p(mu(x)) alone (ablation) | probability estimation on toy dataset · Toy dataset (downward-convex loss) | correlation with p(x): 0.434 -> 0.771 | Helped |
| use the explicit decomposed loss D(x,x̆)+D(x̆,x̂)+βD_KL during training on CelebA (ablation) | VAE isometricity · CelebA | mean of (2/β)σ²D' (isometric norm): 1.83 -> 0.92 | Helped |
| use vanilla VAE with single Gaussian prior for anomaly detection instead of GMM prior | VAE anomaly detection · KDDCup99 / KDDCup-rev | F1: KDDCup99 0.9642 vs RaDOGAGA(log(d)) 0.9638; KDDCup-rev 0.9880 vs 0.9865 | Helped |
| use vanilla VAE with single Gaussian prior for anomaly detection | VAE anomaly detection · Thyroid and Arrhythmia | F1: Thyroid 0.6596 vs RaDOGAGA(log(d)) 0.6702; Arrhythmia 0.4985 vs RaDOGAGA(d) 0.5433 | Mixed |
| VAE trained with square error loss, score exp(-L_x/beta) as probability estimate | toy dataset · Toy dataset (square error loss) | correlation with p(x) | Helped |
| Gaussian-data posterior variance/isometry analysis: no direct effect measured on ratio beyond orthogonality claims; transform loss ignored | VAE · Toy dataset | ratio D(x,x̆)/D(x̆,x̂): 0.023 (SSE) and 0.024 (downward-convex) | No clear effect |
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