[QUESTION] Clarification about likelihood and PDF

[AlirezaTheH]

In chapter 9's notebook cell 100:

resolution = 100
grid = np.arange(-10, 10, 1 / resolution)
xx, yy = np.meshgrid(grid, grid)
X_full = np.vstack([xx.ravel(), yy.ravel()]).T

pdf = np.exp(gm.score_samples(X_full))
pdf_probas = pdf * (1 / resolution) ** 2
pdf_probas.sum()

You have used score_samples() as PDF, but Scikit-Learn's documentation says it's the likelihood. Also later in cell 109:

n_clusters = 3
n_dims = 2
n_params_for_weights = n_clusters - 1
n_params_for_means = n_clusters * n_dims
n_params_for_covariance = n_clusters * n_dims * (n_dims + 1) // 2
n_params = n_params_for_weights + n_params_for_means + n_params_for_covariance
max_log_likelihood = gm.score(X) * len(X) # log(L^)
bic = np.log(len(X)) * n_params - 2 * max_log_likelihood
aic = 2 * n_params - 2 * max_log_likelihood
print(f"bic = {bic}")
print(f"aic = {aic}")
print(f"n_params = {n_params}")

You have used score() (which is the mean of score_samples()) as likelihood. I'm a little confused. Can you explain why?

[AlirezaTheH]

@ageron 🤔