Mention Bayesian GMM to determine optimal number of components

Author: krasserm

latent_variable_models_part_1.ipynb

@@ -563,6 +563,8 @@
    "source": [
     "There is a strong increase in the lower bound value until $C = 3$ and then the lower bound more or less doesn't increase any more. With more components there are of course more options to overfit but the simplest model that reaches a relatively high lower bound value is a GMM with 3 components. This is exactly the number of components used to generate the data.\n",
     "\n",
+    "A more principled approach to determine the optimal number of components requires a Bayesian treatment of model parameters. In this case the lower bound would also take into account model complexity and we would see decreasing lower bound values for $C \\gt 3$ and a maximum at $C = 3$. For details see section 10.2.4 in \\[1\\].\n",
+    "\n",
     "### Implementation with scikit-learn\n",
     "\n",
     "The low-level implementation above was just for illustration purposes. Scikit-learn already comes with a `GaussianMixture` class that can be readily used."