Nan result for one leave out cross validation

Question

In this code, I get nan for the test result, what is the reason?

Average Train R^2: 0.504

Average Test R^2: nan

loo = LeaveOneOut()
train_r2_scores = []
test_r2_scores = []
for train_index, test_index in loo.split(X):

    X_train, X_test = X.iloc[train_index], X.iloc[test_index]
    y_train, y_test = y.iloc[train_index], y.iloc[test_index]
    model = LinearRegression()
    model.fit(X_train, y_train)
    y_train_pred = model.predict(X_train)
    train_r2 = r2_score(y_train, y_train_pred)
    train_r2_scores.append(train_r2)

    y_test_pred = model.predict(X_test)
    test_r2 = r2_score(y_test, y_test_pred)
    test_r2_scores.append(test_r2)

print("Average Train R^2:", np.mean(train_r2_scores))
print("Average Test R^2:", np.mean(test_r2_scores))```

Answer 1

You are using leave-one-out in the wrong way. A side-effect is the error you are facing, here.

Let me explain

For leave-one-out, the test set consists of exactly one sample in every iteration. This means, you cannot compute a meaningful test score (like $r^2$) on a single test sample.

Especially for the case of $r^2$, the sum of squared errors is divided by the variance of the true values. The variance of a single sample is always zero, which causes your problem.

How to fix this

You need to collect predictions and true values inside the loop and compute the $r^2$-score outside of it:

pred_test = []
true_test = []
for train_index, test_index in loo.split(X):

    # ...

    y_test_pred = model.predict(X_test)
    pred_test.append(y_test_pred)
    true_test.append(y_test

test_r2_score = r2_score(true_test, pred_test)
print("Average Train R^2:", np.mean(train_r2_scores))
print("Test R^2:", test_r2_score )