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

Statistical machine learning

Statistical machine learning

Academic year 2021/2022

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 

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

Course delivery

The course is composed of 48 hours of lectures. Two thirds of the lectures are devoted to the methodological/theoretical aspects of statistical machine learning, with reproducible examples given to support the understanding of methods. The remaining lectures are devoted to their practical implementation in R. Students are free to use any programming language; however, R is the officially supported language for this course. Students will be able to use RMarkdown for creating HTML and pdf documents. 

Please check this page for the teaching modalities foreseen for the a.y. 2021/22.

All course material will be posted on Moodle.

Learning assessment methods

Until the end of the Covid-19 emergency (including Sept. 2021), the written exam will be held remotely via Webex with video surveillance. More specific instructions will be given to students registered to the exam via their institutional email addresses.

1) Winter (January/February) exam session: your final grade will be based on a weighted average of a data analysis project (60%) and a closed-books written exam on theory (40%). For the data analysis, students can work individually or in teams (max 3 people) on a project of their choosing. Each student/team will have to submit a project report due on Friday, December 18. A team's report will be reviewed by another group. The review process will be "double blind", meaning that both the project report and review report will be anonymous. 

For students who have failed to submit their data analysis (in total or in part), case (2) below applies.

2) Summer and Fall exam sessions: the final exam consists of a long written test (4 hours) on theory (50%) and data analysis in R (50%). 

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

Regression:

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

Classification: Logistic regression; Multinomial logit/probit regression

Resampling methods: Cross-validation, bootstrap

Model selection: 

• Shrinkage methods
• Dimension reduction methods

Beyond linearity:

• Polynomial regression
• Step functions
• Splines, smoothing splines, thin-plate splines
• Generalised additive models
• Kernels

Tree-based methods:

• Regression & classification trees
• Bagging, boosting, random forests

Support vector machines

Introduction to neural networks & deep learning: 

• (Single- and) multi-hidden layers back-propagation networks
• Issues in training neural networks
• Convolutional neural networks
• Autoencoders

Gaussian processes

Course literature

The main books used during the course are:

• HASTIE, TIBSHIRANI AND FRIEDMAN. The elements of statistical learning: data mining, inference and prediction. Springer-Verlag 
• JAMES, WITTEN, HASTIE, TIBSHIRANI. An introduction to statistical learning with applications in R. Springer. Provides a nice introduction to the field of statistical machine learning for non-mathematical sciences

Slides for the course will be provided. If you see any typos in my notes (no matter how small), please tell me about them! Doing so will not only benefit you, but also myself, your classmates and any future students of this course.

Supplementary reading

There are many books written on machine learning, and new books keep appearing all the time. These books can approach the field from different perspectives (e.g., statistics, computer science, probability). Here are links to a few additional resources:

• Bishop. Pattern Recognition and Machine Learning Springer
• Murphy. Machine learning - a probabilistic perspective, MIT Press
• Barber. Bayesian Reasoning and Machine Learning, Cambridge University Press

Class schedule

Note

Electronic communication: I will occasionally send e-mails to the class (to the account listed for you in the SDS directory), so please check that account regularly.

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