Foundations of Data Science II - Statistics & Applied Maths

This half day session is a nice combination of Statistics & Applied Maths and is delivered by Prof James Gleeson, UL & Dr Riccardo Rastelli, UCD

Prof James Gleeson will cover the topic of networks approaches: approximation methods for dynamics on networks and Dr Riccardo Rastelli will concentrate on Statistical network models (e.g. ERGMs, latent position models, stochastic block models), topped off with a hands on session before lunch. Please ensure you bring your laptop to this session.

Abstract - Dr Riccardo Rastelli

Nowadays, large amounts of stored data describe how entities interact with each other. For example, these data may represent friendship relations between scholars, coauthorship relations between researchers, mutual claims between financial institutions, or functional connectivity between different areas of the brain. Random graphs are the mathematical tools that are used to represent these interaction datasets.

Researchers and practitioners are often interested in modelling the random graphs, and in understanding their structures and capturing some of their features of interest. For these purposes, a number of statistical models have been introduced in recent times. One family of these statistical models relies on a "latent variable" formalism, whereby one assumes that the nodes are characterised by some latent information that determines their connectivity behaviour.

In this session will focus on two latent variable models for random graphs: the stochastic block model and the latent position model. Riccardo will introduce the theory behind these models, and give an overview of their mathematical properties. Then, he will focus on the R packages that can be used to fit them, and will coordinate an interactive session where the models will be used to analyse real data-sets.

Abstract - Prof James Gleeson

Title: Approximation methods for dynamics on networks

The structure of a large-scale network can strongly affect dynamics that take place on the nodes of the network. For example, if the nodes of a network represent people, with edges representing contacts that enable transmission of an infectious disease such as influenza, it is of considerable interest to understand how the connectivity of the network can affect the time-dependence of disease spreading through a population. In this lecture we will introduce some examples of dynamical processes on networks, and then look at standard approaches to examining how network structure affects dynamics, with a particular focus on how the degree distribution of a configuration model network impacts disease spreading. Using some arguments from linear stability analysis and so-called mean-field approximations we can show that certain types of networks are extremely vulnerable to epidemic outbreaks. We will discuss the limitations of the approximations used, and the relevance of the results to real-world dynamics and networks.

Please see below details of the full week's training as you may be interested in other training days available:

Monday 2nd December (Applied Maths)

Tuesday 3rd December (Machine Learning)

Wednesday 4th December (Statistics)

Thursday 5th December (Statistics)