Bayesian machine learning notebooks

This repository is a collection of notebooks about Bayesian Machine Learning. The following links display some of the notebooks via nbviewer to ensure a proper rendering of formulas.

• Bayesian regression with linear basis function models. Introduction to Bayesian linear regression. Implementation from scratch with plain NumPy as well as usage of scikit-learn for comparison. See also PyMC4 implementation and PyMC3 implementation.

• Gaussian processes. Introduction to Gaussian processes for regression. Example implementations with plain NumPy/SciPy as well as with libraries scikit-learn and GPy (requirements.txt).

• Gaussian processes for classification. Introduction to Gaussian processes for classification. Example implementations with plain NumPy/SciPy as well as with scikit-learn (requirements.txt).

• Bayesian optimization. Introduction to Bayesian optimization. Example implementations with plain NumPy/SciPy as well as with libraries scikit-optimize and GPyOpt. Hyper-parameter tuning as application example.

• Variational inference in Bayesian neural networks. Demonstrates how to implement a Bayesian neural network and variational inference of network parameters. Example implementation with Keras (requirements.txt). See also PyMC4 implementation.

• Reliable uncertainty estimates for neural network predictions. Uses noise contrastive priors in Bayesian neural networks to get more reliable uncertainty estimates for OOD data. Implemented with Tensorflow 2 and Tensorflow Probability (requirements.txt).

• Latent variable models, part 1: Gaussian mixture models and the EM algorithm. Introduction to the expectation maximization (EM) algorithm and its application to Gaussian mixture models. Example implementation with plain NumPy/SciPy and scikit-learn for comparison. See also PyMC3 implementation.

• Latent variable models, part 2: Stochastic variational inference and variational autoencoders. Introduction to stochastic variational inference with variational autoencoder as application example. Implementation with Tensorflow 2.x.

• Deep feature consistent variational autoencoder. Describes how a perceptual loss can improve the quality of images generated by a variational autoencoder. Example implementation with Keras.

• Conditional generation via Bayesian optimization in latent space. Describes an approach for conditionally generating outputs with desired properties by doing Bayesian optimization in latent space learned by a variational autoencoder. Example application implemented with Keras and GPyOpt.