Continuous Causal States (CONCAUST home page)
This page holds the latest information and a reference implementation for the method described in the papers:
- Discovering Causal Structure with Reproducing-Kernel Hilbert Space ε-Machines
by Nicolas Brodu, James P. Crutchfield - Inferring Kernel ε-Machines: Discovering Structure in Complex Systems
by Alexandra M. Jurgens, Nicolas Brodu
This method consists in identifying causal states: states of a process which always lead to the same kind of behaviors, in probability. The dynamic of these states describes how, starting from initial knowledge from current observations, the known information is diffused with time. As you can see in the example on this page, the method also identifies the geometric structure by which causal states evolve. This corresponds to an attractor in the case of chaotic dynamical systems, but the theory, which has been developped for more that 40 years, is actually fully stochastic and generalizes deterministic chaos.
Our method exploits reproducing kernel Hilbert spaces (RKHS) in order to cleanly represent causal states as geometric points, as well as to easily infer that representation from data. We further refine the method by encoding the causal states using a few number of coordinates. These causal diffusion components thus theoretically encode the information needed to discriminate between future behaviors, statistically. The first of these components encode most of the information, with decreasing gains as more components are added. Intuitively, this can be seen as analogous to a non-linear principal component analysis, but which is based on predictive information instead of variance. Practically, representing the causal states in these reduced dimension spaces highlights the hidden geometric predictive stucture of a process, showing constraints in its evolution, patterns such as anomalies in the data, and much more that yet needs to be found!
Source code and Additional information
The latest version of the source code is provided for reproducing the results of our second (preprint) article above, but it’s API is considered work in progress. We plan to release a proper Python package when the article is published in a journal.
This presentation was given at the Grenoble Artificial Intelligence for Physical Sciences. It presents the main ideas behind the CONCAUST method.
Interactive examples
We have made interactive versions of some figures from this article. See the article for the legends and figure captions. Click on the following titles to load and explore these figures:
Solar activity
Crop in Grignon
Butane molecule
Want to join us?
Do not hesitate to contact us if you are highly motivated rather than bored at this point! We can:
- Provide post-docs and other temporary positions. Some may be announced in the job offers section of this site, but we could sometimes create new positions. We can support your application for a grant to funding agencies and in particular the European Union (e.g., Marie-Curie fellowships and ERC starting grants).
- Support you for a permanent position at Inria. We are currently creating a team around these issues, so recruiting colleagues to complement that team is our priority.
- Collaborate in any case.
