Statistical Machine Learning
Instructor: Prof. Pier Francesco Palamara
University of Oxford, Big Data Institute EPSRC CDT in Health Data Science, Michaelmas 2021
|Course Team||Pier Palamara (module leader, lecturer), Sharib Ali (practical leader)|
|Lectures||Monday Oct 18 to Friday Oct 22, 9am-12pm.|
|Practicals||Monday Oct 18 to Friday Oct 22, 1pm-4pm.|
PracticalsPlease check material on Canvas.
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.
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.
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 »|
This is a set of problems+solutions about the material covered in the lectures above.
|1||Sheet »||Solutions »|
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Resources for Python
Resources for R
- Part A Statistical Programming at Oxford
- DataCamp tutorial
- Coursera R programming course
- Intro to tidyverse (advanced)
Background Review Aids
- Matrix and Gaussian identities - short useful reference for machine learning.
- Linear Algebra Review and Reference - useful selection for machine learning.
- Video reviews on Linear Algebra by Zico Kolter.
- Video reviews on Multivariate Calculus and SVD by Aaditya Ramdas.
- The Matrix Cookbook - extensive reference.