580MidtermDecisionTreeSol&MCQ#9.ipynb

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    "**Only for students in CSCI 580, Fall 2024. Do not share**\n",
    "---\n",
    "\n",
    "## Solution to the Decision Tree Problem in the Mideterm Exam\n",
    "\n",
    "You want to predict whether a customer will **Buy** or **Not Buy** a product based on two attributes:\n",
    "1. **Income** (Low, High)\n",
    "2. **Age** (≤30, 31–50, >50)\n",
    "\n",
    "| Income  | Age  | Buy?    |\n",
    "|---------|------|---------|\n",
    "| Low     | ≤30  | No      |\n",
    "| Low     | 31–50| No      |\n",
    "| High    | ≤30  | Yes     |\n",
    "| High    | 31–50| No      |\n",
    "| High    | >50  | Yes     |\n",
    "| Low     | >50  | No      |\n",
    "| High    | >50  | Yes     |\n",
    "\n",
    "### Step 1: Compute Gini Index for the Dataset\n",
    "\n",
    "To begin, we calculate the Gini index for the entire dataset.\n",
    "\n",
    "- **Total instances = 7**\n",
    "- **No = 4, Yes = 3**\n",
    "\n",
    "Gini index for the whole dataset:\n",
    "$$\n",
    "Gini = 1 - \\left(\\frac{4}{7}\\right)^2 - \\left(\\frac{3}{7}\\right)^2 = 1 - 0.327 - 0.184 = 0.489\n",
    "$$\n",
    "\n",
    "### Step 2: Compute Gini Index for Each Attribute\n",
    "\n",
    "#### **Attribute 1: Income**\n",
    "We split the data based on two values of Income (Low, High).\n",
    "\n",
    "##### Subgroup 1: Income = Low\n",
    "- **Total instances = 3**\n",
    "- **No = 3, Yes = 0**\n",
    "\n",
    "Gini index:\n",
    "$$\n",
    "Gini_{\\text{Low}} = 1 - \\left(\\frac{3}{3}\\right)^2 - \\left(\\frac{0}{3}\\right)^2 = 1 - 1 = 0\n",
    "$$\n",
    "\n",
    "##### Subgroup 2: Income = High\n",
    "- **Total instances = 4**\n",
    "- **No = 1, Yes = 3**\n",
    "\n",
    "Gini index:\n",
    "$$\n",
    "Gini_{\\text{High}} = 1 - \\left(\\frac{1}{4}\\right)^2 - \\left(\\frac{3}{4}\\right)^2 = 1 - 0.0625 - 0.5625 = 0.375\n",
    "$$\n",
    "\n",
    "##### Weighted Gini for Income:\n",
    "$$\n",
    "\\text{Weighted Gini} = \\left(\\frac{3}{7} \\times 0\\right) + \\left(\\frac{4}{7} \\times 0.375\\right) = 0 + 0.214 = 0.214\n",
    "$$\n",
    "\n",
    "#### **Attribute 2: Age**\n",
    "Now we calculate the Gini index for splits based on Age.\n",
    "\n",
    "##### Subgroup 1: Age ≤ 30\n",
    "- **Total instances = 2**\n",
    "- **No = 1, Yes = 1**\n",
    "\n",
    "Gini index:\n",
    "$$\n",
    "Gini_{\\text{≤30}} = 1 - \\left(\\frac{1}{2}\\right)^2 - \\left(\\frac{1}{2}\\right)^2 = 1 - 0.25 - 0.25 = 0.5\n",
    "$$\n",
    "\n",
    "##### Subgroup 2: Age 31–50\n",
    "- **Total instances = 2**\n",
    "- **No = 2, Yes = 0**\n",
    "\n",
    "Gini index:\n",
    "$$\n",
    "Gini_{\\text{31–50}} = 1 - \\left(\\frac{2}{2}\\right)^2 - \\left(\\frac{0}{2}\\right)^2 = 1 - 1 = 0\n",
    "$$\n",
    "\n",
    "##### Subgroup 3: Age > 50\n",
    "- **Total instances = 3**\n",
    "- **No = 1, Yes = 2**\n",
    "\n",
    "Gini index:\n",
    "$$\n",
    "Gini_{\\text{>50}} = 1 - \\left(\\frac{1}{3}\\right)^2 - \\left(\\frac{2}{3}\\right)^2 = 1 - 0.111 - 0.444 = 0.444\n",
    "$$\n",
    "\n",
    "##### Weighted Gini for Age:\n",
    "$$\n",
    "\\text{Weighted Gini} = \\left(\\frac{2}{7} \\times 0.5\\right) + \\left(\\frac{2}{7} \\times 0\\right) + \\left(\\frac{3}{7} \\times 0.444\\right) = 0.143 + 0 + 0.190 = 0.333\n",
    "$$\n",
    "\n",
    "### Step 3: Choose Attribute with Lowest Gini Index\n",
    "- **Weighted Gini for Income** = 0.214\n",
    "- **Weighted Gini for Age** = 0.333\n",
    "\n",
    "Since **Income** has the lowest Gini index, we choose **Income** as the first attribute to split the dataset.\n",
    "\n",
    "### Step 4: Split Based on Income\n",
    "- For **Income = Low**, the Gini is 0, so we create a leaf node: **No** (because all customers with low income did not buy).\n",
    "- For **Income = High**, we need to split further using the **Age** attribute (since this group is impure).\n",
    "\n",
    "### Step 5: Further Split Based on Age (for High Income only, because Low Income was split out already)\n",
    "Now we split the **Income = High** group based on **Age**:\n",
    "- **Age ≤ 30**: Gini = 0 (Yes), create a leaf node: **Yes**\n",
    "- **Age 31–50**: Gini = 0 (No), create a leaf node: **No**\n",
    "- **Age > 50**: Gini = 0 (Yes), create a leaf node: **Yes**\n",
    "\n",
    "Alternatively, we can make a binary split here:\n",
    "- **Age 31–50**: Gini = 0 (No), create a leaf node: **No**\n",
    "- **Otherwise**: Gini = 0 (Yes), create a leaf node: **Yes**\n",
    "\n",
    "### Final Decision Tree:\n",
    "\n",
    "```\n",
    "               Income\n",
    "              /     \\\n",
    "           Low      High\n",
    "           No     /  |  \\\n",
    "               ≤30 31–50 >50\n",
    "               Yes   No   Yes\n",
    "```\n",
    "or\n",
    "```\n",
    "               Income\n",
    "              /     \\\n",
    "           Low      High\n",
    "           No      /    \\\n",
    "                31–50   other\n",
    "                 No      Yes\n",
    "```\n",
    "\n",
    "\n",
    "### Explanation:\n",
    "- If a customer has **Low income**, they will not buy.\n",
    "- If a customer has **High income**, the decision depends on their age:\n",
    "  - If their **Age ≤ 30** or **Age > 50**, they will buy.\n",
    "  - If their **Age is 31–50**, they will not buy.\n",
    "\n",
    "This solution illustrates how Gini index and weighted Gini are used to split the dataset and construct a decision tree."
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    "## Answer and Experiemental Code for MCQ#9\n",
    "\n",
    "9. How does decreasing the temperature in softmax search affect the behavior of the algorithm?\n",
    "- A) It makes the search more random\n",
    "- **B**) It makes the search more deterministic\n",
    "- C) It increases the likelihood of selecting suboptimal actions\n",
    "- D) It has no effect on the search behavior\n",
    "\n",
    "X values can be the scores of the next game play step. Higher score indicates better next step (in game play). When temperature is low, high score gets higher probability - the algorithm always picks the high score the next step, that is, more **deterministic**."
   ]
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define a function to calculate softmax probabilities\n",
    "def softmax(scores, temperature):\n",
    "    exp_scores = np.exp(scores / temperature)\n",
    "    return exp_scores / np.sum(exp_scores)\n",
    "    \n",
    "# Define a range of x values\n",
    "x_values = np.linspace(-10, 10, 100)\n",
    "\n",
    "# Plot softmax for different temperature values\n",
    "def plot_softmax_curves(x_values):\n",
    "    temperatures = [1, 2, 4, 8]  # Simulate different temperature settings\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    \n",
    "    for t in temperatures:\n",
    "        softmax_values = softmax(x_values, t)\n",
    "        plt.plot(x_values, softmax_values, label=f'Softmax(x/{t})')\n",
    "\n",
    "    plt.title('Softmax Curves at Different Temperatures')\n",
    "    plt.xlabel('x values')\n",
    "    plt.ylabel('Softmax Probability')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "\n",
    "# Visualize the softmax curves\n",
    "plot_softmax_curves(x_values)"
   ]
  }
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