Laurea Magistrale (M.Sc.) in Stochastics and Data Science

Statistical machine learning

Statistical machine learning

Academic year 2017/2018

Sommario del corso

• Course objectives
• Results of learning outcomes
• Course delivery
• Learning assessment methods
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

The course introduces methods and models to extract important patterns and trends from big amount of data, and presents basic concepts of machine learning and data mining from a statistical perspective. Topics covered include modern regression, classification, cross validation, model selection and regularisation, and tree-based methods, among others. The course emphasizes selection of appropriate methods and justification of choice, use of programming for implementation of the method, and evaluation and effective communication of results in data analysis reports. 

Results of learning outcomes

Knowledge and understanding 

• Advances knowledge of parametric and nonparametric models for prediction and classification

Applying knowledge and understanding

• Ability to convert various problems and data into statistical models to perform prediction/classification

Making judgements

• Students will be able to discern the different aspects of statistical learning in modern settings

Communication skills

• Students will properly use statistical language to comunicate the results of their findings

Learning skills

• The skills acquired will give students the opportunity to improve and deepen their knowledge of statistical modeling

Course delivery

Half of the lectures are devoted to the theorerical aspects of statistical machine learning, and the remaining half to their practical implemetation. We will use R as a programming language for data analysis and use existing packages written in R to support the course. 

Learning assessment methods

The exam consists of two parts: the first part is a written exam on theory; the second part is a practical session with R. 

Program

Introduction to Statistical Learning

• Context and motivations;
• Trade-off between goodness-of-fit and model complexity (i.e. variance and bias);
• Training and test set; 
• RMarkdown

Regression

• Exploratory data analysis
• Simple & multiple linear regression
• Residual analysis & model checking

Classification: Logistic regression 

Resampling methods: Cross-validation, coverage & bootstrap

Model selection:

• Subset selection 
• Shrinkage methods
• Dimension reduction methods

Beyond linearity:

• Polynomial regression
• Step functions
• Splines & smoothing splines
• Generalised additive models
• Kernels
• Local regression

Tree-based methods:

• Regression & classification trees
• Bagging, boosting, random forests, Bayesian additive regression trees

Support vector machines

This is an applied course, which will be based on:

• JAMES, WITTEN, HASTIE, TIBSHIRANI. An introduction to statistical learning with applications in R. Springer. 

This is available freely at www-bcf.usc.edu/~gareth/ISL. You are welcome to download it and print it out.

Another useful resource (also available freely online) is:

• HASTIE, TIBSHIRANI AND FRIEDMAN. The elements of statistical learning: data mining, inference and prediction. Springer-Verlag.

Slides for the course will be provided.

Class schedule

Note

This course will be delivered at the ESOMAS Department.

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums