Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Stochastic Theory and Methods in Data Science
Code MATH368
Coordinator Dr A Alpers
Mathematical Sciences
Andreas.Alpers@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2022-23 Level 6 FHEQ Second Semester 15

Aims

1. To develop a understanding of the foundations of stochastics normally including processes and theory.

2. To develop an understanding of the properties of simulation methods and their applications to statistical concepts.

3. To develop skills in using computer simulations such as Monte-Carlo methods

4. To gain an understanding of the learning theory and methods and of their use in the context of machine learning and statistical physics.

5. To obtain an understanding of particle filters and stochastic optimisation.


Learning Outcomes

(LO1) Develop understanding of the use of probability theory.

(LO2) Understand stochastic models and the use statistical data.

(LO3) Demonstrate numerical skills for the understanding of stochastic processes.

(LO4) Understand the main machine learning techniques.


Syllabus

 

1 REVIEW OF ESSENTIAL BACKGROUND FROM PROBABILITY/STATISTICS
1.1 Conditioning
2.2 Law of large numbers and central limit theorem
2.3 Independence
3.3 Elements of stochastic processes in time and space

2 SIMULATION: THEORY AND PRACTICE
2.1: Pseudo random number generator, simulation methods for univariate distributions
2.2: Monte Carlo methods
2.2: Variance reduction techniques, importance sampling methods

3 MARKOV CHAIN METHODS
3.1 Simulation in presence of dependence
3.2 Sampling methods: Gibbs, independence sampling, Metropolis
3.3 Further MCMC schemes (optional): adaptive, Hamiltonian, and time-reversal

4 LEARNING THEORY AND METHODS
4.1: The process of learning;
4.2 Data classification, Vapnik-Chervonenkis dimension
4.3 Supervised learning: support vector machines, neural networks, Gaussian methods, decision trees
4.4 Unsupervised learning: clustering, learning on huge f eature spaces
4.5 Reinforcement learning
4.6 Statistical physics: Hopfield networks, Boltzmann machines, simulated annealing

5. OPTIONAL TOPICS
5.1. State estimation and filtering: Kalman filtering, Particle filtering
5.2. Stochastic and heuristic optimization


Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH263 Statistical Theory and Methods I; MATH264 STATISTICAL THEORY AND METHODS II; MATH362 APPLIED PROBABILITY; MATH162 INTRODUCTION TO STATISTICS 

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

 

Programme(s) (including Year of Study) to which this module is available on a required basis:

 

Programme(s) (including Year of Study) to which this module is available on an optional basis:

 

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final written exam  120    70       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Group project 1 Based on the first part of the module (stochastic theory).    15       
Group project 2 Based on the second part of the module (data science).    15