Evidential Deep Learning in PyTorch

Implementation of Evidential Deep Learning to Quantify Classification Uncertainty and Deep Evidential Regression, a deterministic method for quantifying uncertainty for neural network models.

Install

pip install edl_pytorch

Usage

See examples/mnist.py and examples/cubic.py for examples of classification/regression respectively, producing the figures above.

For classification, use the Dirichlet layer as the final layer in the model and evidential_classification loss:

import torch
from torch import nn
from edl_pytorch import Dirichlet, evidential_classification

model = nn.Sequential(
    nn.Linear(2, 16),  # two input dim
    nn.ReLU(),
    Dirichlet(16, 2),  # two output classes
)

x = torch.randn(1, 2)  # (batch, dim)
y = torch.randint(0, 2, (1, 1))

pred_dirchlet = model(x)  # (1, 2)

loss = evidential_classification(
    pred_dirchlet, # predicted Dirichlet parameters
    y,             # target labels
    lamb=0.001,    # regularization coefficient 
)

For regression, use the NormalInvGamma layer as the final layer in the model and evidential_regression loss:

import torch
from torch import nn
from edl_pytorch import NormalInvGamma, evidential_regression

model = nn.Sequential(
    nn.Linear(1, 16),  # one input dim
    nn.ReLU(),
    NormalInvGamma(16, 1),  # one target variable
)

x = torch.randn(1, 1)  # (batch, dim)
y = torch.randn(1, 1)

pred_nig = model(x)  # (mu, v, alpha, beta)

loss = evidential_regression(
    pred_nig,      # predicted Normal Inverse Gamma parameters
    y,             # target labels
    lamb=0.001,    # regularization coefficient 
)

See Also

• https://muratsensoy.github.io/uncertainty.html, original code for Evidential Deep Learning to Quantify Classification Uncertainty in Tensorflow
• aamini/evidential-deep-learning, original code for Deep Evidential Regression in Tensorflow/Keras

Todo

• add examples
• allow specification of evidence function, currently F.softplus

Citations

@article{sensoy2018evidential,
  title={Evidential deep learning to quantify classification uncertainty},
  author={Sensoy, Murat and Kaplan, Lance and Kandemir, Melih},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}

@article{amini2020deep,
  title={Deep evidential regression},
  author={Amini, Alexander and Schwarting, Wilko and Soleimany, Ava and Rus, Daniela},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={14927--14937},
  year={2020}
}