Statistics with Machine Learning MSc

In this module, the fundamental principles and techniques underlying modern statistical and data analysis will be introduced. You will gain experience in using a statistical package and interpreting its output. The course will cover a 'common core' consisting of:

• statistical concepts and methods
• linear models
• probability techniques
• Markov chains

You will explore the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.

You cover topics including:

• sufficiency
• estimating equations
• likelihood ratio tests
• best-unbiased estimators

There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

The module will give you hands-on experience of using statistical software and interpreting its output, as well as short-report writing.

Machine Learning is a topic at the interface between statistics and computer science that concerns models that can adapt to and make predictions based on data. This module builds on principles of statistical inference and linear regression. It introduces a variety of methods of regression and classification, trade-off, and on methods to measure and compensate for overfitting.

You will benefit with hands-on learning using computational methods to tackle challenging real world machine learning problems.

You will work on a substantial investigation on a topic in statistics or probability. The study will be largely self-directed, although a supervisor will provide oversight and input where necessary. The topic could be based on the statistical analysis of a substantial dataset, an investigation into the statistical methodology or an investigation into a topic of applied probability or probability theory. It is expected that most projects will contain an element of statistical computing.

During this module you will explore the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction. Key topics to be covered include: principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset; modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution; classification of observation vectors into subpopulations using a training sample; canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables. Further topics to be covered include methods of clustering and multidimensional scaling.

This module explores how computers allow the easy implementation of standard, but computationally intensive, statistical methods and also explores their use in the solution of non-standard analytically intractable problems by innovative numerical methods. Particular topics covered include a selection from simulation methods, Markov chain Monte Carlo methods, the bootstrap and nonparametric statistics, statistical image analysis, and wavelets. You will gain experience of using a statistical package and interpreting its output.

We consider modern machine learning tools including Gaussian processes and deep neural networks within a framework for building and training surrogates for computer models derived from Differential Equations (DEs).

We employ these tools within the study of advanced techniques for uncertainty propagation and parameter inference in DEs. Uncertainty propagation techniques comprise Monte Carlo methods, stochastic colocation and stochastic Galerkin.

Modern techniques for parameter inference for DEs are covered from the deterministic as well as the Bayesian perspective.

The aim of the module is to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. The probabilistic ideas that underlie the problems of portfolio selection, and of pricing and hedging options, are introduced. You will gain experience of a topic of considerable contemporary importance, both in research and in applications. You will undertake a project which will involve independent reading, and a written report.

This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly occurring models will be discussed and their properties derived. Methods for model identification for real-time series data will be considered. Techniques for estimating the parameters of a model, assessing its fit and forecasting future values will be developed. You will gain experience of using a statistical package and interpreting its output.