Faster model fitting for quantile additive models

Reliable electricity load forecasts are an essential input for electricity production planning and power grid management. The UK has historically relied heavily on fossil fuel power plants, whose high ramp-up rates made adjusting for forecasting errors easy. As such stations are replaced with less flexible nuclear plants and renewables, the network will become much more reliant on accurate forecasts.

The need to reduce carbons emission is driving the growth of electric vehicles sales, in addition to the transition to renewable production technologies (e.g., solar panels and wind turbines). Future grid management systems will coordinate distributed production and storage resources to manage, in a cost-effective fashion, the increased load and variability brought by the electrification of transportation and by a higher share of weather-dependent production.

Electricity demand forecasts at a low level of aggregation, possibly down to the individual household, will be key inputs for such systems.

The project will focus on developing new non-parametric regression methods aimed at tackling upcoming forecasting challenges in the electricity industry. The particular model class which will be considered is that of generalized additive models (GAMs), which are widely-used in energy applications because they provide an appealing balance between flexibility, interpretability and scalability to Big Data.

The project will build particularly on Fasiolo et al. (2020), which proposed new methods for distribution-free quantile GAMs (QGAMs). QGAMs often outperform standard GAMs in terms of accuracy in probabilistic electricity demand forecasting, due to the lack of any parametric assumption on the distribution of the response variable. However, QGAMs are computationally slower than GAMs, which limits the utility of such methods for larger data sets (e.g., smart meter data).

The project will focus on developing new statistical methods for accelerating QGAM model fitting. Doing so will require theoretical/methodological work aimed at developing the underlying statistical methodology as well as computational work involving numerical linear algebra methods. It is potentially high impact because faster fitting methods will dramatically increase the usefulness of QGAMs for electricity demand forecasting on large data set.

Further, the new methods should apply to loss-based models in general and could be used in many other application areas of (Q)GAMs, such as ecology, epidemiology, precision agriculture and business analytics to name a few.