LASSO remaining features for different penalisation I am using the sklearn LASSOCV function and I am changing the penalisation parameter in order to adjust the number of features killed off. For example for $\alpha = 0.01$ I have 55 features remaining and for $\alpha=0.5$ I have 6 remaining features. 

I would expect that the 6 features I am getting for the second case are a subset of the 55 features I am getting in the first case. This is not what is happening however. 4 out of 6 features are not in the 55 of the first case. 

Could someone explain to me the intuition behind why this is happening?

Thanks, 
P
Lambda is a tuning parameter („how much regularisation“, I think called alpha in sklearn) and you would choose lambda so that you optimise fit (e.g. by MSE). You can do this by running cross validation. 

This page (for the GLMnet package in R) explains how to apply Lasso in a very instructive way (alpha is the elastic-net mixing parameter here, Lambda is the tuning parameter).

You may also look at „ Introduction to Statistical Learning“, Ch. 6.2, in which Lasso is discussed in a very good way.

There are also Python Labs for the book, which should give you a blueprint for how to use Lasso in Python (see Section 6.6.2).