Smoothed Target Encoding

Encode a categorical feature as the smoothed mean of the target for each category.

One-hot encoding a column with thousands of categories makes thousands of columns. Target encoding makes one: each category is replaced by the average target of the training rows in that category. Rare categories have noisy means, so blend each mean with the global mean. The blend uses m, the number of "virtual" rows at the global mean:

enc(c) = (n_c * mean_c + m * global_mean) / (n_c + m)

n_c is the count of category c in the training data, mean_c is the mean target over those rows, and global_mean is the mean of all training targets. A category that never appears in training gets global_mean.

Fit on the training data and return the encoding of cats_test.

Function signature

def target_encode(cats_train, y_train, cats_test, m=1.0):

Example

Input

target_encode(["a", "a", "b"], np.array([1.0, 0.0, 1.0]), ["a", "b", "c"], m=1.0)

Output

array([0.55555556, 0.83333333, 0.66666667])

Reasoning

The global mean is 2 / 3. Category a has 2 rows with mean 0.5, so its code is (2 * 0.5 + 2/3) / 3 = 0.556. Category b has 1 row with mean 1, so its code is (1 + 2/3) / 2 = 0.833. Category c is unseen, so it gets 0.667.

Constraints and notes

• Categories can be any hashable values, such as strings or ints.
• With m = 0, the code is the raw category mean.
• Return a float array with one value per entry of cats_test.