HMM_with_initial_parameters.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xiY7PwTX8esh"
      },
      "source": [
        "# Example : Predicting teacher's mood"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Dv2vk8e8AxT"
      },
      "source": [
        "**Problem statement :**\n",
        "\n",
        "In the context of predicting a teacher's mood, the goal is to leverage HMMs to forecast the teacher's emotional state based on the observed t-shirt colors worn on consecutive days."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-etJnnoP7YFQ"
      },
      "source": [
        "### Step 1: Import the required libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "agd8M2Ks8JOh",
        "outputId": "e02c0ea0-e9ca-43b1-d0bb-912e40680233"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Collecting hmmlearn\n",
            "  Downloading hmmlearn-0.3.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (160 kB)\n",
            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/160.4 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━\u001b[0m \u001b[32m153.6/160.4 kB\u001b[0m \u001b[31m4.8 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m160.4/160.4 kB\u001b[0m \u001b[31m3.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy>=1.10 in /usr/local/lib/python3.10/dist-packages (from hmmlearn) (1.23.5)\n",
            "Requirement already satisfied: scikit-learn!=0.22.0,>=0.16 in /usr/local/lib/python3.10/dist-packages (from hmmlearn) (1.2.2)\n",
            "Requirement already satisfied: scipy>=0.19 in /usr/local/lib/python3.10/dist-packages (from hmmlearn) (1.11.4)\n",
            "Requirement already satisfied: joblib>=1.1.1 in /usr/local/lib/python3.10/dist-packages (from scikit-learn!=0.22.0,>=0.16->hmmlearn) (1.3.2)\n",
            "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn!=0.22.0,>=0.16->hmmlearn) (3.2.0)\n",
            "Installing collected packages: hmmlearn\n",
            "Successfully installed hmmlearn-0.3.0\n"
          ]
        }
      ],
      "source": [
        "!pip install hmmlearn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "jfL6yzi24U97"
      },
      "outputs": [],
      "source": [
        "# import the necessary libraries\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from hmmlearn import hmm"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y7iGxD2Z7akW"
      },
      "source": [
        "### Step 2: Define the model parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3FMZ-bmm7J47",
        "outputId": "109fe826-a839-4370-f216-17e227a7febb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of hidden states : 2\n",
            "Number of observations : 3\n"
          ]
        }
      ],
      "source": [
        "# Define the state space\n",
        "states = [\"Happy\", \"Sad\"]\n",
        "n_states = len(states)\n",
        "print('Number of hidden states :',n_states)\n",
        "\n",
        "# Define the observation space\n",
        "observations = [\"Red\", \"Green\", \"Blue\"]\n",
        "n_observations = len(observations)\n",
        "print('Number of observations :',n_observations)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7XYd3SRd7OMT",
        "outputId": "852a4135-6870-4590-d3a6-65a5cd0a6039"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "State probability:  [0.4 0.6]\n",
            "\n",
            "Transition probability:\n",
            " [[0.7 0.3]\n",
            " [0.5 0.5]]\n",
            "\n",
            "Emission probability:\n",
            " [[0.8 0.1 0.1]\n",
            " [0.2 0.3 0.5]]\n"
          ]
        }
      ],
      "source": [
        "# Define the initial state distribution\n",
        "state_probability = np.array([0.4, 0.6])\n",
        "print(\"State probability: \", state_probability)\n",
        "\n",
        "# Define the state transition probabilities\n",
        "transition_probability = np.array([[0.7, 0.3],\n",
        "\t\t\t\t\t\t\t\t                   [0.5, 0.5]])\n",
        "print(\"\\nTransition probability:\\n\", transition_probability)\n",
        "\n",
        "# Define the observation likelihoods\n",
        "emission_probability= np.array([[0.8, 0.1, 0.1],\n",
        "\t\t\t\t\t\t\t\t                [0.2, 0.3, 0.5]])\n",
        "print(\"\\nEmission probability:\\n\", emission_probability)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F-IsnP4B7dXZ"
      },
      "source": [
        "### Step 3: Create an instance of the HMM model and Set the model parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "-bDhHLS-7Sh1"
      },
      "outputs": [],
      "source": [
        "model = hmm.CategoricalHMM(n_components=n_states, n_features=n_observations, algorithm='viterbi')\n",
        "model.startprob_ = state_probability\n",
        "model.transmat_ = transition_probability\n",
        "model.emissionprob_ = emission_probability"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yGjIlzJG7ijB"
      },
      "source": [
        "### Step 4: Define an observation sequence"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YJio2g3K7kM9",
        "outputId": "16752352-cea4-41c2-e6cd-a1f72bfa929d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2],\n",
              "       [0],\n",
              "       [1]])"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Define the sequence of observations\n",
        "observations_sequence = np.array([1, 2, 0, 1]).reshape(-1, 1) # [\"Green\", \"Blue\", \"Red\", \"Green\"]\n",
        "observations_sequence"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m-7rouYN7nOS"
      },
      "source": [
        "### Step 5: Predict the most likely sequence of hidden states"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aVIhMP6R7qnV",
        "outputId": "a000fd05-9739-49dc-931f-7f6911a0b962"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Most likely hidden states: ['Sad', 'Sad', 'Happy', 'Sad']\n"
          ]
        }
      ],
      "source": [
        "# Predict the most likely sequence of hidden states\n",
        "hidden_states = model.predict(observations_sequence)\n",
        "print(\"Most likely hidden states:\", [states[i] for i in hidden_states])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1EzNE4Se7seP"
      },
      "source": [
        "### Step 6: Decode the observation sequence"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jEBkfUjQ7ubh",
        "outputId": "11973857-aff0-4bdc-b6b6-112f656c45ef"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Log Probability : -6.425329129737845\n",
            "Most likely hidden states: ['Sad', 'Sad', 'Happy', 'Sad']\n"
          ]
        }
      ],
      "source": [
        "#the same result as predict but with the Log probability also\n",
        "log_probability, hidden_states = model.decode(observations_sequence,\n",
        "\t\t\t\t\t\t\t\t\t\t\t                        lengths = len(observations_sequence),\n",
        "\t\t\t\t\t\t\t\t\t\t\t                        algorithm ='viterbi' ) # Decoding using the Viterbi algorithme\n",
        "\n",
        "print('Log Probability :', log_probability)\n",
        "print(\"Most likely hidden states:\", [states[i] for i in hidden_states])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ukfy4Hpa7yZv"
      },
      "source": [
        "### Step 7: Plot the results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "W4uclN8BE2Kr",
        "outputId": "9fbb70e8-32b7-4925-b66b-e1c928b1c53b"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Define a mapping between numeric observations and emotions / colors\n",
        "emotion_mapping = {0: 'Happy', 1: 'Sad'}\n",
        "color_mapping = {0: 'Red', 1: 'Green', 2: 'Blue'}\n",
        "\n",
        "# Map numeric observations to corresponding emotions / colors\n",
        "emotions = [emotion_mapping[state] for state in hidden_states]\n",
        "colors = [color_mapping[obs] for obs in observations_sequence.flatten()]\n",
        "\n",
        "# Plot the results\n",
        "plt.scatter(range(len(hidden_states)), emotions, c=colors, marker='o')\n",
        "plt.xticks(range(len(hidden_states)), colors)\n",
        "plt.xlabel('Observations = Colors', labelpad=20, weight='bold')\n",
        "plt.ylabel('States = Emotions', labelpad=20, weight='bold')\n",
        "plt.title(\"Hidden States Sequence\", pad=20, weight='bold')\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "include_colab_link": true,
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.11.5"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}