Contenuti sintetici

Programma esteso


Modalità didattica

Materiale didattico

Periodo di erogazione dell'insegnamento

Modalità di verifica del profitto e valutazione

Orario di ricevimento


The course aims to provide a gentle introduction to causal inference and in particular to causal newtworks and structural causal models.  
In particular, the course gives strong motivations because, at the current state-of-the-art, modern machine learning experts need causality, and tools from causal modeling, to correctly address and effectively solve problems of decision making under uncertainty.


Main contents are as follows; the potential outcome framework, main definitions and properties of probabilistic graphical models with specific reference to Bayesian networks, causal networks and structural causal models, randomized experiments, nonparametric identification of causal effect, estimation of causal effect, unobserved confounding, instrumental variables, structural learning from observational data and from observational and intervention data, basic concepts of tranfer learning and transportability, and finally a basic introduction to counterfactuals.

Detailed program

  • Introduction to causality and why causality matters
  • The potential outcome framework; the fundamental problem of causal inference, ITE, ATE, main properties as ignorability, exchangeability, ...
  • Bayesian networks; definition, collider, chain and fork, factorization, ...
  • Causal models; do.operator, backdoor adjustement, structural causal models.
  • Randomized control trials; comparability and covariate bancing, exchangeability, no backdoor paths.
  • Nonparametric identification; frontdoor adjustment, identification from the graph structure.
  • Estimation; conditional outcome modeling, grouped conditional causal modeling, propensity score and inverse probability weighting.
  • Unobserved counfounding; no assumptions bound, optimal treatment selection, sensitivity analysis.
  • Instrumental variables; nonparametric identification of ATE, nonparametric identification of local ATE.
  • Causal discovery from observational data; constraint-based and score-based algorithms.
  • Causal discovery from interventional data; structure interventions, parametric interventions, interventional Markov equivalence.
  • Transfer learning and transportability.
  • Counterfactuals.


Basic knowledge of graph theory, optimization, probability and statistics, programming; mainly R and Python.

Teaching form

The course is expected to be delivered in presence, even if at the current stage of knowledge, due to the pandemic, we could well say "ics sunt leones".

Textbook and teaching resource

Slides from teachers, reading material and main textbooks related to causal inference and causal networks, to be announced soon.


First semester, in particular September 2021

Assessment method

Group assignment and final oral examination.

Office hours

Just send me an email message at

Enrolment methods

  • Manual enrolments



  • Picture of Luca Bernardinello
    Luca Bernardinello
  • Picture of Fabio Antonio Stella
    Fabio Antonio Stella