in a text I have found the following:
"The LASSO regerssion method offers a sparse solution and as such the interpretability of the model can be improved".
Can someone help me to understand what is meant by this? As far as I know, a sparse decomposition of a solution to a system of equation is that vector of dimension l with minimum pseudo-l norm such that the system is still satisfied. How would a sparse solution, which is setting some regression coefficients to zero, be of help in the interpretation?
Sparse matrix/array or whatever is by definition when your matrix contains mostly zeros and few non-zero entries. In the other hand, a dense matrix/array is when you have few zeros.
When you apply LASSO regression, the sparsity of your learned coefficients depends on the amount of the penalty (lambda). The higher the penalty, the more sparse coefficients you get. That is, the non-zero coefficients (selected variables). For example, if you have 100 independent variables in your regression, the LASSO may return only 10 non-zero variables. That means 10 non-zero variables and 90 zero variables. This is exactly what is the meaning of sparsity.
Having few selected variables (non-zero) means interpretable model as you can explain it with few variables (in the above example 10 variables) instead of using the 100 variables.