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README.md

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- [Reliable uncertainty estimates for neural network predictions](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/noise-contrastive-priors/ncp.ipynb).
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Applies noise contrastive priors to Bayesian neural networks to get more reliable uncertainty estimates for OOD data.
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Implemented with Tensorflow 2 and Tensorflow Probability.
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Implemented with Tensorflow 2 and Tensorflow Probability ([requirements.txt](noise-contrastive-priors/requirements.txt)).
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- [Variational inference in Bayesian neural networks](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks.ipynb).
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Demonstrates how to implement a Bayesian neural network and variational inference of network parameters. Example implementation
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with Keras (see also
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[PyMC4 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks_pymc4.ipynb)).
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with Keras ([requirements.txt](bayesian-neural-networks/requirements.txt)). See also
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[PyMC4 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks_pymc4.ipynb).
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- [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_2.ipynb)
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[Latent variable models, part 2: Stochastic variational inference and variational autoencoders](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_2.ipynb).
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- [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_1.ipynb)
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[Latent variable models, part 1: Gaussian mixture models and the EM algorithm](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_1.ipynb).
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Introduction to the expectation maximization (EM) algorithm and its application to Gaussian mixture models. Example
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implementation with plain NumPy/SciPy and scikit-learn for comparison (see also
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[PyMC3 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_1_pymc3.ipynb)).
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implementation with plain NumPy/SciPy and scikit-learn for comparison. See also
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[PyMC3 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_1_pymc3.ipynb).
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- [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-optimization/bayesian_optimization.ipynb)
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[Bayesian optimization](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-optimization/bayesian_optimization.ipynb).
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- [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb)
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[Gaussian processes](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb).
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Introduction to Gaussian processes. Example implementations with plain NumPy/SciPy as well as with libraries
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scikit-learn and GPy.
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scikit-learn and GPy ([requirements.txt](gaussian-processes/requirements.txt)).
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- [Bayesian regression with linear basis function models](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-linear-regression/bayesian_linear_regression.ipynb).
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Introduction to Bayesian linear regression. Implementation from scratch with plain NumPy as well as usage of scikit-learn
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for comparison (see also
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for comparison. See also
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[PyMC4 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-linear-regression/bayesian_linear_regression_pymc4.ipynb) and
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[PyMC3 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-linear-regression/bayesian_linear_regression_pymc3.ipynb)).
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[PyMC3 implementation](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-linear-regression/bayesian_linear_regression_pymc3.ipynb).
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- [Deep feature consistent variational autoencoder](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/autoencoder-applications/variational_autoencoder_dfc.ipynb).
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Describes how a perceptual loss can improve the quality of images generated by a variational autoencoder. Example

bayesian-neural-networks/bayesian_neural_networks.ipynb

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"source": [
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"# Variational inference in Bayesian neural networks\n",
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"\n",
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"This article demonstrates how to implement and train a Bayesian neural network with Keras following the approach described in [Weight Uncertainty in Neural Networks](https://arxiv.org/abs/1505.05424) (*Bayes by Backprop*). The implementation is kept simple for illustration purposes and uses Keras 2.2.4 and Tensorflow 1.12.0 (see also [requirements.txt](requirements.txt)). For more advanced implementations of Bayesian methods for neural networks consider using [Tensorflow Probability](https://www.tensorflow.org/probability), for example.\n",
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"This article demonstrates how to implement and train a Bayesian neural network with Keras following the approach described in [Weight Uncertainty in Neural Networks](https://arxiv.org/abs/1505.05424) (*Bayes by Backprop*). The implementation is kept simple for illustration purposes and uses Keras 2.2.4 and Tensorflow 1.12.0. For more advanced implementations of Bayesian methods for neural networks consider using [Tensorflow Probability](https://www.tensorflow.org/probability), for example.\n",
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"\n",
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"Bayesian neural networks differ from plain neural networks in that their weights are assigned a probability distribution instead of a single value or point estimate. These probability distributions describe the uncertainty in weights and can be used to estimate uncertainty in predictions. Training a Bayesian neural network via variational inference learns the parameters of these distributions instead of the weights directly.\n",
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"\n",

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