## Advanced Statistical Machine Learning and Pattern Recognition – CO495

### Aims

The aim of the course is to provide the students the necessary theoretical and computational skills to understand, design and implement modern statistical machine learning methodologies regarding statistical component analysis, statistical linear dynamical systems (i.e., HMMs and Kalman filters) and other statistical models such as Markov Random Fields (MRFs).

### Role

Course Leader

## Computational Techniques – CO233

### Aims

The aim of the course is to provide the students the necessary theoretical and computational skills to understand concepts such as:

Vectors, matrices, special matrices, operations and algorithms. Vector and matrix norms Vector spaces, linear dependence, bases, null space, rank space. Eigenvalues, eigenvectors, singular values, singular value decomposition. Solution of systems of linear equations: Triangular systems, Gaussian and Gauss-Jordan elimination, computational implications, LU decomposition, Cholesky factorisation, computational form. Least squares problems. Solution of systems of linear differential equations. Condition of a mathematical problem. Basics of sparse computing. Convergent sequences: Metric spaces. Limits. Cauchy sequences. Fixed-point theorem for contractions. Iterative methods. Functions of several variables: Partial differentiation, the gradient, the Hessian. Taylor expansion. Newton’s method for min f (x). Quadratic forms and linear systems. Method of conjugate gradients.

### Role

Responsible for half the course