During the past 20 years or so, building models in a data-driven way by using loss-penalty paradigms, regularisation, cross-validation, etc. has become increasingly popular. Sparsity, in the general sense of a limited number of non-zero “entities”, is a widely used concept in this context. Sparsity provides a particular form of regularisation that favours model interpretability.

Sparsity may be in terms of individual parameters, groups of parameters, singular values of matrices (low rank models), and more. Sparsity is often obtained by regularisation with L1-norms and variants thereof, leading to non-differentiable convex optimisation problems. I will talk about statistical models providing sparsity, the optimisation problems that come with them, and a little about how these problems can be solved. Illustrations will be given with examples from e.g. the life sciences.