title: Negative BIC values for GaussianMixture in scikit-learn (sklearn)
body: <p>In <code>scikit-learn</code>, the <code>GaussianMixture</code> object has the method <code>bic(X)</code> that implements the Bayesian Information Criterion to choose the number of components that better fits the data.
  This is an example of usage:</p>
  <pre><code>from sklearn import mixture
  for n in range(0,10):
      gmm = mixture.GaussianMixture(n_components=n, max_iter=1000, covariance_type='diag', n_init=50)
      gmm.fit(data)
      bic_n = gmm.bic(data)
  </code></pre>
  <p>I am fitting a GMM on a dataset with 600k rows and 7 columns. The BIC values are always negative, e.g. <code>[-2000, -3000, -3300, ..]</code>. <br>
  In the documentation of the method <code>bic()</code>, it says &quot;The lower the better&quot;. In the case of negative values as in my example, is then <code>-3300</code> the best value, or it refers to the lowest value in absolute terms?</p>