Explained variance score

The problem, from first principles

R-squared score penalizes a prediction that is shifted away from the truth, because the shift shows up in the residual sum of squares. Sometimes that is not what you want. If a model is consistently 3 units too high but otherwise tracks every movement of the target perfectly, the explained variance score ignores the constant offset and still rewards the model for tracking the variation. It measures how much of the target's variance the errors fail to explain, with the mean error removed.

Implement explained_variance_score(y_true, y_pred), which returns 1 - Var(y_true - y_pred) / Var(y_true), using population variance (ddof = 0).

Constraints

• Shapes must match, otherwise raise ValueError.
• If y_true is constant, Var(y_true) is zero: raise ValueError.
• A constant offset in the predictions leaves the score at 1.
• Do not modify the inputs.

Hints

Open one at a time. Each gives away a little more than the last.