Abstract: 

In this tutorial, I will give a gentle introduction to Gaussian Processes. Gaussian Processes are a non-parametric tool to model complex non-linear relationships from data by assuming a prior distribution over functions. Compared to many classical machine learning approaches, Gaussian Processes have two main advantages:
They require only learning a small set of parameters which may prevent over-fitting, and they endow all their predictions with uncertainties which is important in safety-critical applications.

Starting from Gaussian distributions and linear regression, we will derive Gaussian Process regression models. We will then continue to the function-space view where Gaussian Processes can be completely defined by their covariance function. The covariance function encodes all assumptions about the form of function by describing the similarity between the data points. Choosing an appropriate covariance function is therefore crucial for any successful Gaussian Process application. The tutorial will give guidelines on how to select the most appropriate covariance function.

We will then move beyond the standard regression setting and show how Gaussian Processes can be generalized to multiple correlated outputs and to time-series data. Both problems can be tackled by allowing for an augmented input space of the covariance function: for multi-output learning, we need to allow for task-specific inputs to capture the similarity between the outputs. For time-series data, we augment the input space to past input values to arrive at the
non-linear exogenous model.

Throughout the tutorial, example code and demonstrations will be given in Python. Only minimal concepts of linear algebra and statistics are required to follow the tutorial.

Bio: 

Barbara Rakitsch has been working as a research scientist at the Bosch Center for Artifical Intelligence in Renningen since 2017. Her interests lie in the area of Bayesian modeling with a focus on Gaussian processes and time-series data.

In 2014, she received her PhD in in probabilistic modeling for computational biology at the Max Planck Institute for Intelligent Systems in Tuebingen. Before joining Bosch, she worked on machine learning problems as a post-doc at the European Bioinformatics Institute in Cambridge and as a researcher in a cancer startup.