The methods we have discussed until now for dealing with the poorly conditioned LS problem improve stability of the LS model by purposely reducing the effective rank of \({\boldsymbol {X}} \) and or \({\boldsymbol {Y}}\) . An alternative approach is regularisation, which improves the modelling process by incorporating prior information into the model in some form. Regularisation is an extensive topic in the computer science, statistical, signal processing, and machine learning literature. The regularisation methods we discuss here are ridge regression, smoothness regularisation, and sparsity regularisation. All forms exist to mitigate the effects of poor conditioning, which results when the columns of \({\boldsymbol {X}} \) become close to linear dependence, resulting in near rank deficiency and hence at least one small eigenvalue. This implies that the variables corresponding to each column are too dependent on one another, or in other words, there is not enough joint information in the columns/variables to create a stable model. Regularisation imposes additional prior information on the solution to help mitigate this situation. Regularisation methods are commonly used with least squares problems and play an important role in the training of neural networks.