We introduce Bayesian convolutional neural networks with variational inference, a variant of convolutional neural networks (CNNs), in which the intractable posterior probability distributions over weights are inferred by Bayes by Backprop. We demonstrate how our proposed variational inference method achieves performances equivalent to frequentist inference in identical architectures on several datasets (MNIST, CIFAR10, CIFAR100) as described in the paper.

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Filter weight distributions in a Bayesian Vs Frequentist approach

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Fully Bayesian perspective of an entire CNN

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Make your custom Bayesian Network?

To make a custom Bayesian Network, inherit layers.misc.ModuleWrapper instead of torch.nn.Module and use layers.BBBLinear.BBBLinear and layers.BBBConv.BBBConv2d instead of torch.nn.Conv2d and torch.nn.Linear. Moreover, no need to define forward method. It'll automatically be taken care of.

For example:

class Net(nn.Module):

  def __init__(self):
    super().__init__()
    self.conv = nn.Conv2d(3, 16, 5, strides=2)
    self.bn = nn.BatchNorm2d(16)
    self.relu = nn.ReLU()
    self.fc = nn.Linear(800, 10)

  def forward(self, x):
    x = self.conv(x)
    x = self.bn(x)
    x = self.relu(x)
    x = x.view(-1, 800)
    x = self.fc(x)
    return x

Above Network can be converted to Bayesian as follows:

class Net(ModuleWrapper):

  def __init__(self):
    super().__init__()
    self.conv = BBBConv2d(3, 16, 5, strides=2, alpha_shape=(1,1), name='conv')
    self.bn = nn.BatchNorm2d(16)
    self.relu = nn.ReLU()
    self.flatten = FlattenLayer(800)
    self.fc = BBBLinear(800, 10, alpha_shape=(1,1), name='fc')

Notes:

1. Add FlattenLayer before first BBBLinear block.
2. forward method of the model will return a tuple as (logits, kl).
3. Keyword argument name is optional and is required to use only when recording mean and variances in turned ON.

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How to perform standard experiments?

Currently, following datasets and models are supported.

• Datasets: MNIST, CIFAR10, CIFAR100
• Models: AlexNet, LeNet, 3Conv3FC

Bayesian

python main_bayesian.py

• set hyperparameters in config_bayesian.py

Frequentist

python main_frequentist.py

• set hyperparameters in config_frequentist.py

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Directory Structure:

layers/: Contains ModuleWrapper, FlattenLayer, Bayesian layers (BBBConv2d and BBBLinear).
models/BayesianModels/: Contains standard Bayesian models (BBBLeNet, BBBAlexNet, BBB3Conv3FC).
models/NonBayesianModels/: Contains standard Non-Bayesian models (LeNet, AlexNet).
checkpoints/: Checkpoint directory for the best model will be saved here.
tests/: Basic unittest cases for layers and models.
main_bayesian.py: Train and Evaluate Bayesian models.
config_bayesian.py: Hyperparameters for main_bayesian file.
main_frequentist.py: Train and Evaluate non-Bayesian (Frequentist) models.
config_frequentist.py: Hyperparameters for main_frequentist file.
visualize_mean_var.py: Plotting Distributions and Line graphs of mean and variances.

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Recording Mean and Variance:

If record_mean_var is True, then mean and variances for layers in record_layers list will be logged in checkpoints directory. Your can also specify recording frequency per epoch. All these mentioned parameters can be modified in config_bayesian.py.
Note that, the recording will only take place during the training phase of the model.

In order to visualize the recorded values, visualize_mean_var.py contains draw_distributions and draw_lineplot methods. Just pass the path for the log file, type of values (mean/variance) and the weight for which recording need to be visualized.

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Uncertainty Estimation:

There are two types of uncertainties: Aleatoric and Epistemic. Aleatoric uncertainty is a measure for the variation of data and Epistemic uncertainty is caused by the model.
Here, two methods are provided in utils.py i.e, calc_uncertainty_softmax and calc_uncertainty_normalized which are respectively based on equation 4 from this paper and equation 15 from this paper.
Also, a script uncertainty_estimation.py is provided which can be used to compare uncertainties by a Bayesian Neural Network on MNIST and notMNIST dataset. You can provide arguments like:

1. net_type: lenet, alexnet or 3conv3fc. Default is lenet.
2. weights_path: Weights for the given net_type. Default is 'checkpoints/MNIST/bayesian/model_lenet.pt'.
3. not_mnist_dir: Directory of notMNIST dataset. Default is 'data\'.
4. num_batches: Number of batches for which uncertainties need to be calculated.

Notes:

1. You need to download the notMNIST dataset from here.
2. The script uncertainty_estimation.py calculates average uncertainty over a mini-batch whereas, the calc_uncertainty_softmax and calc_uncertainty_normalized calculates uncertainty over a single input sample.

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If you are using this work, please cite:

@article{shridhar2019comprehensive,
  title={A comprehensive guide to bayesian convolutional neural network with variational inference},
  author={Shridhar, Kumar and Laumann, Felix and Liwicki, Marcus},
  journal={arXiv preprint arXiv:1901.02731},
  year={2019}
}

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