Learn

In this section, you can find tutorial notebooks that describe the internals of pyhgf, the theory behind the Hierarchical Gaussian filter, and step-by-step application and use cases of the model. At the beginning of every tutorial, you will find a badge to run the notebook interactively in a Google Colab session.

Theory

An introduction to the Hierarchical Gaussian Filter

How the generative model of the Hierarchical Gaussian filter can be turned into update functions that update nodes through value and volatility coupling?

Creating and manipulating networks of probabilistic nodes

How to create and manipulate a network of probabilistic nodes for reinforcement learning? Working at the intersection of graphs, neural networks and probabilistic frameworks.

Generalised Bayesian filtering

Predict, filter and smooth any distribution from the exponential family using generalisations of the Hierarchical Gaussian Filter.

The Hierarchical Gaussian Filter

The binary Hierarchical Gaussian Filter

Introducing with example the binary Hierarchical Gaussian filter and its applications to reinforcement learning.

The categorical Hierarchical Gaussian Filter

The categorical Hierarchical Gaussian Filter is a generalisation of the binary HGF to handle categorical distribution with and without transition probabilities.

The continuous Hierarchical Gaussian Filter

Introducing with example the continuous Hierarchical Gaussian filter and its applications to signal processing.

Tutorials

Advanced customisation of predictive coding neural networks and Bayesian modelling for group studies.

Using custom response functions

How to adapt any model to specific behaviours and experimental design by using custom response functions.

Embedding the Hierarchical Gaussian Filter in a Bayesian network for multilevel inference

How to use any model as a distribution to perform hierarchical inference at the group level.

Parameter recovery, prior and posterior predictive sampling

Recovering parameters from the generative model and using the sampling functionalities to estimate prior and posterior uncertainties.

Use cases

Examples of possible applications and extensions of the standards Hierarchical Gaussian Filters to more complex experimental designs

Inferring cardiac beliefs using Bayesian filtering

Application of continuous Bayesian filtering to cardiac physiological recordings to infer interoceptive beliefs and their volatility.

Value and volatility coupling with an input node

Dynamic inference over both the mean and variance of a normal distribution.

Multi-armed bandit task with independent reward and punishments

A generalisation of the binary Hierarchical Gaussian Filter to multiarmed bandit where the probabilities of the outcomes are evolving independently.

Exercises

Hand-on exercises to build intuition around the main components of the HGF and use an agent that optimizes its action under noisy observations.

Applying the Hierarchical Gaussian Filter through practical exercises

In-depth introduction to the Hierarchical Gaussian Filter for computational psychiatry (Computational Psychiatry Course, Zurich). About 4 hours.