DATA ANALYSIS AND STATISTICAL LEARNING

Learning Objectives

• Data Analysis and Statistical Learning

  1. Knowledge and understanding (Conoscenza e capacità di comprensione). The first “Statistical Learning” module mainly concerns the fundamentals of two of the main methods used in unsupervised learning: principal component analysis and cluster analysis. 2. Applying knowledge and understanding (Capacità di applicare conoscenza e comprensione). On completion, the student will be able: i) to implement the main methods used in unsupervised learning; ii) to summarize the main features of a dataset and extract knowledge from data properly. 3. Making judgements (Autonomia di giudizio). On completion, the student will be able to choose a suitable statistical model, apply it, and perform the analysis using a statistical software. 4. Communication skills (Abilità comunicative). On completion, the student will be able to present the results from the statistical analysis, and which conclusions can be drawn. 5. Learning skills (Capacità di apprendimento). On completion, the student will be able to understand the structure of unsupervised learning.

• Statistical Learning
  1. Knowledge and understanding (Conoscenza e capacità di comprensione). The objectives of the module aim at acquiring knowledge about: i) setting of the learning problem and introducing the general model of the risk functional from empirical data; ii) main statistical learning techniques for regression and data classification.
  2. Applying knowledge and understanding (Capacità di applicare conoscenza e comprensione). On completion, The student will be able: i) to implement main statistical models for supervised and unsupervised learning; ii) to summarize the main features of a dataset and extract knowledge from data properly.
  3. Making judgements (Autonomia di giudizio). On completion, students will able how to choose a suitable statistical model, apply sound statistical methods, and perform the analyses using statistical software
  4. Communication skills (Abilità comunicative). On completion, students will be able how to present the results from the statistical analyses, and which conclusions can be drawn from the analyses.
  5. Learning skills (Capacità di apprendimento). On completion, students will be able to understand the structure of the statistical learning.

Course Structure

• Data Analysis and Statistical Learning

  Lectures via slides. The freely available R statistical software will be also used.

• Statistical Learning

  Lectures and practical data modeling in R.

Required Prerequisites

• Data Analysis and Statistical Learning

  Basic notions in statistics, linear algebra, and computing.

• Statistical Learning

  Basics of statistics and data analysis, Matrix Algebra, Calculus

Attendance of Lessons

• Data Analysis and Statistical Learning

  Recommended.

• Statistical Learning

  Mandatory

Detailed Course Content

• Data Analysis and Statistical Learning
  1. Statistical Models for Univariate Random Variables. Discrete and continuous random variables. Basic distribution functions. Expectation and variance. Statistical models for random variables. Parametric Inference: classical properties of estimators; the maximum likelihood approach and its properties. Goodness-of-fit tests. R functions and packages. Illustration in R.
  2. Basics of Matrices. Matrices. Special matrices. Basic matrix identities. Trace. Inverse and determinant. Eigen-decomposition. Quadratic forms and definite matrices.
  3. Basics of Multivariate Modelling. Random vectors and their distributions. Mean vector, covariance and correlation matrices. Multivariate normal distribution: properties and effect of the covariance matrix on the shape of the contours. Data Matrix, centered data matrix and standardized data matrix.
  4. Cluster Analysis (CA). Clustering distance/dissimilarity measures. Data types in CA. Data standardization. Distance matrix computation. R functions and packages.
  5. Hierarchical clustering methods. Peculiarities. Agglomerative hierarchical clustering. Algorithm. Dendrogram. Linkage methods. Simplified example. Agglomerative hierarchical clustering methods using the data matrix. Illustration in R.
  6. Partitioning (or partitional) clustering methods. Peculiarities. K-means clustering. Algorithm. R functions and packages. Illustration in R. K-medoids clustering. PAM Algorithm. R functions and packages. Illustration in R.
  7. Cluster Validation. Overview. Assessing Clustering Tendency. R functions and packages. Illustration in R. Determining the Optimal Number of Clusters. R functions and packages. Illustration in R. Cluster Validation Statistics: Internal and external measures. R functions and packages. Illustration in R. Choosing the Best Clustering Algorithm(s). Measures for comparing clustering algorithms. Cluster stability measures. R functions and packages. Illustration in R.
  8. Model-Based Clustering. Preliminaries. Mixture models. Clustering with mixture models. Maximum a posteriori probability criterion. Gaussian mixtures. Parsimonious modelling via eigen-decomposition. Choosing the number of mixture components and the best parsimonious configuration: the Bayesian information criterion. R functions and packages. Illustration in R.
• Statistical Learning

  Statistical Learning. Estimation of dependences based on empirical data. Supervised and Unsupervised Learning. Regression and Classification problems. Parametric and non-parametric models. Assessing Model Accuracy.

  Linear Regression. Simple linear regression. Multiple linear regression. Least squares criterion and parameter estimation. Assessing the accuracy of the coefficient estimates and of the model. Use of qualitative predictors. Extension of the linear model and non-linear relationships.

  Classification. Logistic regression; parameter estimation. Linear and quadratic discriminant analysis.

  Linear Model Selection an Regularization. Variable selection. Dimension reduction methods.

  Support Vector Machines and Neural Networks. Support vector classifiers. Deep learning and multilayer perceptrons.

  Mixture models. Mixtures of distributions. Mixtures of regressions.

Textbook Information

• Data Analysis and Statistical Learning
  1. Bishop C. M. (2007). Pattern Recognition and Machine Learning, Springer, Cambridge.
  2. James G., Witten D., Hastie T., Tibshirani R. (2017). An Introduction to Statistical Learning with Applications in R, Springer, New York.
  3. Kassambara A. (2017). Practical Guide to Cluster Analysis in R.
  4. McNeil A. J., Frey R., Embrechts P. (2005). Quantitative Risk Management Concepts, Techniques and Tools. Princeton University Press, Princeton, New Jersey.
• Statistical Learning
  1. James G., Witten D., Hastie T., Tibshirani R. (2017). An Introduction to Statistical Learning with Applications in R, Springer, New York.
  2. Hastie T., Tibshirani R., Friedman (2008). The Elements of Statistical Learning, Springer, New York
  3. Course notes

Course Planning

Learning Assessment

Learning Assessment Procedures

• Data Analysis and Statistical Learning

  The exam aims to evaluate the achievement of the learning objectives. It is carried out through an oral exam that includes questions related to the program in addition to the discussion of a report concerning a real data analysis peformed using both the methodologies treated during the course and the R statistical software.

• Statistical Learning

  Practical activities (data analysis and modeling with R) and oral exam

Examples of frequently asked questions and / or exercises

• Data Analysis and Statistical Learning
  • Principal component analysis.
  • Hierarchical clustering.
  • Model-based clustering.