Syllabus: Linear Algebra part (Gnecco, 10 hours):

Lecture Contents:
– Historical introduction.
– Sum of two matrices, scalar multiplication, convex combination. Application to image processing.
– Vectors, vector norms, and transposition. Application to movie ratings and digit recognition.
– Product of a row vector and a column vector, cosine similarity. Application to movie ratings.
– Matrix product. Application to image processing.
– Linear systems, Gaussian elimination, Cramer’s rule. Application to cryptography and to computed tomography.
– Least squares. Application to score prediction in races.
– Eigenvalues and eigenvectors. Application to graph centrality and spectral clustering.
– Matrix powers. Application to genetics.
– Principal component analysis, linear discriminant analysis, singular value decomposition. Application to image processing.
– Markov chains. Application to games and web surfing.
– Exercises on the blackboard on the following topics: sum of matrices, scalar multiplication, matrix product, Cramer’s rule, Gaussian elimination, eigenvectors and eigenvalues, determinants.

Statistics part (Serti, 20 hours):

Lecture Contents:
The topics covered will be:
– Introduction to probability: random variables, discrete and continuous distributions
– Introduction to statistics: definition of statistical model, estimate and estimator, point estimation and interval estimation
– Statistical tests: parametric and non parametric tests
– Analysis of Variance: one-way and two-way ANOVA
– Relation between variables: linear model, multiple regression

Syllabus: The contents of the course are:

the European Statistical System and its Data Production Model,
Definition of poverty and living conditions (e.g. Laeken Indicators of Poverty and/or multidimensional indicators of poverty),
survey methods and estimation strategies (Horvitz -Thompson estimator, Hayek estimator),
introduction to economic official data and aggregates to study poverty and the main european surveys on households (EUSilc: European Survey on Income and Living Conditions, Household Budget Survey, Labour Force Survey). Issues on data integration and new data sources as Big data.

Syllabus: Module 1: Spatial and Mobility Data

Fundamentals of Geographical Information Systems
Geographic coordinates systems
Vector data model
Trajectories
Spatial Tessellations
Flows
Practice: Python packages for geospatial analysis (Shapely, GeoPandas, folium, scikit-mobility)
Digital spatial and mobility data
Mobile Phone Data
GPS data
Social media data
Other data (POIs, Road Networks, etc.)
Practice: reading and exploring spatial and mobility datasets in Python
Preprocessing mobility data
filtering compression
stop detection
trajectory segmentation
trajectory similarity and clustering
Practice: data preprocessing with scikit-mobility

Module 2: Mobility Patterns and Laws

individual mobility laws/patterns
collective mobility laws/patterns
Practice: analyze mobility data with Python

Module 3: Predictive and Generative Models

Prediction
Next-location prediction
Crowd flow prediction
Spatial interpolation
Generation
Trajectory generation
Flow generation
Practice: mobility prediction and generation in Python

Module 4: Applications

Epidemic spreading (COVID-19)
Urban segregation models
Routing and navigation apps
Traffic simulation with SUMO

Syllabus: The course presents principles, models, and state-of-the-art techniques for the analysis and generation of natural language, focusing mainly on statistical machine-learning approaches and Deep Learning in particular. Students will learn how to apply these techniques in a wide range of applications using modern programming libraries.

Foundations of Natural Language Processing
Introduction to NLP, Historical developments, Key applications
Statistical Methods in NLP: Language Models, Hidden Markov Model, Viterbi Algorithm, Generative vs. Discriminative Models
Linguistic Essentials: Words, Lemmas, Morphology, Parts of Speech (PoS) Tagging, Phrases and Sentence Structure, Named Entity Recognition (NER)
Parsing Techniques: Constituency Parsing, Dependency Parsing

NLP Methods and Techniques
Annotation Pipelines, Linguistic Annotation, Semantic Annotation, Text Annotation Tools and Frameworks
Lexical Semantics: Collocations and multi-word expressions, Corpora and Corpus Linguistics, Thesauri and Gazetteers
Distributional Semantics: Word Embeddings, Character Embeddings, Semantic Similarity
Deep Learning for Natural Language

Applications and Case Studies
Information Extraction: Entity Recognition, Entity Linking
Text Classification and Summarization: Classification Techniques, Summarization Models
Advanced NLP Applications: Opinion Mining and Sentiment Analysis, Question Answering, Dialogic Interfaces (Chatbots), Machine Translation
The syllabus is subject to change based on the pace of the class and emerging trends in Human Language Technologies.

Syllabus: — Stochastic Models for financial markets. Binomial models. Brownian Motion. Martingale. Stochastic Calculus, Itô’s Formula. Levy processes and jump processes. Stochastic Calculus with jump processes. Stochastic Differential Equations (SDE). Kolmogorov’s Equations. Feynman-Kac’s theorem.

— Evaluation of Options. Models of Cox-Ross-Rubinstein and of Black-Scholes. Risk Neutral evaluation (European Options, American Options, Exotic Options). Dynamic evaluations. Market premium and change of numeraire. Affine processes in continuous time and valuation formulae. Models of Merton and Bates.

— Volatility. Volatility surfaces. Extensions of the Black and Scholes Formula and local volatility models. Stochastic Volatility models in continuous time. Estimation of volatility. Stable convergence and infill asymptotic. Realized Measures of Volatility: Asymptotic properties.

— Numerical methods for the estimation of models. Maximum Likelihood Methods: Estimation of coefficients of SDE.

Syllabus: Introduction. Components of a time series (trend, cycle, seasonal, irregular), stationarity, autocorrelation and dependencies, approaches to time series analysis. Review of estimation methods (Least Squares, Maximum Likelihood, Generalized Method of Moments).

Linear models. ARMA processes, partial autocorrelation, invertibility, ARIMA models for non-stationary series. Inference of linear models: identification and fitting, diagnostics, Ljung-Box statistic; model selection. Vector AutoRegressive models, reduced form, structural form e identification issues. Granger causality.

State space models. Filtering, prediction and smoothing; Kalman recursions; local level models. Particle filtering and smoothing, Score Driven models, Hidden Markov Models.

Neural networks for time series. Introduction to (Deep) Neural Networks, Inference of time series models with Machine Learning methods. Overview of time series forecasting via ML and Deep Learning Libraries: TensorFlow, Keras. Recurrent Neural Networks (RNN), Gated Architectures (LSTMs, GRUs), Bi-directional RNNs, Deep RNN. Reservoir computing and Echo State Networks. Applications and examples.

Introduction to Reinforcement Learning.

Syllabus: – Introduction.

– Probability spaces, Entropy and its property.

– Probability spaces as simplexes.

– Interacting particle systems and Ising models. Ising model in d=1 with free and periodic boundary conditions.

– Dichotomic functions and their Fourier expansion.

– Simple notions for Ising models at d>1

– The thermodynamic limit and correlation inequalities.

– Mean field models. Curie-Weiss model.

– Thermodynamic limit for mean field models.

– The solution of the Curie Weiss model with bounds from above and below.

– Large number theorem and central limit theorem for the magnetization. Free model and model with interaction.

– Large deviation theory and solution of the Curie Weiss model.

– Theoretical inverse problem: from thermodynamic quantities to parameters.

– Phenomenological inverse problem: from real data to thermodynamic quantities.

– Maximum likelihood.

– The Sherrington and Kirkpatrick model. Parisi solution. Guerra Talagrand proof for the free energy. Panchenko proof for ultrametricity.

– Associative memory and the Hopfield model.

– The multi-specie generalization of the SK model.

– Deep-learning architecture with cilindrical and conical boundary conditions. Bounds for the free energy.

– Learning and retrieval equivalence.

– Seminars on recent advances.