4. Supervised Learning/4.1 Regression/4.1.5 Dimensionality Reduction-Based Regression/4.1.5.2 Partial Least Squares Regression (PLS).ipynb

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    "# 4.1.5.2 Partial Least Squares Regression (PLS)\n",
    "\n",
    "\n",
    "## Explanation of Partial Least Squares Regression and Its Applications\n",
    "\n",
    "**Partial Least Squares Regression (PLS)** is a statistical method that combines features of principal component analysis and multiple regression. It is particularly useful when the predictors are highly collinear or when the number of predictors exceeds the number of observations.\n",
    "\n",
    "## **Key Concepts**:\n",
    "- **Latent Variables**: PLS creates new predictor variables, known as latent variables, which are linear combinations of the original predictors.\n",
    "- **Maximizing Covariance**: Unlike PCA, which focuses on explaining the variance in the predictors, PLS focuses on finding latent variables that maximize the covariance between predictors and the response variable.\n",
    "- **Dimensionality Reduction**: PLS reduces the dimensionality of the data while maintaining the relationship between predictors and the response.\n",
    "\n",
    "In this section, we will explore the implementation of Partial Least Squares Regression using scikit-learn.\n"
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    "## Procedure for Partial Least Squares Regression (PLS)\n",
    "\n",
    "1. **Standardize the Data**:\n",
    "   Standardizing the predictors to have mean zero and variance one.\n",
    "\n",
    "2. **Select the Number of Components**:\n",
    "   Choose the number of latent variables (components) to include in the model.\n",
    "\n",
    "3. **Fit the PLS Model**:\n",
    "   Use the training data to fit the PLS model, extracting the latent variables that best explain the relationship between the predictors and the response.\n",
    "\n",
    "4. **Predict and Evaluate**:\n",
    "   Use the fitted model to make predictions and evaluate its performance using appropriate metrics such as Mean Squared Error (MSE) or R-squared.\n"
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    "<hr><hr>\n",
    "\n",
    "## Principle, Formulas, and Terms in Partial Least Squares Regression (PLS)\n",
    "\n",
    "### Principle of Partial Least Squares Regression\n",
    "\n",
    "Partial Least Squares Regression (PLS) aims to find the directions (latent variables) in the predictor space that explain the maximum variance in the response variable. It seeks to maximize the covariance between the predictors and the response by projecting the original data into a new space defined by these latent variables. The primary goal is to extract the relevant information from the predictors that is most useful for predicting the response."
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    "### Formulas and Terms\n",
    "\n",
    "1. **Latent Variables**: \\( T \\) and \\( U \\)\n",
    "   - $ T = XW $ : Latent variables for predictors.\n",
    "   - $ U = YC $ : Latent variables for response.\n",
    "\n",
    "\n",
    "2. **Weight Vectors**: \\( W \\)\n",
    "   - \\( W \\) are the weight vectors that define the linear combinations of the original predictors to form the latent variables.\n",
    "\n",
    "\n",
    "3. **Loading Matrices**: \\( P \\) and \\( Q \\)\n",
    "   - \\( P \\) and \\( Q \\) are the loading matrices for \\( X \\) and \\( Y \\), respectively.\n",
    "\n",
    "\n",
    "4. **Regression Coefficients**: \\( B \\)\n",
    "   - $ B = W \\left( P^T W \\right)^{-1} Q^T $\n",
    "   - The regression coefficients \\( B \\) relate the predictors to the response in the latent space.\n",
    "\n",
    "5. **Deflation**: Removing the information explained by each latent variable from the original predictors and response."
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    "___\n",
    "\n",
    "### Example\n",
    "\n",
    "Consider a dataset with three predictors $ X_1 $, $ X_2 $, and $ X_3 $, and a response variable $ Y $. The relationship can be described as:\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_3 + \\epsilon $$\n",
    "\n",
    "Using PLS, we aim to find new variables $ T_1 $ and $ T_2 $  (latent variables) that capture the relevant information from $ X $ for predicting $ Y $.\n",
    "\n",
    "1. **Standardize the Predictors**: \n",
    "   Standardize $ X $ to have mean zero and variance one.\n",
    "\n",
    "2. **Calculate Weight Vectors**:\n",
    "   Find weight vectors $ W_1 $ and $ W_2 $ that define the linear combinations of $ X $ to form $ T_1 $ and $ T_2 $.\n",
    "\n",
    "   $$ T_1 = W_1^T X $$\n",
    "   $$ T_2 = W_2^T X $$\n",
    "\n",
    "3. **Deflate the Predictors**:\n",
    "   Remove the information explained by $ T_1 $ from $ X $:\n",
    "\n",
    "   $$ X_{\\text{deflated}} = X - T_1 P_1^T $$\n",
    "\n",
    "4. **Repeat for \\( T_2 \\)**:\n",
    "   Perform the same steps for $ T_2 $ to obtain the final latent variables.\n",
    "\n",
    "5. **Fit the PLS Model**:\n",
    "   Use the latent variables $ T_1 $ and $ T_2 $ to predict $ Y $:\n",
    "\n",
    "   $$ Y \\approx T_1 Q_1 + T_2 Q_2 $$\n",
    "\n",
    "6. **Regression Coefficients**:\n",
    "   Calculate the regression coefficients \\( B \\) using:\n",
    "\n",
    "  $$ B = W \\left( P^T W \\right)^{-1} Q^T $$\n",
    "___\n",
    "### Example Calculation\n",
    "\n",
    "Let's assume the following standardized predictors and response:\n",
    "\n",
    "$$ X = \\begin{bmatrix} 0.5 & -0.2 & 0.1 \\\\ -0.1 & 0.4 & -0.3 \\\\ 0.3 & -0.1 & 0.2 \\end{bmatrix} $$\n",
    "$$ Y = \\begin{bmatrix} 1.2 \\\\ 0.8 \\\\ 1.1 \\end{bmatrix} $$\n",
    "\n",
    "1. **Weight Vector Calculation**:\n",
    "   Calculate $ W_1 $ and $ W_2 $.\n",
    "\n",
    "2. **Latent Variables**:\n",
    "   $$ T_1 = W_1^T X $$\n",
    "   $$ T_2 = W_2^T X_{\\text{deflated}} $$\n",
    "\n",
    "3. **Predict and Evaluate**:\n",
    "   Use $ T_1 $ and $ T_2 $ to predict $ Y $ and evaluate the performance using metrics such as MSE and $ R^2 $.\n",
    "\n",
    "In summary, PLS regression provides a robust framework for dealing with multicollinear and high-dimensional data by extracting latent variables that capture the essential information from the predictors for predicting the response.\n",
    "\n",
    "\n",
    "<hr><hr>"
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    "### Readings:\n",
    "- [Partial Least Squares](https://readmedium.com/en/https:/towardsdatascience.com/partial-least-squares-f4e6714452a)\n",
    "- [Partial Least Squares (PLS) Regression - The University of Texas at Dallas](https://personal.utdallas.edu/~herve/Abdi-PLS-pretty.pdf)\n",
    "- [An Introduction to Partial Least Squares Regression, SAS Institute](https://stats.oarc.ucla.edu/wp-content/uploads/2016/02/pls.pdf)\n",
    "- [Sklearn | Partial Least Squares Regression](https://towardsdev.com/sklearn-partial-least-squares-regression-plsregression-e513c0bd344d)\n",
    "- [Predictive Regression using splines, partial-least squares, penalization, cross-validation, and model averaging](https://blog.devgenius.io/predictive-regression-using-splines-partial-least-squares-penalization-cross-validation-and-339b74a7e108)\n",
    "  \n",
    "___\n",
    "___"
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    "# Importing necessary libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
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    "# Generating some random data for demonstration\n",
    "np.random.seed(0)\n",
    "n_samples = 100\n",
    "n_features = 3\n",
    "X = np.random.rand(n_samples, n_features)  # Random features\n",
    "Y = 4 + 3 * X[:, 0] + 2 * X[:, 1] + X[:, 2] + np.random.randn(n_samples)  # Linear combination with noise"
   ]
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    "# Standardizing the data\n",
    "scaler = StandardScaler()\n",
    "X_scaled = scaler.fit_transform(X)"
   ]
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   "source": [
    "# Implementing Partial Least Squares Regression using scikit-learn\n",
    "n_components = 2  # Number of PLS components\n",
    "pls = PLSRegression(n_components=n_components)\n",
    "pls.fit(X_scaled, Y)"
   ]
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     "text": [
      "Mean Squared Error: 0.8649554431487241\n",
      "R-squared: 0.5596319598411288\n"
     ]
    }
   ],
   "source": [
    "# Predicting\n",
    "Y_pred_pls = pls.predict(X_scaled).ravel()\n",
    "\n",
    "# Evaluating the model\n",
    "mse = mean_squared_error(Y, Y_pred_pls)\n",
    "r2 = r2_score(Y, Y_pred_pls)\n",
    "print(f'Mean Squared Error: {mse}')\n",
    "print(f'R-squared: {r2}')"
   ]
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      "text/plain": [
       "<Figure size 1400x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the results (for demonstration, we'll plot against the first and second components)\n",
    "plt.figure(figsize=(14, 6))\n",
    "\n",
    "# Plot for the first component\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(pls.x_scores_[:, 0], Y, color='blue', label='Actual data')\n",
    "plt.scatter(pls.x_scores_[:, 0], Y_pred_pls, color='red', label='PLS predictions')\n",
    "plt.xlabel('First PLS Component')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Partial Least Squares Regression (First Component)')\n",
    "plt.legend()\n",
    "\n",
    "# Plot for the second component\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(pls.x_scores_[:, 1], Y, color='blue', label='Actual data')\n",
    "plt.scatter(pls.x_scores_[:, 1], Y_pred_pls, color='red', label='PLS predictions')\n",
    "plt.xlabel('Second PLS Component')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Partial Least Squares Regression (Second Component)')\n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b54b2dc8-2636-4997-a31f-79933b1b36b1",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "Partial Least Squares Regression (PLS) is a powerful method for handling datasets with multicollinearity and high-dimensional data. By extracting latent variables that maximize the covariance between predictors and the response variable, PLS provides a robust and interpretable model. Implementing PLS using scikit-learn is straightforward and efficient, making it a practical choice for various applications. Proper selection of the number of components is crucial for optimizing the model's performance and achieving accurate predictions.\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "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": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}