Update README.md

Author: Jaan Altosaar

README.md

@@ -6,3 +6,38 @@ I recommend the PyTorch version.
 Mean-field 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
+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
+```