Introduction to Optimality conditions
Introduction to unconstrained local optimization methods
Stochastic gradient and variants
Basic constrained optimization methods
Exact global optimization methods
Heuristic global optimization methods
Numerical Calculus and Linear Algebra
Errori e aritmetica finita
Elementi di analisi delle matrici
Risoluzione numerica di sistemi lineari: metodi diretti
Sistemi sovradeterminati (fattorizzazione QR e decomposizione ai valori singolari)
Risoluzione numerica di sistemi lineari: metodi iterativi stazionari
Generalità sui Metodi di Krylov
Probability and Stochastic Processes
Discrete random variables: Probability distributions, probability mass functions, cumulative distribution functions, mean and variance. Discrete models.
Joint probability distribution, Marginal distributions, Conditional probability, conditional mean and variance. Discrete models.
Continuous random variables: Probability distributions, probability density functions, cumulative distribution functions, mean and variance. Conditional probability. Continuous models.
Convergence theorems and normal approximation. Poisson Process and applications.
Introduction to Markov Chains and their transition matrix.
Classification of states, invariant distributions.
Simulated annealing and Metropolis algorithm.
Birth-and-death chains on finite state spaces.
Statistical Inference and Modelling
Inference and linear models:
Frequentist (classical) inference
Generalized linear models:
Regression with a binary response
The general linear logistic model
Inference and prediction
Generalized linear models
Contingency tables and Poisson models
The Ising model in 3 binary variables
Algorithms and Programming in Python and R for Data Science
Introduction to Python and simple Data
Python Modules and Functions
Selections and Iterations
Recursion and Strings
Lists and Dictionary
Classes and Objects, Files
Analysis of Algorithms
Sorting and Searching
Introduction to R: the R console, R packages, files .R
Elementary objects of R: vectors, matrices, arrays, lists; different typologies of objects (numerical, characters, logical, factorial)
Basic mathematical functions; personalization of functions
The dataframe: definition and manipulation
Data import and data export in R (.txt files, Excel files, Stata/SAS/SPSS files, .R Data files)
Manipulations of objects - 1: variable recoding, time variables, missing data, record linkage
Manipulations of objects - 2: statistical descriptive analyses (tables, synthetic measures, basic graphical display)
Introduction to Machine Learning
Supervised versus unsupervised ML, essential probability theory, statistics, and distributions for ML, Bayesian versus frequentist interpretations for ML
Linear models for supervised regression and classification
The bias-variance decomposition, overfitting, underfitting, and model regularization
Maximum Likelihood Estimation (MLE), the expectation-maximization (EM) algorithm, Maximum a Posteriori (MAP) versus Bayesian inference
Connectionist models and introduction to artificial neural networks
From neurons to artificial neural networks: training as a non-linear optimization problem
Backpropagation and gradient-based methods
Linear Support Vector Machines (SVMs)
Non-linear SVMs and radial basis function networks
Using the LIBSVM library
Introduction to statistical learning:
Statistical point of view of machine learning
Data generating process
Monte Carlo simulations
Networks and concentration graph models
DAG and Bayesian network
Supervised statistical learning based on trees:
Bagging and Random forest
Interpretable statistical learning:
Predicting vs explaining
Interpretability, transparency, fairness
Introduction to supervised learning and regression.
Online learning: the perceptron learning algorithm.
Gradient descent and stochastic gradient descent: analysis, MATLAB implementation, backpropagation.
Unsupervised learning. MATLAB implementation of principal component analysis and spectral clustering.
Introduction to statistical learning theory.
Structural risk minimization and support vector machines.
Trade-off between sample size and precision of supervision.
A comparison of approximation error bounds for neural networks and linear approximators.
Application of neural networks to optimal control problems.
Radial basis function interpolating networks and their application to surrogate modeling and optimization.
Connection between supervised learning and reinforcement learning.
Deep Learning, Neural Networks, and Reinforcement Learning
Sequence learning and recurrent networks
Explainable machine learning
Explainable deep learning
Geo-spatial and Network Data Modelling
Network data modelling:
Introduction to network data
Network representation: types of relations, graph representation, matrix representation
Hints on network visualization
Descriptive analysis of network data: network statistics
Descriptive analysis of network data: nodal statistics
Exponential Random Graph models
Latent space models
Geo-spatial data modelling:
Introduction to spatial and geographical data
Stochastic spatial processes and their properties
Analysis of point process data
Analysis of geodata random surface
Analysis of areal data (lattice data)
Spatial interaction data: gravity models
Introduction to Geographical Information Systems
Complex System Analysis
Dynamical systems in 1D, 2D and 3D
Fixed points and stability
Turing instability in reaction diffusion models
Examples and applications
Text Mining and NLP
Network and Media Analysis
Introduction to complex networks:
degree and ANND.
Introduction to Twitter data:
User features and power law distributions:
information per user: tweets, retweets, followers and friends
power law distributions: scale free networks
Gonzalez-Bailon user classification
The retweet network:
building retweet network from data;
visualize the network;
assign attributes to nodes.
Hub and Authorities;
Community detection algorithms:
Girvan-Newman and the definition of Modularity;
The importance of null-model;
Louvain community detection
Analytics in Economics and Business
New Tricks for Econometrics and Artificial Intelligence
Statistical Learning with Sparsity: The Lasso and Generalizations
Classification and Regression Trees
Matrix Completion and Networks
Using Big Data for Measurement and Research
Mining Text and Images
Bayesian Inference and Causal Machine Learning
Hands on R and STATA for Data Science:
Introduction to R and STATA
Data Modeling for policy evaluation:
Data Modeling: inference and predictive analysis
Data Modeling: causal machine learning
Hands on Python for Data Science:
Introduction to Python for data science:
Neural networks and deep learning
Support Vector Machine
Experiments and Real-World Evidence in Economics
From theory to data (and the way back). Introduction to behavioral and experimental economics.
2. Learning from the data. Correlation is not causation. In search for practicable ways to go beyond correlations in social and economic phenomena.
The controlled solution: Experiments (online, in the laboratory, in the field).
The less controlled solution: Natural and Quasi-experiments.
3. Statistical analysis of experimental data. Mediator variables, modulator variables, specific statistical tests, multiple testing of hypotheses.
4. Case studies.
Examples of controlled experiments and their analysis (e.g., risky behaviors, addiction, strategic behaviors, moral dilemmas, marketing, persuasion, nudging).
Examples of natural experiments and their analysis (e.g., Italian clemency bill and criminal behaviors).
Examples of quasi-experiments and their analysis (e.g., evaluating educational programs in primary schools).
Policy Evaluation and Impact Analysis
Introduction to microeconometrics:
Structure, Endogeneity, and Identification Problems
Least-squares, Probit, and Logit Estimators
Static panel data
Dynamic panel data
The Evaluation Problem:
Randomization and Matching Models
The Difference-in-difference Estimators
Regression Discontinuity Design
Causality and Non-linear Models:
Models for Count Data
Models with Control Functions
Non-parametric time series analysis
GARCH models for heteroskedasticity
Forecasting methods and assessment of forecast accuracy
Introduction to multivariate time series analysis: VAR models
Optimization of Financial Portfolios
Financial assets, returns, statistical features of returns
Portfolio choice criteria: expected utility vs. Markowitz mean-variance
Mean-variance portfolio selection in action
Further topics: dealing with high-dimensional portfolios; constraints on concentration and turnover; the Black-Litterman model; sensitivity w.r.t. inputs ("estimation risk"); mean-VaR and mean-CVaR portfolio selection
Portfolio optimization in Matlab: 'quadprog' function and 'portfolio' object via Financial Toolbox
Health Analytics and Data-Driven Medicine
Causal inference in healthcare with MEPS data
Predictive healthcare and patient outcome (digital records, diagnostic procedure and intervention)
Clinical trials and prescription behavior: market analysis and regulation
Epidemiology and COVID-19
Environmental and Genomic Data Analysis
Ethics and Law for Data Science
Governo dei dati e tutela dei diritti fondamentali
Data Localization e sovranità dei dati
Data Governance: considerazioni introduttive
Big data e automazione
Big data e IOT