Supervisors info:
Φώτιος Σιαννης, Επίκουρος Καθηγητής, Μαθηματικό, ΕΚΠΑ
Summary:
In this dissertation, we are tying to model Causality inference so as to identify and extract her
from empirical data. In statistics, when we find two random variables to be dependent, doesn’t
mean that they have also causal relation,Cause-Effect. As a result, if we want to model Causality
between random variables, we need to model the direction of this dependency, from the Causes to
Effects, except from how depended or correlated are these variables. In order to do that we use the
Directed Acyclic Graphs, DAGs. As a result, in the First,Second and Third Chapter we illustrate
how capable the DAGs are as tool to store Probabilistic dependence-independence Knowledge.
Also, we illustrate two basic assumptions: the Markov and the Faithfulness. These two play a significant role in that procedure. At the Forth chapter, we propose the Structural Causal Models,
SCMs, as a way to model Causal information. The SCMs can induce distribution Functions and
compatible DAGs to that distribution at the same time. In statistics, we use Distribution Functions as
a data generation process. In Causality inference we use the SCMs the same way with the exception that these can give us much more information about the data than classical Distribution Functions.
The main reason that we use the SCMs as a modelling tool is their additional ability to produce information about randomized-trial or their ability to induce Intervention distributions. One way
to identify that one variable has causal influence in the outcome of an other variable is by keeping all the factors that influence the outcome variable static except the one we are interested in. This
is very difficult in practice. However, the SCMs give us the solution. In the Fifth Chapter of this dissertation, assuming a known SCM which generate the data, we give a brief illustration about how we can compute the Causal influence of a variable in a system based on the randomize trial or precisely, the knowledge of intervention distributions. Finally, in the Sixth Chapter we illustrate
algorithms which extract the correct SCM from empirical data, and in the last Seventh chapter we
compare these algorithms under their ability to predict a correct SCM.
Keywords:
SCM, causality inference, Baysian Networks, Causality, Additive Noise Models, PC-algorythm, Interventions, Counterfactuals,Randomize trials, Front door criterion, Adjustment formula, Do-Calculus
