Statistical and Machine Learning

Upon completion of the course, the PhD-student shall be able to:

• Select a suitable statistical models, and methods for a data analysis problem in the real world based on reasoned argument, especially when the underlying data generating mechanism is unknown.
• Apply various supervised and unsupervised statistical learning algorithms in a range of real world problems.
• Evaluate and optimise the performances of the learning models and algorithms, and communicate the expected accuracy of the model/algorithm.
• Combine several models to achieve higher predictive accuracy.
• Apply Neural Networks to real world problem solving.
• Conduct comparative analysis, both theoretical and empirical, in order to
 decide which Neural Network is most suitable for a particular task.
• Design different kinds of Neural Network, evaluate their performance, and
 use them to solve complex problems.
• Apply deep learning to real world problems.

The course consists of two parts, statistical learning (Part 1, corresponding to Learning Outcomes 1-4) and Machine Learning (Part 2, Learning outcomes 5-8). Both parts of the course focuses mainly on the applied aspects of statistical learning and machine learning with Part 2 emphasizing on neural networks and deep learning.

In Part 1, the most important basic properties of, and relations between different statis-tical learning models and algorithms are also included, however. This part covers supervised learning algorithms, with special emphasis on classification methods such as logistic regression, classification trees, linear discriminant analysis, quadratic discri-minant analysis, K nearest neighbour, support vector machine, and regression methods such as linear regression, smoothing splines, generalised additive model, and regression trees. Part 1 also covers unsupervised learning methods such as principal component analysis, k mean clustering, and hierarchical clustering. Model validation through cross validation, and bootstrap methods are covered. Regularisation for model selection, high dimensional data analysis, and improving prediction performance through model averaging, bagging, and boosting techniques are also covered.

Part 2 of the course gives an introduction to machine learning and an overview of neural networks. The perceptron as the basic element for linear seperability and its limitations in classification is discussed. Then, different activation functions and the sigmoid perceptron is studied to solve non-linear classification problems.
The different types of learning paradigms such as supervised, unsupervised,and reinforcement is covered in a machine learning context. Feed-forward neural networks and the back-propagation algorithm will be presented. The course will also cover recurrent neural networks. Finally, deep learning is discussed with emphasis on the basic principles and different types of deep learning neural networks.

The Swedish grades U–G.