###Causal graphical models without using structural equation models
Project ID: 2228bd1142 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Statistical Science
Lead Supervisor: Kayvan Sadeghi
Project Summary:
Inferring causal relationships has always been one of the main objectives of science. Examples in today’s world include, but are not limited to, inferring potential causes of cancer, the effect of gene manipulation, and much more.
Statistical procedures, known generically as causal models, must be used to infer such causal relationships from observed data. Extensive research has been conducted on defining, interpreting, and applying causal models. Today, a very popular method for inferring causal relationships is based on the use of statistical models over graphs with nodes that are random variables representing the quantities of interest. There are called causal graphical models.
Almost all causal graphical models assume that the distribution comes from structure causal models as it is quite intuitive to define the concept intervention on them, which is essential to define causal relationships.
We have recently worked on axiomatization of interventional probability distributions without assuming SCMs or, in fact, the existence of a ”true causal graph”. This extended theory will lead to developing a new plethora of models and causal learning algorithms by directly investigation such axioms in a systematic way.
We propose to use this newly developed axiomatization to extend and develop an analogous theory to the existing theory of causal inference for larger class of graphs with three types of edges that cover a much more general case of simultaneous representation of “direct effects”, “confounding”, and “non-causal symmetric associations”, which could receive different causal interpretations; but, more importantly, the class also allows for causal cycles.
To conduct the project successfully, the candidate must be theoretically inclined, and have a good knowledge of statistical modelling and multivariate statistics. A major part of the project aims at developing and proving properties of such causal models, but some programming skills will also be needed for implementing the models.