# Lasso regression doesn't converge in case of zero Y-vector

I try to use lasso regression to solve linear problem with big amount of equations (~10 000). Everything worked fine, but I noticed that if in Y-vector all elements are equal, "fit" function hang for infinite time. As I understand it is the same if Y is the zero-vector (because I set normilize = True)

Then I created minimal examle and wrote this very simple python code:

X = np.array([[1,0], [0, 1]])
Y = np.array([0, 0])
clf = sklearn.linear_model.Lasso()
clf.fit(X, Y)


X - 2x2 identity matrix, Y - zero vector Here I got the following error:

C:\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.0, tolerance: 0.0
positive)

So, conclusion here is that lasso regression doesn't converge in case of zero vector And my question is why? Is it fundamental problem? Or it is a bug in sklearn implementation?

It looks strange for me because there is obvious sollution here: all coefs are zero (and norm of this vector is zero as well).

P.S. If I replace Lasso -> Ridge everything works fine again

• I am going to speculate that the convergence criterion is based on an estimate of the typical size and/or variation of $y.$ When all the values of $y$ are zero (or perhaps even just constant) you have pulled the rug out from that estimator and exposed a bug. Since this appears purely to be a software issue, people have voted to close the question. – whuber Oct 17 at 22:28