David Huk 

Title: Probabilistic forecasting with censored spatial copulas via scoring rules  

Abstract: This work develops a novel method for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are modelled independently of one another. Secondly, a spatial dependency structure is learned in order to make these marginal distributions spatially coherent.

To learn marginal distributions over rainfall values, we propose a class of models termed Joint Generalised Neural Models (JGNMs) which expand the linear part of generalised linear models with a deep neural network allowing them to take into account non-linear trends of the data while learning the parameters for a distribution over the outcome space.

In order to understand the spatial dependency structure of the data, a model based on censored copulas is presented and trained via scoring rules. Utilising the underlying spatial structure as a starting point, we construct a matrix of pair-wise distances between locations which is then transformed by a Gaussian Process Kernel depending on a few parameters. To estimate these parameters, we propose a general framework for the estimation of Gaussian copulas relying on scoring rules as a measure of divergence between distributions.

Uniting our two contributions, namely the JGNM and the Censored Spatial Copulas into a single model, we get a probabilistic model capable of generating possible scenarios on short to long-term timescales, able to be evaluated at any given location, seen or unseen. We show an application of it to a precipitation downscaling problem on a large UK rainfall dataset and compare it to existing methods.

Alexander Kent 

Title: Local Differential Privacy with Time Series Data 

Abstract: The issue of maintaining user privacy whilst simultaneously preserving statistical utility of user data has become increasingly prevalent in recent decades. Government regulation and user demands require data to be kept secure and used only for reasonable purposes, whilst modern machine learning methods allow for remarkable results provided large amounts of data can be obtained and used freely. As a result, privatising data so that it can be used for statistical purposes whilst satisfying these constraints is of importance, and Local Differential Privacy has arisen as the leading framework for carrying out statistical procedures on data whilst maintaining user privacy in the case where there is no trusted aggregator for the data.

Whilst there has been a large amount of research in Local Differential Privacy recently, developments regarding time series data are less common despite the prevalence and importance of this kind of data, primarily due to the difficulties that arise as a result of privatising such data.

In this talk, I will motivate and introduce the ideas of differential privacy and summarise the result of my work with Dr Tom Berrett and Dr Yi Yu so far. I will also briefly introduce minimax theory as a framework for evaluating the performance of any (not necessarily private) estimator, and present the surprising minimax performance that arises due to this intersection of Local Differential Privacy and time series data.