Statistical Machine Learning

Instructor: Prof. Pier Francesco Palamara

University of Oxford, Big Data Institute EPSRC CDT in Health Data Science, Michaelmas 2022

General Information

Course Team Pier Palamara (module leader, lecturer), Jiazheng Zhu (practical leader)
Lectures Friday Oct 14 to Thursday Oct 20, 9am-12pm.
Practicals Friday Oct 14 to Thursday Oct 20, 1pm-4pm.


Please check material on Canvas.


Recommended prerequisites:
Equivalent of the following Oxford undergraduate courses: Part A A9 Statistics and A8 Probability. SB2a Foundations of Statistical Inference useful by not essential.

Aims and Objectives:
Machine learning studies methods that can automatically detect patterns in data, and then use these patterns to predict future data or other outcomes of interest. It is widely used across many scientific and engineering disciplines. This course covers statistical fundamentals of machine learning, with a focus on supervised learning and empirical risk minimisation. Both generative and discriminative learning frameworks are discussed and a variety of widely used classification algorithms are overviewed.

Visualisation and dimensionality reduction: principal components analysis, biplots and singular value decomposition. Multidimensional scaling. K-means clustering. Introduction to supervised learning. Evaluating learning methods with training/test sets. Bias/variance trade-off, generalisation and overfitting. Cross-validation. Regularisation. Performance measures, ROC curves. K-nearest neighbours as an example classifier. Linear models for classification. Discriminant analysis. Logistic regression. Generative vs Discriminative learning. Naive Bayes models. Decision trees, bagging, random forests, boosting.

Useful reading
C. Bishop, Pattern Recognition and Machine Learning, Springer, 2007.
T. Hastie, R. Tibshirani, J Friedman, Elements of Statistical Learning, Springer, 2009.
K. Murphy, Machine Learning: a Probabilistic Perspective, MIT Press, 2012.

Further Reading
B. D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, 1996.
G. James, D. Witten, T. Hastie, R. Tibshirani, An Introduction to Statistical Learning, Springer, 2013.


Please email me to report any typos or errors.

1 Introduction, unsupervised learning: exploratory data analysis Slides »
2 Principal component analysis Slides »
3 SVD, Biplots, multidimensional scaling, Isomap Slides »
4 Clustering (K-means, hierarchical) Slides »
5 Supervised learning: empirical risk minimization, regression (linear, polynomial), overfitting Slides »
6 Generalization, cross-validation, bias-variance trade-off Slides »
7 Regularization (demo, source, data), gradient descent, classification: the Bayes classifier Slides »
8 Classification: linear and quadratic discriminant analysis (LDA, FDA) Slides »
9 QDA, logistic regression Slides »
10 Logistic regression (cont.), generative vs. discriminative learning, naïve Bayes Slides »
11 Naïve Bayes (cont.), K-nearest neighbors, evaluating performance, ROC curves Slides »
12 Decision trees Slides »
13 Bagging, random forests Slides »
14 Boosting Slides »

Problem Sheets

This is a set of problems+solutions about the material covered in the lectures above.

1 Sheet » Solutions »
2 Sheet » Solutions »
3 Sheet » Solutions »
4 Sheet » Solutions »

Resources for Python

Resources for R

Background Review Aids