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

Statistical machine learning

Statistical machine learning

Academic year 2018/2019

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

The course is composed of 48 hours of class lectures. 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. Students will use RMarkdown for creating HTML and pdf documents. 

Learning assessment methods

1) Winter (January/February) exam session: your grade will be based on a weighted average of homework (30%), data analysis in R (40%), and a closed-book final exam on theory (30%). There will be three problems sets assigned throughout the course. You may work with other students on the homework assignments, but all students must write and turn in their own solutions. Assignments may be submitted either electronically or as a physical copy, and must be turned in as a .pdf file (i.e., no Word or hand-written documents). Assignments may also involve writing code to analyze data. Late submissions of homework assignments will not be accepted. For students who have failed to submit their homework solutions, case (2) below applies.

2) Summer and Fall exam sessions: the final exam consists of a long written test (4h) 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

• 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, overview of Bayesian additive regression trees

Support vector machines

Introduction to neural networks

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. 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.

Class schedule

Note

This course will be delivered at the ESOMAS Department.

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