Comment out Math comments, to make plots work

EM/Multivariate/playground-3d.ipynb

@@ -33,12 +33,13 @@
    "source": [
     "## Generate Data\n",
     "\n",
-    "Covariance Matrix $\\Sigma$ must be positive semi-definite.\n",
+    "Covariance Matrix Sigma must be positive semi-definite.\n",
     "\n",
     "One way to make sure that we have a positive semi-definite matrix when generating random matrices is:\n",
     "\n",
     "- Generate Random Matrix A\n",
-    "- $C = A^\\intercal A$ will be positive semi-definite"
+    "- Multiply A with its transpose\n",
+    "- The result will be positive semi-definite"
    ]
   },
   {
@@ -140,11 +141,11 @@
     "\n",
     "### Multivariate Normal Distribution\n",
     "\n",
-    "$$\n",
+    "<!-- $$\n",
     "p(\\boldsymbol{x}; \\mu, \\Sigma) = \\det(2 \\pi \\Sigma)^{-\\frac{1}{2}} e^{-\\frac{1}{2} (\\boldsymbol{x} - \\mu)^\\intercal \\Sigma^{-1} (\\boldsymbol{x} - \\mu)}\n",
     "$$\n",
     "\n",
-    "Where Covariance Matrix $\\Sigma$ must be positive semi-definite."
+    "Where Covariance Matrix $\\Sigma$ must be positive semi-definite. -->"
    ]
   },
   {
@@ -216,10 +217,10 @@
    "source": [
     "### Expectation Step\n",
     "\n",
-    "$$\n",
+    "<!-- $$\n",
     "\\large\n",
     "\\gamma (z_{nk}) = \\frac{\\pi_k \\mathcal{N}(\\boldsymbol{x}_n | \\mu_k, \\Sigma_k)}{\\sum\\limits_{j=1}^{K} \\pi_j \\mathcal{N}(\\boldsymbol{x}_n | \\mu_j, \\Sigma_j)}\n",
-    "$$"
+    "$$ -->"
    ]
   },
   {
@@ -250,7 +251,7 @@
    "source": [
     "### Maximization Step\n",
     "\n",
-    "Define\n",
+    "<!-- Define\n",
     "\n",
     "$$\n",
     "N_k = \\sum\\limits_{n=1}^{N} \\gamma(z_{nk})\n",
@@ -269,7 +270,7 @@
     "\n",
     "$$\n",
     "\\Sigma^*_k = \\frac{1}{N_k} \\sum\\limits_{n=1}^{N} \\gamma(z_{nk}) (\\boldsymbol{x}_n - \\mu_k)(\\boldsymbol{x}_n - \\mu_k)^\\intercal\n",
-    "$$\n"
+    "$$ -->\n"
    ]
   },
   {
@@ -302,9 +303,9 @@
    "source": [
     "### Log Likelihood\n",
     "\n",
-    "$$\n",
+    "<!-- $$\n",
     "\\ln p(\\boldsymbol{X}) = \\sum_{n=1}^{N} \\ln \\sum_{k=1}^{K} \\pi_k \\mathcal{N}(\\boldsymbol{x}_n | \\mu_k, \\Sigma_k)\n",
-    "$$"
+    "$$ -->"
    ]
   },
   {