This course provides a conceptual introduction to the new and exciting field of Algorithmic Information Dynamics focusing on mathematical and computational aspects in the study of causality. To this end, the course first covers key aspects from graph theory and network science, information theory, dynamical systems and algorithmic complexity in a tour the force to finally tackle causation from a model-driven approach removed from traditional statistics and classical probability theory. The course will venture into ongoing research to show exciting new avenues to uncharted territory.

It is desirable that students have some idea of basic mathematics but optional modules will be provided in a parallel track. Also desirable is some computer programming skills, but also some basics of the Wolfram Language and a 6-month access to Wolfram|One (Mathematica) will be granted (extendable by other 6 months). However, the course does not require you to adopt any particular programming language nor it requires one.

Because of its nature, the course is aimed to a wide range of possible students who have had some basic knowledge of college-level math or physics to active researchers seeking to take advantage of new tools for algorithmic data science beyond traditional machine learning.

After a conceptual overview of the main motivation and some historical developments, we review some preliminary aspects needed to understand the most advanced topics. These include basic concepts of statistics and probability, notions of computability and algorithmic complexity and brief introductions to graph theory and dynamical systems. We then dig deeper into the core of the course, that of Algorithmic Information Dynamics which brings all these areas together in harmony to serve in the challenge of causality discovery, the most important topic in science. Central to the course and the field is the theory of algorithmic probability that establishes a formal bridge between computation, complexity and probability.

Finally, we move towards new measures and tools related to reprogramming artificial and biological systems, applications to biological evolution, evolutionary programming, phase space and space-time reconstruction, epigenetic landscapes and aspects relevant to data analytics and machine learning such as model generation, feature selection, dimensionality reduction and causal deconvolution. We will showcase the tools and framework in applications to systems biology, genetic networks and cognition by way of behavioural sequences. Because of the wide scope of application students will be able apply the tools to their own data and own problems as we will be explaining how to do it in detail, and we will be providing all the tools and code for it.

Throughout the course, students will be given assignments that will go from the conceptual to the mathematical and computational intended to keep everybody engaged.

**About the Instructor(s):**

Hector Zenil has a PhD in Computer Science from the University of Lille 1 and a PhD in Philosophy and Epistemology from the Pantheon-Sorbonne, University of Paris. He co-leads the Algorithmic Dynamics Lab at the Science for Life Laboratory (SciLifeLab), Unit of Computational Medicine, Center for Molecular Medicine at the Karolinska Institute in Stockholm, Sweden. He is also the head of the Algorithmic Nature Group, the Paris-based lab that started the Online Algorithmic Complexity Calculator and the Human Randomness Perception and Generation Project. Previously, he was a Research Associate at the Behavioural and Evolutionary Theory Lab at the Department of Computer Science at the University of Sheffield in the UK before joining the Department of Computer Science, University of Oxford as a faculty member and senior researcher.

Narsis Kiani has a PhD in Mathematics and has been a postdoctoral researcher at Dresden University of Technology and at the University of Heidelberg in Germany. She has been a VINNOVA Marie Curie Fellow in Sweden and co-leads the Algorithmic Dynamics Lab at the Science for Life Laboratory (SciLifeLab), Unit of Computational Medicine, Center for Molecular Medicine at the Karolinska Institute in Stockholm, Sweden.

Hector and Narsis are co-leaders of the Algorithmic Dynamics Lab at the Unit of Computational Medicine at Karolinska Institute.

**Course Team:**

Antonio Rueda-Toicen has an MSc degree in Bioengineering and a Licentiate degree in Computer Science. He is an instructor and researcher at Instituto Nacional de Bioingeniería (INABIO) at Universidad Central de Venezuela and is a Research Programmer at the Algorithmic Dynamics Lab.