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Reference implementation for a variational autoencoder in TensorFlow and PyTorch.
I recommend the PyTorch version. It includes an example of a more expressive variational family, the inverse autoregressive flow.
Variational inference is used to fit the model to binarized MNIST handwritten digits images. An inference network (encoder) is used to amortize the inference and share parameters across datapoints. The likelihood is parameterized by a generative network (decoder).
Blog post: https://jaan.io/what-is-variational-autoencoder-vae-tutorial/
Example output with importance sampling for estimating the marginal likelihood on Hugo Larochelle's Binary MNIST dataset. Finaly marginal likelihood on the test set of -97.10 nats.
$ python train_variational_autoencoder_pytorch.py --variational mean-field
step: 0 train elbo: -558.69
step: 0 valid elbo: -391.84 valid log p(x): -363.25
step: 5000 train elbo: -116.09
step: 5000 valid elbo: -112.57 valid log p(x): -107.01
step: 10000 train elbo: -105.82
step: 10000 valid elbo: -108.49 valid log p(x): -102.62
step: 15000 train elbo: -106.78
step: 15000 valid elbo: -106.97 valid log p(x): -100.97
step: 20000 train elbo: -108.43
step: 20000 valid elbo: -106.23 valid log p(x): -100.04
step: 25000 train elbo: -99.68
step: 25000 valid elbo: -104.89 valid log p(x): -98.83
step: 30000 train elbo: -96.71
step: 30000 valid elbo: -104.50 valid log p(x): -98.34
step: 35000 train elbo: -98.64
step: 35000 valid elbo: -104.05 valid log p(x): -97.87
step: 40000 train elbo: -93.60
step: 40000 valid elbo: -104.10 valid log p(x): -97.68
step: 45000 train elbo: -96.45
step: 45000 valid elbo: -104.58 valid log p(x): -97.76
step: 50000 train elbo: -101.63
step: 50000 valid elbo: -104.72 valid log p(x): -97.81
step: 55000 train elbo: -106.78
step: 55000 valid elbo: -105.14 valid log p(x): -98.06
step: 60000 train elbo: -100.58
step: 60000 valid elbo: -104.13 valid log p(x): -97.30
step: 65000 train elbo: -96.19
step: 65000 valid elbo: -104.46 valid log p(x): -97.43
step: 65000 test elbo: -103.31 test log p(x): -97.10
Using a non mean-field, more expressive variational posterior approximation (inverse autoregressive flow, https://arxiv.org/abs/1606.04934), the test marginal log-likelihood improves to -95.33 nats:
$ python train_variational_autoencoder_pytorch.py --variational flow
step: 0 train elbo: -578.35
step: 0 valid elbo: -407.06 valid log p(x): -367.88
step: 10000 train elbo: -106.63
step: 10000 valid elbo: -110.12 valid log p(x): -104.00
step: 20000 train elbo: -101.51
step: 20000 valid elbo: -105.02 valid log p(x): -99.11
step: 30000 train elbo: -98.70
step: 30000 valid elbo: -103.76 valid log p(x): -97.71
step: 40000 train elbo: -104.31
step: 40000 valid elbo: -103.71 valid log p(x): -97.27
step: 50000 train elbo: -97.20
step: 50000 valid elbo: -102.97 valid log p(x): -96.60
step: 60000 train elbo: -97.50
step: 60000 valid elbo: -102.82 valid log p(x): -96.49
step: 70000 train elbo: -94.68
step: 70000 valid elbo: -102.63 valid log p(x): -96.22
step: 80000 train elbo: -92.86
step: 80000 valid elbo: -102.53 valid log p(x): -96.09
step: 90000 train elbo: -93.83
step: 90000 valid elbo: -102.33 valid log p(x): -96.00
step: 100000 train elbo: -93.91
step: 100000 valid elbo: -102.48 valid log p(x): -95.92
step: 110000 train elbo: -94.34
step: 110000 valid elbo: -102.81 valid log p(x): -96.09
step: 120000 train elbo: -88.63
step: 120000 valid elbo: -102.53 valid log p(x): -95.80
step: 130000 train elbo: -96.61
step: 130000 valid elbo: -103.56 valid log p(x): -96.26
step: 140000 train elbo: -94.92
step: 140000 valid elbo: -102.81 valid log p(x): -95.86
step: 150000 train elbo: -97.84
step: 150000 valid elbo: -103.06 valid log p(x): -95.92
step: 150000 test elbo: -101.64 test log p(x): -95.33
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