fixing errors

book/tutorials/tree_models/Tree_Models_in_ML.ipynb

@@ -437,12 +437,12 @@
     "\n",
     "The root node (node #0) assigns values of **bare_eart_dem** lesser than or equal to 3076.523 to the right branch and values of **bare_eart_dem** greater than 3076.523 to the left node. Observations with **bare_eart_dem** lesser than or equal to 3076.523 are further partitioned based on **unwrapped_phase** values. Overall, the regression tree splits the observations into four disjoint groups or regions ($R_i$) of the feature space.\n",
     "\n",
-    "\\begin{align*}\n",
+    "\\begin{align}\n",
     "R_1 &= \\left\\lbrace  X \\ | \\ \\text{bare\\_earth\\_dem} \\le 3076.523,\\ \\text{unwrapped\\_phase} \\le -8.048 \\right\\rbrace & \\hat{y}_{R_1} = 0.941 \\\\\n",
     "R_2 &= \\left\\lbrace  X \\ | \\ \\text{bare\\_earth\\_dem} \\le 3076.523,\\ \\text{unwrapped\\_phase} > -8.048 \\right\\rbrace & \\hat{y}_{R_2} = 1.159 \\\\\n",
     "R_3 &= \\left\\lbrace  X \\ | \\ \\text{bare\\_earth\\_dem} > 3076.5235,\\ \\text{vegetation\\_height} \\le 9.101 \\right\\rbrace & \\hat{y}_{R_3} = 1.293 \\\\\n",
     "R_4 &= \\left\\lbrace  X \\ | \\ \\text{bare\\_earth\\_dem} > 3076.523,\\ \\text{vegetation\\_height} > 9.101 \\right\\rbrace & \\hat{y}_{R_4} = 1.081 \\\\\n",
-    "\\end{align*}\n",
+    "\\end{align}\n",
     "\n",
     "\n",
     "where $\\hat{y}_{R_i}$ is the mean of the respective regions. The regions $R_i, \\ i = 1,2,3, 4$ are called **terminal nodes** or **leaves**, the points where the feature space ($\\textbf{x}$) is partitioned are called **internal nodes** and the line segments connecting the nodes are referred to as **branches**. Generally, to know which region an observation belongs to, we ask series of question(s) starting from the root node until we get to the terminal node and the value predicted for the observation is mean of all training observations in that region. Mathematically we write;\n",