ConcreteDropout

Concrete Dropout updated implementation for Tensorflow 2.0 and PyTorch, following the original code from the paper.

Installation

To install this package, please use:

pip install concretedropout

Introduction

Concrete dropout allows for the dropout probability of a layer to become a trainable parameter. For more information, see the original paper: https://arxiv.org/abs/1705.07832

This package implements Concrete Dropout for the following layers: Tensorflow:

• Dense - tensorflow.ConcreteDenseDropout
• Conv1D - tensorflow.ConcreteSpatialDropout1D
• Conv2D - tensorflow.ConcreteSpatialDropout2D
• Conv3D - tensorflow.ConcreteSpatialDropout3D
• DepthwiseConv1D - tensorflow.ConcreteSpatialDropoutDepthwise1D
• DepthwiseConv2D - tensorflow.ConcreteSpatialDropoutDepthwise2D

PyTorch:

• Linear - pytorch.ConcreteLinearDropout
• Conv1d - pytorch.ConcreteDropout1d
• Conv2d - pytorch.ConcreteDropout2d
• Conv3d - pytorch.ConcreteDropout3d

Please notice that the dropout layer will be applied before the chosen layer.

Arguments

Each concrete dropout layer supports the following arguments:

• layer: an instance of the layer to which concrete dropout will be applied. Only required for Tensorflow.
• weight_regularizer=1e-6: A positive number which satisfies weight_regularizer = $l^2 / (\tau * N)$ with prior lengthscale l, model precision τ (inverse observation noise), and N the number of instances in the dataset. Note that kernel_regularizer is not needed. The appropriate weight_regularizer value can be computed with the utility function get_weight_regularizer(N, l, tau)
• dropout_regularizer=1e-5: A positive number which satisfies dropout_regularizer = $2 / (\tau * N)$ with model precision τ (inverse observation noise) and N the number of instances in the dataset. Note the relation between dropout_regularizer and weight_regularizer: weight_regularizer / dropout_regularizer = $l^2 / 2$ with prior lengthscale l. Note also that the factor of two should be ignored for cross-entropy loss, and used only for the eculedian loss. The appropriate dropout_regularizer value can be computed with the utility function get_dropout_regularizer(N, tau, cross_entropy_loss=False). By default, a regression problem will be assumed.
• init_min=0.1: minimum value for the random initial dropout probability
• init_max=0.1: maximum value for the random initial dropout probability
• is_mc_dropout=False: enables Monte Carlo Dropout (i.e. dropout will remain active also at prediction time). Default: False.
• data_format=None: channels_last or channels_first (only for Tensorflow). Defaults to channels_last for Tensorflow. PyTorch defaults to channel_first.
• temperature: temperature of the concrete distribution. For more information see arXiv:1611.00712. Defaults to 0.1 for dense layers, and 2/3 for convolution layers.

Example

The suggested way to employ concrete dropout layers is the following. Tensorflow:

import tensorflow as tf
from concretedropout.tensorflow import ConcreteDenseDropout, get_weight_regularizer, get_dropout_regularizer 

#... import the dataset
Ns = x_train.shape[0]
# get the regularizers
wr = get_weight_regularizer(Ns, l=1e-2, tau=1.0) # tau is the inverse 
dr = get_dropout_regularizer(Ns, tau=1.0, cross_entropy_loss=True)

# ... a neural network with output x
dense1 = tf.keras.layers.Dense(N_neurons)
x = ConcreteDenseDropout(dense1, weight_regularizer=wr, dropout_regularizer=dr)(x)

PyTorch:

import torch 
from concretedropout.pytorch import ConcreteDropout, ConcreteLinearDropout, get_weight_regularizer, get_dropout_regularizer

#... import the dataset
Ns = x_train.shape[0]
# get the regularizers
wr = get_weight_regularizer(Ns, l=1e-2, tau=1.0) # tau is the inverse 
dr = get_dropout_regularizer(Ns, tau=1.0, cross_entropy_loss=True)

# ... a neural network with output x
linear = torch.nn.Linear(n_input, N_neurons)
x = ConcreteLinearDropout(weight_regularizer=wr, dropout_regularizer=dr)(x, linear)

# inside the train step of your model, you need to add a new regularization term, which is due to the concrete dropout:
def training_step(self, batch, batch_nb):
    x, y = batch
    output = self(x)
    
    reg = torch.zeros(1) # get the regularization term
    for module in filter(lambda x: isinstance(x, ConcreteDropout), self.modules()):
        reg += module.regularization

    loss = self.loss(output, y) + reg # add the reg term
    return loss

For a practical example on how to use concrete dropout for the mnist dataset, see this Tensorflow example and this PyTorch example.

Bayesian neural network with MCDropout

You can find here an example on how to use MCDropout and Concrete Dropout to implement a Bayesian Neural Network with MCDropout on Tensorflow. For more information, see arXiv:1506.02142.

Known issues

Due to the way the additional dropout loss term is added to the main loss term, during training and evaluation the model loss might become a negative number. This has no impact on the actual optimisation of the model. If you desire to track your loss function separately, as a work around it is advised to add it to the list of metrics.

Aknowledgements

This library stems from a research project supported with Cloud TPUs from Google's TPU Research Cloud (TRC).