Final project Numerical Methods for Kernel Machines.

Topics Covered

• Unsupervised learning

  • Dimensionality reduction: PCA, MDS, kernel PCA
  • Manifold learning: Principal curves, local-MDS, ISOMAP, t-SNE

• Kernel methods for supervised learning

  • Theoretical background for kernel machines: Functional analysis, reproducing kernel Hilbert spaces and kernel functions
  • Kernel ridge regression
  • SVM for classification and regression
  • Examples of applications of kernel machines in image recognition, time series, genomics, etc.

Learning Objectives

Upon completion of the course, the student should have acquired advanced competences on the general topics of statistical machine learning and unsupervised topics, especially data visualization. In particular, the student should be able to produce machine learning solutions for many complex problems, including those in which a reduction of dimension is necessary, those where the data comes as variables of different mixed types, or those where the number of variables greatly exceeds the number of observations, such as problems typically found in genomics.