HMM_with_training.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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "agd8M2Ks8JOh",
        "outputId": "e02c0ea0-e9ca-43b1-d0bb-912e40680233"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: hmmlearn in d:\\anaconda\\lib\\site-packages (0.3.0)\n",
            "Requirement already satisfied: numpy>=1.10 in d:\\anaconda\\lib\\site-packages (from hmmlearn) (1.24.3)\n",
            "Requirement already satisfied: scikit-learn!=0.22.0,>=0.16 in d:\\anaconda\\lib\\site-packages (from hmmlearn) (1.3.0)\n",
            "Requirement already satisfied: scipy>=0.19 in d:\\anaconda\\lib\\site-packages (from hmmlearn) (1.11.4)\n",
            "Requirement already satisfied: joblib>=1.1.1 in d:\\anaconda\\lib\\site-packages (from scikit-learn!=0.22.0,>=0.16->hmmlearn) (1.2.0)\n",
            "Requirement already satisfied: threadpoolctl>=2.0.0 in d:\\anaconda\\lib\\site-packages (from scikit-learn!=0.22.0,>=0.16->hmmlearn) (2.2.0)\n"
          ]
        }
      ],
      "source": [
        "!pip install hmmlearn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "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": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [],
      "source": [
        "np.set_printoptions(precision=4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y7iGxD2Z7akW"
      },
      "source": [
        "### Step 2: Define the model parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "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": "markdown",
      "metadata": {
        "id": "F-IsnP4B7dXZ"
      },
      "source": [
        "### Step 3: Create an instance of the HMM model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "id": "-bDhHLS-7Sh1"
      },
      "outputs": [],
      "source": [
        "model = hmm.CategoricalHMM(n_components=n_states, n_features=n_observations, algorithm='viterbi')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yGjIlzJG7ijB"
      },
      "source": [
        "### Step 4: Train the model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YJio2g3K7kM9",
        "outputId": "16752352-cea4-41c2-e6cd-a1f72bfa929d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2],\n",
              "       [1],\n",
              "       [1],\n",
              "       [0],\n",
              "       [1],\n",
              "       [0],\n",
              "       [2],\n",
              "       [2],\n",
              "       [1],\n",
              "       [0]])"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Define the sequence of observations\n",
        "train_observations_sequence = np.array([1, 2, 1, 1, 0, 1, 0, 2, 2 , 1, 0]).reshape(-1, 1) \n",
        "train_observations_sequence"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Even though the 'startprob_' attribute is set, it will be overwritten during initialization because 'init_params' contains 's'\n"
          ]
        },
        {
          "data": {
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              "               random_state=RandomState(MT19937) at 0x1CE449D7B40)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">CategoricalHMM</label><div class=\"sk-toggleable__content\"><pre>CategoricalHMM(n_components=2, n_features=3,\n",
              "               random_state=RandomState(MT19937) at 0x1CE449D7B40)</pre></div></div></div></div></div>"
            ],
            "text/plain": [
              "CategoricalHMM(n_components=2, n_features=3,\n",
              "               random_state=RandomState(MT19937) at 0x1CE449D7B40)"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "model.fit(train_observations_sequence)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(array([9.9986e-01, 1.4360e-04]),\n",
              " array([[0.1919, 0.8081],\n",
              "        [0.7087, 0.2913]]),\n",
              " array([[0.0064, 0.8151, 0.1785],\n",
              "        [0.5237, 0.1149, 0.3615]]))"
            ]
          },
          "execution_count": 47,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "model.startprob_,model.transmat_, model.emissionprob_ #the result of fitting the model, PS: if you already know these values you can skip the fitting and pass directly to prediction"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m-7rouYN7nOS"
      },
      "source": [
        "### Step 5: Predict the most likely sequence of hidden states"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {},
      "outputs": [],
      "source": [
        "test_observations_sequence = np.array([1, 0, 2, 1, 1, 1]).reshape(-1, 1)  # [\"Green\", \"Red\", \"Blue\", \"Green\", \"Green\", \"Green\", \"Green\"]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "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: ['Happy', 'Sad', 'Sad', 'Happy', 'Sad', 'Happy']\n"
          ]
        }
      ],
      "source": [
        "# Predict the most likely sequence of hidden states\n",
        "hidden_states = model.predict(test_observations_sequence)\n",
        "print(\"Most likely hidden states:\", [states[i] for i in hidden_states])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jEBkfUjQ7ubh",
        "outputId": "11973857-aff0-4bdc-b6b6-112f656c45ef"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Log Probability : -6.790268700883583\n",
            "Most likely hidden states: ['Happy', 'Sad', 'Sad', 'Happy', 'Sad', 'Happy']\n"
          ]
        }
      ],
      "source": [
        "#the same result as predict but with the Log probability also\n",
        "log_probability, hidden_states = model.decode(test_observations_sequence,\n",
        "\t\t\t\t\t\t\t\t\t\t\t                        lengths = len(test_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 6: Plot the results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "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 test_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
}