pi-vae-pytorch

A Pytorch implementation of Poisson Identifiable VAE (pi-VAE).

View the Project on GitHub

Poisson Identifiable VAE (pi-VAE)

This is a Pytorch implementation of Poisson Identifiable VAE (pi-VAE), used to construct latent variable models of neural activity while simultaneously modeling the relation between the latent and task variables (non-neural variables, e.g. sensory, motor, and other externally observable states).

The original implementation by Ding Zhou and Xue-Xin Wei in Tensorflow 1.13 is available here.

Another Pytorch implementation by Lyndon Duong is available here.

A special thank you to Zhongxuan Wu who helped in the design and testing of this implementation.

Install

pip install pi-vae-pytorch

From Source

For those interested in modifying and testing the codebase, using an editable pip installation is recommended:

# pi-vae-pytorch/

pip install -e .

Model Architecture

pi-VAE is comprised of three main components: the encoder, the label prior estimator, and the decoder.

MLP Structure

The Multi Layer Perceptron (MLP) is the primary building block of the aforementioned components. Each MLP used in this implementation is configurable by specifying the appropriate parameters when PiVAE is initialized:

Encoder

The model’s encoder is comprised of a single MLP, which learns the distribution q(z | x).

Label Prior Estimator

The model’s label prior estimator learns the distribution p(z | u). In the discrete label regime this module is comprised of two nn.Embedding submodules, while in the continuous label regime the module is comprised of a single MLP.

Decoder

The model’s decoder learns to map a latent sample z to its predicted firing rate in the model’s observation space. Inputs to the decoder are passed through the following submodules.

NFlowLayer

This module is comprised of a MLP which maps z to the concatenation of z and t(z).

GINBlock

Outputs from the NFlowLayer are passed to a series of GINBlock modules. Each GINBlock is comprised of a specified number of AffineCouplingLayer modules. Each AffineCouplingLayer is comprised of a MLP and performs an affine coupling transformation.

Initialization

pi_vae_pytorch.PiVAE(
    x_dim,
    u_dim,
    z_dim,
    discrete_labels=True,
    encoder_n_hidden_layers=2,
    encoder_hidden_layer_dim=128,
    encoder_hidden_layer_activation=nn.Tanh,
    decoder_n_gin_blocks=2,
    decoder_gin_block_depth=2,
    decoder_affine_input_layer_slice_dim=None,
    decoder_affine_n_hidden_layers=2,
    decoder_affine_hidden_layer_dim=None,
    decoder_affine_hidden_layer_activation=nn.ReLU,
    decoder_nflow_n_hidden_layers=2,
    decoder_nflow_hidden_layer_dim=None,
    decoder_nflow_hidden_layer_activation=nn.ReLU,
    decoder_observation_model='poisson',
    decoder_fr_clamp_min=1E-7,
    decoder_fr_clamp_max=1E7,
    z_prior_n_hidden_layers=2,
    z_prior_hidden_layer_dim=32,
    z_prior_hidden_layer_activation=nn.Tanh)

Attributes

Basic operation

For every observation space sample x and associated label u provided to pi-VAE’s forward method, the encoder and label statistics (mean & log of variance) are obtained from the encoder and label prior modules. These values are used to obtain the same statistics from the full posterior q(z | x,u).

The reparameterization trick is performed with the resulting mean & log of variance to obtain the sample’s representation in the model’s latent space. This latent representation is then passed to the model’s decoder module, which generates the predicted firing rate in the model’s observation space.

Inputs

Outputs

A dict with the following items:

Inference Mode

A dict with the following items:

Examples

Continuous Labels

import torch
from pi_vae_pytorch import PiVAE

model = PiVAE(
    x_dim = 100,
    u_dim = 3,
    z_dim = 2,
    discrete_labels=False
)

x = torch.randn(1, 100) # Size([n_samples, x_dim])

u = torch.randn(1, 3) # Size([n_samples, u_dim])

outputs = model(x, u) # dict

Discrete Labels

import torch
from pi_vae_pytorch import PiVAE

model = PiVAE(
    x_dim = 100,
    u_dim = 3,
    z_dim = 2,
    discrete_labels=True
)

x = torch.randn(1, 100) # Size([n_samples, x_dim])

u = torch.randint(u_dim, (1,)) # Size([n_samples])

outputs = model(x, u) # dict

Class Methods

Loss Function - ELBOLoss

pi-VAE learns the deep generative model and the approximate posterior q(z | x, u) of the true posterior p(z | x, u) by maximizing the evidence lower bound (ELBO) of p(x | u). This loss function is implemented in the included ELBOLoss class.

Parameters

Inputs

Examples

Poisson observation model

from pi_vae_pytorch import ELBOLoss

loss_fn = ELBOLoss()

outputs = model(x, u) # Initialized with decoder_observation_model='poisson'

loss = loss_fn(
    x=x,
    firing_rate=outputs['firing_rate'],
    lambda_mean=outputs['lambda_mean'],
    lambda_log_variance=outputs['lambda_log_variance'],
    posterior_mean=outputs['posterior_mean'],
    posterior_log_variance=outputs['posterior_log_variance']
)

loss.backward()

Gaussian observation model

import torch
from pi_vae_pytorch import ELBOLoss

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

model = model.to(device) # Initialized with decoder_observation_model='gaussian'

loss_fn = ELBOLoss(observation_model='gaussian', device=device)

outputs = model(x, u) 

loss = loss_fn(
    x=x,
    firing_rate=outputs['firing_rate'],
    lambda_mean=outputs['lambda_mean'],
    lambda_log_variance=outputs['lambda_log_variance'],
    posterior_mean=outputs['posterior_mean'],
    posterior_log_variance=outputs['posterior_log_variance'],
    observation_noise_model=model.observation_noise_model
)

loss.backward()

Citation

@misc{zhou2020learning,
    title={Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE}, 
    author={Ding Zhou and Xue-Xin Wei},
    year={2020},
    eprint={2011.04798},
    archivePrefix={arXiv},
    primaryClass={stat.ML}
}