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Machine Learning [M12]

The lecture course gives an introduction to machine learning, a field which is interdisciplinary bringing together expertise developed in Mathematics, Computing, Engineering, Physics and more. The goal of machine learning is to gain knowledge from data, the sources of which can be very varied. From this, understanding of the underlying principles is gained in order to make decisions or predictions. Different techniques with their advantages and disadvantages will be introduced at a high level with theoretical underpinning and pointers to more in depth sources of information. The central questions explored for different methods are: "Why does it work?", "When should it be applied?" and "Where and why can it go wrong?". Where appropriate, techniques will be illustrated by an application.

The course will cover the following topics

Classification

  • Linear classification
    • Features
    • Fisher's discriminant analysis
    • Linear Discriminant Analysis (LDA)
    • Multiple classes
    • Online learning
    • Perceptron
    • Support Vector Machine (SVM)
    • Passive Aggressive algorithm (PA)
  • Non-linear classification
    • Quadratic Discriminant Analysis (QDA)
    • Kernel trick
    • k Nearest Neighbours (k-NN)
    • Boosting
    • Cascades
    • Neural Networks
  • Regression
    • Linear regression
    • Polynomial regression
    • Ordinary Least Squares (OLS)
    • Over-fitting and under-fitting
    • Partial Least Squares (PLS)
    • Regularization
    • Bayesian regression
    • Expectation Maximization algorithm (EM)
    • Relevance Vector Machine (RVM)
  • Clustering
    • K-means
    • Mixture models and Gaussians
    • Dirichlet Process
    • Chinese Restaurant Process
  • Dimensionality Reduction and Factor Analysis
    • Factor Analysis
    • Principal Component Analysis (PCA)
    • Independent Component Analysis (ICA)
  • Representation and Feature Learning
    • Auto encoders
    • Restricted Boltzmann machine
    • Sparse Coding and K-SVD
    • Beta Process Factor Analysis
    • Indian Buffet Process
  • Sampling
    • Inverse CDF Sampling
    • Rejection Sampling
    • Importance Sampling
    • Markov Chain Monte-Carlo