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Pytorch implementations of density estimation algorithms: BNAF, Glow, MAF, RealNVP, planar flows

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Reimplementations of density estimation algorithms from: * Block Neural Autoregressive Flow * Glow: Generative Flow with Invertible 1×1 Convolutions * Masked Autoregressive Flow for Density Estimation * Density Estimation using RealNVP * Variational Inference with Normalizing Flows

https://arxiv.org/abs/1904.04676

Implementation of BNAF on toy density estimation datasets.

Density estimation of 2d toy data and density estimation of 2d test energy potentials (cf. Figure 2 & 3 in paper):

The models were trained for 20,000 steps with the architectures and hyperparameters described in the Section 5 of the paper, with the exception of

ringsdataset (bottom right) which had 5 hidden layers. The models trained significantly faster than the planar flow model in Rezende & Mohamed and were much more stable; interestingly, BNAF stretches space differently and requires a lot more test points to show a smooth potential.

| Density matching on 2d energy potentials | Density estimation on 2d toy data | | --- | --- | | | | | | | | | | | | |

To train model:

python bnaf.py --train --dataset # choice from u1, u2, u3, u4, 8gaussians, checkerboard, 2spirals --log_interval # how often to save the model and visualize results --n_steps # number of training steps --n_hidden # number of hidden layers --hidden_dim # dimension of the hidden layer --[add'l options]Additional options are: learning rate, learning rate decay and patience, cuda device id, batch_size.

To plot model:

python bnaf.py --plot --restore_file [path to .pt checkpoint]

- Official implementation by the authors https://github.com/nicola-decao/BNAF

https://arxiv.org/abs/1807.03039

Implementation of Glow on CelebA and MNIST datasets.

I trained two models: - Model A with 3 levels, 32 depth, 512 width (~74M parameters). Trained on 5 bit images, batch size of 16 per GPU over 100K iterations. - Model B with 3 levels, 24 depth, 256 width (~22M parameters). Trained on 4 bit images, batch size of 32 per GPU over 100K iterations.

In both cases, gradients were clipped at norm 50, learning rate was 1e-3 with linear warmup from 0 over 2 epochs. Both reached similar results and 4.2 bits/dim.

Temperatures ranging 0, 0.25, 0.5, 0.6, 0.7, 0.8, 0.9, 1 (rows, top to bottom):

| Model A | Model B | | --- | --- | | | |

| Model A | Model B | | --- | --- | | | |

Embedding vectors were calculated for the first 30K training images and positive / negative attributes were averaged then subtracting. The resulting

dzwas ranged and applied on a test set image (middle image represents the unchanged / actual data point).

| Attribute |

dzrange [-2, -1, 0, 1, 2] | | --- | --- | | Brown hair | | | Male | | | Mouth slightly opened | | | Young | |

| Attribute |

dzrange | | --- | --- | | Brown hair | | | Mouth slightly opened | |

To train a model using pytorch distributed package:

python -m torch.distributed.launch --nproc_per_node=NUM_GPUS_YOU_HAVE \ glow.py --train \ --distributed \ --dataset=celeba \ --data_dir=[path to data source] \ --n_levels=3 \ --depth=32 \ --width=512 \ --batch_size=16 [this is per GPU]For larger models or image sizes add

--checkpoint_gradsto checkpoint gradients using pytorch's library. I trained a 3 layer / 32 depth / 512 width model with batch size of 16 without gradient checkpointing and a 4 layer / 48 depth / 512 width model with batch size of 16 which had ~190M params so required gradient checkpointing (and was painfully slow on 8 GPUs).

To evaluate model:

python glow.py --evaluate \ --restore_file=[path to .pt checkpoint] \ --dataset=celeba \ --data_dir=[path to data source] \ --[options of the saved model: n_levels, depth, width, batch_size]

To generate samples from a trained model:

python glow.py --generate \ --restore_file=[path to .pt checkpoint] \ --dataset=celeba \ --data_dir=[path to data source] \ --[options of the saved model: n_levels, depth, width, batch_size] \ --z_std=[temperature parameter; if blank, generates range]

To visualize manipulations on specific image given a trained model:

python glow.py --visualize \ --restore_file=[path to .pt checkpoint] \ --dataset=celeba \ --data_dir=[path to data source] \ --[options of the saved model: n_levels, depth, width, batch_size] \ --z_std=[temperature parameter; if blank, uses default] \ --vis_attrs=[list of indices of attribute to be manipulated, if blank, manipulates every attribute] \ --vis_alphas=[list of values by which `dz` should be multiplied, defaults [-2,2]] \ --vis_img=[path to image to manipulate (note: size needs to match dataset); if blank uses example from test dataset]

To download CelebA follow the instructions here. A nice script that simplifies downloading and extracting can be found here: https://github.com/nperraud/download-celebA-HQ/

- Official implementation in Tensorflow: https://github.com/openai/glow

https://arxiv.org/abs/1705.07057

Reimplementation of MADE, MAF, Mixture of Gaussians MADE, Mixture of Gausssians MAF, and RealNVP modules on UCI datasets and MNIST.

Average test log likelihood for un/conditional density estimation (cf. Table 1 & 2 in paper for results and parameters; models here were trained for 50 epochs):

| Model | POWER | GAS | HEPMASS | MINIBOONE | BSDS300 | MNIST (uncond) | MNIST (cond) | | --- | --- | --- | --- | --- | --- | --- | --- | | MADE | -3.10 +/- 0.02 | 2.53 +/- 0.02 | -21.13 +/- 0.01 | -15.36 +/- 15.06 | 146.42 +/- 0.14 | -1393.67 +/- 1.90 | -1340.98 +/- 1.71 | | MADE MOG | 0.37 +/- 0.01 | 8.08 +/- 0.02 | -15.70 +/- 0.02 | -11.64 +/- 0.44 | 153.56 +/- 0.28 | -1023.13 +/- 1.69 | -1013.75 +/- 1.61 | | RealNVP (5) | -0.49 +/- 0.01 | 7.01 +/- 0.06 | -19.96 +/- 0.02 | -16.88 +/- 0.21 | 148.34 +/- 0.26 | -1279.76 +/- 9.91 | -1276.33 +/- 12.21 | | MAF (5) | 0.03 +/- 0.01 | 6.23 +/- 0.01 | -17.97 +/- 0.01 | -11.57 +/- 0.21 | 153.53 +/- 0.27 | -1272.70 +/- 1.87 | -1268.24 +/- 2.73 | | MAF MOG (5) | 0.09 +/- 0.01 | 7.96 +/- 0.02 | -17.29 +/- 0.02 | -11.27 +/- 0.41 | 153.35 +/- 0.26 | -1080.46 +/- 1.53 | -1070.33 +/- 1.53 |

Toy density model (cf. Figure 1 in paper):

| Target density | Learned density with MADE

and random numbers driving MADE | Learned density with MAF 5 layers

and random numbers driving MAF |
| --- | --- | --- |
| | | |

Class-conditional generated images from MNIST using MAF (5) model; generated data arrange by decreasing log probability (cf. Figure 3 in paper):

To train model:

python maf.py -- train \ -- model=['made' | 'mademog' | 'maf' | 'mafmog' | 'realnvp'] \ -- dataset=['POWER' | 'GAS' | 'HEPMASS' | 'MINIBOONE' | 'BSDS300' | MNIST'] \ -- n_blocks=[for maf/mafmog and realnvp specify # of MADE-blocks / coupling layers] \ -- n_components=[if mixture of Gaussians, specify # of components] \ -- conditional [if MNIST, can train class-conditional log likelihood] \ -- [add'l options see py file]

To evaluate model:

python maf.py -- evaluate \ -- restore_file=[path to .pt checkpoint] -- [options of the saved model: n_blocks, n_hidden, hidden_size, n_components, conditional]

To generate data from a trained model (for MNIST dataset):

python maf.py -- generate \ -- restore_file=[path to .pt checkpoint] -- dataset='MNIST' -- [options of the saved model: n_blocks, n_hidden, hidden_size, n_components, conditional]

Datasets and preprocessing code are forked from the MAF authors' implementation here. The unzipped datasets should be symlinked into the

./datafolder or the data_dir argument should be specified to point to the actual data.

- The original Theano implementation by the authors https://github.com/gpapamak/maf/
- https://github.com/ikostrikov/pytorch-flows

Implementation of Variational Inference with Normalizing Flows

Density estimation of 2-d test energy potentials (cf. Table 1 & Figure 3 in paper).

| Target density | Flow K = 2 | Flow K = 32 | Training parameters | | --- | --- | --- | --- | | | | | weight init Normal(0,1), base dist. scale 2 | | | | | weight init Normal(0,1), base dist. scale 1 | | | | | weight init Normal(0,1), base dist. scale 1, weight decay 1e-3 | | | | | weight init Normal(0,1), base dist. scale 4, weight decay 1e-3 |

To train model:

python planar_flow.py -- train \ -- target_potential=[choice from u_z1 | u_z2 | u_z3 | u_z4] \ -- flow_length=[# of layers in flow] \ -- [add'l options]Additional options are: base distribution (q0) scale, weight initialization scale, weight decay, learnable first affine layer (I did not find adding an affine layer beneficial).

To evaluate model:

python planar_flow.py -- evaluate \ -- restore_file=[path to .pt checkpoint]

- https://github.com/casperkaae/parmesan/issues/22

- python 3.6
- pytorch 1.0
- numpy
- matplotlib
- tensorboardX

- pandas
- sklearn
- h5py