Research map / Probabilistic and scientific modeling / Variational and generative sampling
Identifiability of deep generative models without auxiliary information
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a GMM latent prior and piecewise-affine decoder without observing auxiliary variables | Deep generative models with ReLU or leaky-ReLU decoders · Unsupervised identifiability | Identifiability | Helped |
| Require weak injectivity of the piecewise-affine decoder | GMM latent prior model · Latent distribution from observations | Identifiability up to affine transformation | Helped |
| Add conditional factorization and distinct component variance ratios | Deep generative model with discrete mixture state · Latent variables | Identifiability up to permutation, scaling, and translation | Helped |
| Add the stated maximality and neighborhood conditions on hidden variables | Multivariate discrete latent state U · Latent structure | Identifiability of U and its structure | Helped |
| Remove the weak-injectivity assumption on the decoder (ablation) | GMM latent prior model · Latent distribution from observations | Identifiability up to affine transformation | Hurt |
| Allow the decoder to be arbitrary instead of piecewise affine (ablation) | Deep generative model with GMM prior · Joint latent and decoder identification | Identifiability | Hurt |
| Allow the latent prior to be arbitrary instead of a GMM (ablation) | Piecewise-affine generative model · Joint latent and decoder identification | Identifiability | Hurt |
| Train VaDE repeatedly with different initializations | VaDE · Pinwheel, 3 clusters | weak MCC: 0.87 | Helped |
| Train VaDE repeatedly with different initializations | VaDE · Pinwheel, 3 clusters | dist_Aff,L2: 0.113 with standard deviation 0.065 | Helped |
| Use ReLU rather than LeakyReLU | MFCVAE · MNIST | strong MCC: 0.7 vs 0.69 | Mixed |
| Use ReLU rather than LeakyReLU | MFCVAE · MNIST | weak MCC: 0.91 vs 0.94 | Mixed |
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