Update example

docs/examples/GaussianMixture_Regression_CaliforniaHousing.ipynb

@@ -34,12 +34,22 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "For each component of the mixture, there would be a set of parameters that depend on covariates, and additional mixing coefficients which are also modeled as a function of covariates. This is particularly useful when a single parametric distribution cannot adequately capture the underlying data generating process. A mixture distribution can be represented as follows:\n",
-    "\n",
+    "For each component of the mixture, there would be a set of parameters that depend on covariates, and additional mixing coefficients which are also modeled as a function of covariates. This is particularly useful when a single parametric distribution cannot adequately capture the underlying data generating process. A mixture distribution can be represented as follows:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "\\begin{equation}\n",
     "f\\bigl(y_{i} | \\boldsymbol{\\theta}_{i}(x_{i})\\bigr) = \\sum_{m=1}^{M} w_{i,m}(x_{i}) \\cdot f_{m}\\bigl(y_{i} | \\boldsymbol{\\theta}_{i,m}(x_{i})\\bigr)\n",
-    "\\end{equation}\n",
-    "\n",
+    "\\end{equation}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "where $f(\\cdot)$ represents the mixture density for the $i$-th observation, $f_{m}(\\cdot)$ is the $m$-th component density, each with its own set of parameters $\\boldsymbol{\\theta}_{i,m}(\\cdot)$, and $w_{i,m}(\\cdot)$ represent the weights of the $m$-th component in the mixture, subject to $\\sum_{j=1}^{M} w_{i,m} = 1$. The components can either be a combination of different parametric univariate distributions, such as a combination of a Normal and a StudentT, or, as in our implementation, a combination of the same distribution-type with different parameterizations, e.g., Gaussian-Mixture or StudentT-Mixture. The choice of the component distributions depends on the characteristics of the data and the underlying assumptions. Due to their high flexibility, mixture densities can portray a diverse range of shapes, making them adaptable to a plethora of datasets. "
    ]
   },