ST41915 Advanced Topics in Data Science
Introductory description
This module runs in Term 2 and will be comprised of three selected topics in the area of computational challenges associated with data analysis. The topics may change year to year.
Some examples of topics from previous academic years:
Deep Learning for Natural Language Processing, Decision Trees and Random Forests, Model Comparison and Selection, Artificial Neural Networks, Introduction to Reinforcement Learning and Modelling the Written Word: Compression and HumanComputerInterfaces.
Students will be given selected advanced research material for independent study and examination.
This module is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.
Prerequisites: ST219 Mathematical Statistics B OR ST220 Introduction to Mathematical Statistics OR OR CS260 Algorithms.
Module aims
Data Science is an important frontier in the mathematical sciences and employers across a number of sectors are looking for graduates with strong computational and statistical skills. The aim of this module is to provide students with a working knowledge of three selected topics that emphasize the interplay between data analysis and computation.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Topics will vary from year to year. Example syllabi include:
 Numerical optimization: algorithms to find the minimizer of convex function e.g. gradient descent, Newton and quasiNewton methods. Rates of convergence and computational costs associated with these algorithms in general and / or specific settings. Discussion of relative merits of different methodology.
 The MapReduce programming model: modern approaches to scalingup computation via distribution and parallelization, such as the mapreduce programming model, and systems such as Hadoop and Spark.
 Streaming algorithms: algorithms to process massive streams of data. Hashing, sketching and randomization. Probabilistic counting, counting distinct elements, countmin sketch.
 Highdimensional regression and variable selection: methods for regression with large datasets, and methods for determining which covariates are important. Statistical and computational issues relating to large numbers of covariates and / or measurements. Ridge regression, the LASSO, and variable selection. Crossvalidation. Screening.
 Coding theory: compression and error detection. Lossless coding, entropy, Shannon's theorem. Symbol and dictionarybased approaches. Errorcorrecting codes, parity checks, Hamming (7,4)code.
 Deep Learning for Natural Language Processing, introduction to the theory and practice of deep NNs with focus on the applications in natural language processing (NLP). Neural network architectures such as convolutional NNs, recurrent NNs, attention mechanisms, transformers, sequencetosequence learning and (timepermitting) generative adversarial networks and variational autoencoder. key concepts of artificial NNs, such as activation functions, layers, weights and gradient descent for fitting a NN;
 Decision Trees and Random Forests: CHAID, C4.5, C5.0, ID3 and CART algorithms, bagging, boosting, random forests, the pros and cons of such approaches. Software examples (e.g. R package CHAID and rpart).
 Model comparison and selection, Scientific validity in the context of the data analytics workflow, Basic modelagnostic assessment of supervised/predictive models, Performance quantification of models. Predictive model validationin R/mlr and python/sklearn Julia/MLJ. Statistical formulation of the supervised learning setting,
Biasvariance tradeoff, crossvalidation and resampling estimators, Estimators of the generalization loss and the loss‘s variance, Hypothesis testing for pairwise and portmanteau model comparison, Metastrategies for automated model improvement, Interaction of model tuning and model validation workflows  Artificial Neural Networks. Artificial neural networks (NNs) are a class of learning algorithms for regression, classification, and unsupervised learning that mimic real neural networks. They are very flexible and have become hugely popular in recent years. This topic will provide an introduction to the theory and practice of artificial NNs for supervised learning, building up from simple single layer feedforward networks to complex multilayer 'deep' architectures. We will cover some theory such as universal approximation theorems, as well as practicalities like training and regularization. Convolutional Nns. Advanced component: recurrent NNs and unsupervised NNs.
 Reinforcement Learning: Reinforcement Learning (RL) is one of the main subfields of machine learning, alongside supervised and unsupervised learning, that focuses on decision making under implicit feedback. As such, it is heavily employed and developed in areas such as robotics and Al engines in games like Go and Chess.
This topic will introduce the field of RL and standard agentenvironment framework, covering Bellman's equations, dynamic programming, Monte Carlo and TemporalDifference learning. Advanced Component: eligibility traces, function approximation.  Modelling the Written Word: Modelling of written words, viewed as streams of symbols from a finite
alphabet, is a rich field with an extensive literature. This topic will provide an introduction to some
probabilistic approaches to this problem and will show how these models can be used to efficiently store written text and also to provide efficient mechanisms for entry of text into computer systems which can be used without mastering the keyboard. Advanced Component: Grammarbased language models.
Learning outcomes
By the end of the module, students should be able to:
 Demonstrate understanding of the three selected topics.
 Appreciate the computational challenges associated with data analysis and use some techniques developed to meet these challenges.
 Be able to critically appraise the use of these topics.
 Be able to understand current research and developments in the three selected topics.
 Be critical of current research developments in the three selected topics.
Indicative reading list
General texts in the correct area:
Hastie, T. and Tibshirani R. (2009)"The Elements of Statistical Learning ", Corr. 9th printing 2017 edition; Springer
Bishop, C.M. (2008) "Pattern Recognition and Machine Learning" ; SpringerVerlag New York
Other texts will be specified depending on the topics covered.
View reading list on Talis Aspire
Subject specific skills
This will depend on the topic but will be the ability to understand, evaluate and apply various complex statistical, computational and machine learning tools to a variety of datasets. Students will develop skills in the use of appropriate software.
Transferable skills
The general understanding of data from a variety of contexts. The ability to identify and find new data analysis techniques and to then learn them from suitable documentation. Be able to learn coding type software. To be able to appraise and discuss recent research in a technical area.
Study time
Type  Required  Optional 

Lectures  30 sessions of 1 hour (20%)  2 sessions of 1 hour 
Private study  120 hours (80%)  
Total  150 hours 
Private study description
Study of advanced topic, weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for examination.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group B2
Weighting  Study time  

Inperson Examination  100%  
The examination will contain one compulsory question on the advanced topic and four additional questions of which the best marks of TWO questions will be used to calculate your grade.

Assessment group R1
Weighting  Study time  

Inperson Examination  Resit  100%  
The examination will contain one compulsory question on the advanced topic and four additional questions of which the best marks of TWO questions will be used to calculate your grade. ~Platforms  Moodle

Feedback on assessment
Solutions and cohort level feedback will be provided for the examination.
Courses
This module is Optional for:
 Year 1 of TMAAG1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of TMAAG1P9 Postgraduate Taught Interdisciplinary Mathematics
 Year 1 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 1 of TMAAG1P0 Postgraduate Taught Mathematics
 Year 1 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)

TMAAG1PF Postgraduate Taught Mathematics of Systems
 Year 1 of G1PF Mathematics of Systems
 Year 1 of G1PF Mathematics of Systems
 Year 1 of TSTAG4P1 Postgraduate Taught Statistics

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 4 of G300 Mathematics, Operational Research, Statistics and Economics
This module is Option list A for:

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)

USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list B for:
 Year 4 of USTAG304 Undergraduate Data Science (MSci)
 Year 4 of UCSAG4G3 Undergraduate Discrete Mathematics
This module is Option list D for:
 Year 4 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
This module is Option list E for:
 Year 4 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
This module is Option list F for:
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
 Year 3 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
 Year 4 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)