Parallelising Least Squares Methods under the Multisplitting Theory

In our modern society, we are overwhelmed by digital information and data. Its analysis opens up several perspectives, both from a business as well as a scientific point of view. A major challenge is to statistically analyse high dimensional problems that are too complex to be solved by the current data processing techniques.

We will focus on regression analysis, where the vast amount of available observations allows us to detect even the smallest effects. This often drastically increases the number of variables in our models. As a result, the methods to determine the linear least square solution have become numerically inefficient using a serial implementation.

The scientific world has recognised this challenged and developed parallel implementations of the least squares solver. While most techniques apply a code parallelisation, the Multisplitting technique splits the regression problem in several smaller regression problems, offering a linear speed-up over the alternative techniques. We will accelerate the multisplitting by exploiting hidden structure within the regression design as a pre-processing step. Furthermore, we will analyse its sensitivity to numerical errors throughout the algorithm. By extending the multisplitting methodology to other regression-based methods, many high-dimensional least squares applications: from medical imaging in signal processing to control engineering in machine learning, will benefit from this research.