logisticregression1.ipynb

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    "### Explain the difference between linear regression and logistic regression models. Provide an example of a scenario where logistic regression would be more appropriate.\n",
    "\n",
    "Linear regression and logistic regression are both machine learning models used for different types of tasks and data. Here's an explanation of the differences between them and an example scenario where logistic regression would be more appropriate:\n",
    "\n",
    "1. **Nature of the Dependent Variable**:\n",
    "   - **Linear Regression**: Linear regression is used when the dependent variable (the variable you want to predict) is continuous. In other words, it deals with numerical values. For example, predicting house prices, where the price can take any value on a continuous scale.\n",
    "   - **Logistic Regression**: Logistic regression is used when the dependent variable is categorical, specifically binary (two classes). It is used for classification tasks where the outcome is a discrete category or label, such as 0 or 1, Yes or No, Spam or Not Spam.\n",
    "\n",
    "2. **Output Type**:\n",
    "   - **Linear Regression**: The output of linear regression is a continuous range of values. It predicts a real number as its output.\n",
    "   - **Logistic Regression**: The output of logistic regression is a probability, which represents the likelihood of the input belonging to a specific category. The probability is usually transformed using a logistic (Sigmoid) function to ensure it falls between 0 and 1.\n",
    "\n",
    "3. **Model Function**:\n",
    "   - **Linear Regression**: Linear regression models the relationship between the dependent variable and one or more independent variables by fitting a linear equation to the observed data. The equation is of the form Y = aX + b, where Y is the dependent variable, X is the independent variable, and a and b are coefficients.\n",
    "   - **Logistic Regression**: Logistic regression models the probability that the dependent variable belongs to a particular category. It uses the logistic function to map any real-valued number into a value between 0 and 1.\n",
    "\n",
    "4. **Use Cases**:\n",
    "   - **Linear Regression**: It is typically used for regression tasks, such as predicting house prices, stock prices, or any other numerical value prediction where the outcome is continuous.\n",
    "   - **Logistic Regression**: It is used for binary classification tasks, such as spam detection, customer churn prediction (whether a customer will leave or not), disease diagnosis (e.g., whether a patient has a particular disease or not), and sentiment analysis (positive or negative sentiment in text).\n",
    "\n",
    "**Example Scenario for Logistic Regression**:\n",
    "Let's consider an example scenario where logistic regression would be more appropriate: **Email Spam Detection**.\n",
    "\n",
    "In email spam detection, we have a dataset of emails, and our task is to classify each email as either \"Spam\" or \"Not Spam.\" The dependent variable here is categorical (two classes: Spam or Not Spam), making it a binary classification problem. Logistic regression can be used to build a model that predicts the probability of an email being spam based on features such as the content of the email, sender information, subject line, etc. If the predicted probability is above a certain threshold (e.g., 0.5), you classify the email as spam; otherwise, you classify it as not spam. This is a classic example of where logistic regression is a suitable choice for a machine learning algorithm."
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    "###  What is the cost function used in logistic regression, and how is it optimized?\n",
    "\n",
    "In logistic regression, the cost function used is called the **logistic loss** or **cross-entropy loss** (sometimes referred to as the binary cross-entropy loss in the binary classification case). The cost function measures the error between the predicted probabilities and the actual binary labels (0 or 1) of the data points. The formula for the logistic loss for a single data point is as follows:\n",
    "\n",
    "**For binary classification (two classes, 0 and 1):**\n",
    "\n",
    "              -(y * log(p) + (1 - y) * log(1 - p))\n",
    "\n",
    "Where:\n",
    "- **y** is the actual binary label (0 or 1) for the data point.\n",
    "- **p** is the predicted probability that the data point belongs to class 1 (i.e., the probability of the positive class).\n",
    "\n",
    "The logistic loss is designed such that it penalizes the model more when it makes confident wrong predictions (i.e., predicting a high probability for the wrong class).\n",
    "\n",
    "To optimize the logistic regression model, we typically use an optimization algorithm such as **gradient descent** or its variants (e.g., stochastic gradient descent) to minimize the logistic loss across the entire training dataset. Here's a high-level overview of how the optimization process works:\n",
    "\n",
    "1. **Initialization**: Initialize the model parameters (weights and bias) with small random values.\n",
    "\n",
    "2. **Forward Propagation**: Compute the predicted probabilities for each data point in the training set using the logistic function:\n",
    "\n",
    "            p = 1/(1 + e^(-((w^T)*x + b)\n",
    "\n",
    "   Where:\n",
    "   - **p** is the predicted probability.\n",
    "   - **w** is the weight vector.\n",
    "   - **x** is the input feature vector.\n",
    "   - **b** is the bias term.\n",
    "\n",
    "3. **Compute the Loss**: Calculate the logistic loss for the entire training dataset by averaging the individual losses for each data point using the formula mentioned earlier.\n",
    "\n",
    "4. **Backpropagation**: Compute the gradients of the loss with respect to the model parameters (weights and bias) using the chain rule. This involves calculating the partial derivatives of the loss function.\n",
    "\n",
    "5. **Update Parameters**: Update the model parameters (weights and bias) using the gradients and the chosen optimization algorithm (e.g., gradient descent):\n",
    "\n",
    "             w ← w - α. ∇w.J\n",
    "             b ← b - α. ∇b.J\n",
    "\n",
    "   Where:\n",
    "   - **α** (alpha) is the learning rate, a hyperparameter that controls the step size in the parameter update.\n",
    "   - **∇w.J** and **∇b.J** are the gradients of the loss with respect to the weights and bias, respectively.\n",
    "\n",
    "6. **Repeat**: Steps 2 to 5 are repeated iteratively for a fixed number of iterations (epochs) or until convergence (when the loss stops decreasing significantly).\n",
    "\n",
    "The goal of this optimization process is to find the values of the model parameters (weights and bias) that minimize the logistic loss, effectively learning the decision boundary that best separates the two classes in the binary classification problem. Once trained, the logistic regression model can make predictions by calculating the probability of a new data point belonging to the positive class and making a binary decision based on a chosen threshold (e.g., 0.5)."
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JxfhTwMuy977CH0q5Sld3ZV3hz3Wpf97ajijKGJelLd3iGmV8iQ5F15uhS2Cy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HBkZI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\ne6i9NoKiqql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    }
   },
   "cell_type": "markdown",
   "id": "8d612dd0-1f05-40e7-af7d-5b4c9aa756aa",
   "metadata": {},
   "source": [
    "### Explain the concept of regularization in logistic regression and how it helps prevent overfitting.\n",
    "\n",
    "Regularization is a technique used in logistic regression (and other machine learning models) to prevent overfitting, which occurs when a model becomes too complex and fits the training data too closely, capturing noise and making it perform poorly on unseen data. Regularization adds a penalty term to the cost function that discourages the model from assigning overly large weights to features, thereby promoting simpler and more generalizable models. In logistic regression, two common types of regularization are **L1 regularization** and **L2 regularization**, which are also known as **Lasso regularization** and **Ridge regularization**, respectively.\n",
    "\n",
    "Here's how regularization works in:\n",
    "\n",
    "1. **Original Logistic Regression Cost Function (Loss)**:\n",
    "   The original logistic regression cost function seeks to minimize the logistic loss (cross-entropy loss).\n",
    "\n",
    "2. **Regularization Term**:\n",
    "   In the case of regularization, an additional term is added to the cost function. The choice between L1 and L2 regularization depends on the specific type of regularization we want to apply:\n",
    "\n",
    "   ![L1,L2.png](attachment:a78e3d26-a881-41c6-bb05-e5cc7b3f2a95.png)\n",
    "\n",
    "3. **Regularization Strength**:\n",
    "   The hyperparameter λ controls the strength of regularization. A smaller λ allows the model to fit the data more closely (less regularization), while a larger λ encourages the model to have smaller weights (more regularization). The choice of λ is typically determined through techniques like cross-validation.\n",
    "\n",
    "4. **Effect on Model Parameters**:\n",
    "   Regularization encourages the model to find a balance between fitting the training data and keeping the weights small. This has the effect of shrinking the weights associated with less important features toward zero. In L1 regularization, it can even lead to feature selection, where some feature weights become exactly zero, effectively removing those features from the model.\n",
    "\n",
    "5. **Preventing Overfitting**:\n",
    "   By adding the regularization term to the cost function, logistic regression becomes less likely to overfit the training data because it discourages overly complex models. It promotes simpler models with smaller weights, which tend to generalize better to unseen data. Regularization is especially useful when you have a high-dimensional feature space or when we suspect that some features may be irrelevant."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d96c321-c23a-474e-9409-ae9564df6783",
   "metadata": {},
   "source": [
    "### What is the ROC curve, and how is it used to evaluate the performance of the logistic regression model?\n",
    "\n",
    "The Receiver Operating Characteristic (ROC) curve is a graphical tool used to evaluate and visualize the performance of binary classification models, including logistic regression models. It plots the trade-off between the true positive rate (sensitivity) and the false positive rate (1-specificity) as the discrimination threshold for classifying positive and negative instances is varied.\n",
    "\n",
    "Step-by-step explanation of the ROC curve and how it is used to evaluate the performance of a logistic regression model:\n",
    "\n",
    "1. **Understanding True Positive Rate (Sensitivity) and False Positive Rate (1-Specificity)**:\n",
    "   - **True Positive Rate (TPR), Sensitivity, or Recall**: This measures the proportion of actual positive instances that are correctly classified as positive by the model. It answers the question: \"Of all the actual positives, how many did the model correctly identify?\"\n",
    "   - **False Positive Rate (FPR) or 1-Specificity**: This measures the proportion of actual negative instances that are incorrectly classified as positive by the model. It answers the question: \"Of all the actual negatives, how many did the model incorrectly classify as positive?\"\n",
    "\n",
    "2. **Threshold Variation**:\n",
    "   - In logistic regression and many other classification algorithms, there's a discrimination threshold (often set at 0.5 by default) that determines whether a data point is classified as positive or negative based on the predicted probability from the model.\n",
    "   - By varying this threshold from 0 to 1, you can generate different points on the ROC curve. For each threshold, you calculate the TPR and FPR.\n",
    "\n",
    "3. **Plotting the ROC Curve**:\n",
    "   - The ROC curve is created by plotting the TPR (sensitivity) on the y-axis and the FPR (1-specificity) on the x-axis.\n",
    "   - As you change the threshold, you get different points on the curve. The curve typically starts at the point (0, 0) and ends at (1, 1).\n",
    "\n",
    "4. **Interpreting the ROC Curve**:\n",
    "   - The ideal ROC curve hugs the top-left corner of the plot, which means that the model has a high true positive rate (sensitivity) and a low false positive rate (1-specificity) across various thresholds.\n",
    "   - A random classifier would produce a diagonal line from (0, 0) to (1, 1), and its ROC curve would be close to this line.\n",
    "   - The closer the ROC curve is to the top-left corner, the better the model's performance in distinguishing between positive and negative instances.\n",
    "\n",
    "5. **Area Under the ROC Curve (AUC-ROC)**:\n",
    "   - The AUC-ROC is a single scalar value that quantifies the overall performance of a classification model. It represents the area under the ROC curve.\n",
    "   - A perfect classifier has an AUC-ROC of 1, while a random classifier has an AUC-ROC of 0.5.\n",
    "   - Generally, the higher the AUC-ROC value, the better the model's discriminatory power.\n",
    "\n",
    "6. **Model Comparison**:\n",
    "   - ROC curves and AUC-ROC values are useful for comparing the performance of different models. The model with the higher AUC-ROC is typically considered better at discriminating between classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cb90eb0e-6914-4af9-9e8a-370c430b23fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import roc_curve, roc_auc_score, auc\n",
    "\n",
    "X, y = make_classification(n_samples=1000, n_features=20, random_state=42)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "model = LogisticRegression(random_state=42)\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "# predict probabilities for the test set\n",
    "y_prob = model.predict_proba(X_test)[:, 1]\n",
    "\n",
    "# ROC curve\n",
    "fpr, tpr, thresholds = roc_curve(y_test, y_prob)\n",
    "\n",
    "# AUC-ROC score\n",
    "roc_auc = auc(fpr, tpr)\n",
    "\n",
    "plt.figure(figsize=(4, 3))\n",
    "plt.plot(fpr, tpr, color='darkorange', lw=2, label=f'ROC curve (AUC = {roc_auc:.2f})')\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Receiver Operating Characteristic (ROC) Curve')\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e38eb86-5d83-46aa-938c-9c38bb7f3c5a",
   "metadata": {},
   "source": [
    "### What are some common techniques for feature selection in logistic regression? How do these techniques help improve the model's performance?\n",
    "\n",
    "Common techniques for feature selection in logistic regression:\n",
    "\n",
    "1. **Correlation-based Feature Selection**:\n",
    "   - Calculate the correlation (e.g., Pearson correlation coefficient) between each feature and the target variable (binary outcome).\n",
    "   - Select features with high absolute correlation values, as they are likely to have a strong relationship with the target variable.\n",
    "   - Alternatively, we can compute the mutual information between features and the target variable, which is particularly useful for categorical features.\n",
    "\n",
    "2. **Recursive Feature Elimination (RFE)**:\n",
    "   - RFE is an iterative method that starts with all features and gradually removes the least important ones.\n",
    "   - It uses a model (e.g., logistic regression) to evaluate feature importance during each iteration and eliminates the least important feature.\n",
    "   - The process continues until a specified number of features or a desired performance criterion is reached.\n",
    "\n",
    "3. **L1 Regularization (Lasso)**:\n",
    "   - L1 regularization adds a penalty term to the logistic regression cost function that encourages sparse weight vectors (some weights become exactly zero).\n",
    "   - Features corresponding to non-zero weights are selected, effectively performing feature selection during model training.\n",
    "   - Lasso regularization can help identify and select the most informative features, making the model more interpretable and potentially improving its performance.\n",
    "\n",
    "4. **Tree-Based Feature Selection**:\n",
    "   - Decision tree-based models (e.g., Random Forest or Gradient Boosting) can provide feature importances, indicating how much each feature contributes to the model's decision-making.\n",
    "   - Features with high importances can be selected for logistic regression.\n",
    "   - Random Forest's `feature_importances_` and Gradient Boosting's `feature_importance_` attributes are commonly used for this purpose.\n",
    "\n",
    "5. **Filter Methods**:\n",
    "   - Filter methods assess feature importance independently of the model being used. They evaluate the relationship between each feature and the target variable.\n",
    "   - Common filter methods include chi-squared test, mutual information, and feature ranking based on correlation or statistical tests.\n",
    "   - Features are selected or ranked based on predefined criteria.\n",
    "\n",
    "6. **Embedded Methods**:\n",
    "   - Embedded methods combine feature selection with model training.\n",
    "   - Some algorithms, like recursive feature elimination with cross-validation (RFECV) for logistic regression, perform feature selection as part of their internal process.\n",
    "   - Embedded methods can be computationally efficient because they use model performance as the criterion for feature selection."
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    "### How can you handle imbalanced datasets in logistic regression? What are some strategies for dealing with class imbalance?\n",
    "\n",
    "Handling imbalanced datasets in logistic regression is crucial because when one class significantly outnumbers the other, the model can become biased toward the majority class. This can lead to poor performance on the minority class, which may be the class of greater interest (e.g., fraud detection or rare disease diagnosis). Strategies for dealing with class imbalance in logistic regression:\n",
    "\n",
    "1. **Resampling Techniques**:\n",
    "   - **Oversampling**: Increase the number of instances in the minority class by randomly duplicating samples. This can help balance class proportions. Be cautious not to overfit the model to the minority class.\n",
    "   - **Undersampling**: Decrease the number of instances in the majority class by randomly removing samples. This can help balance class proportions. However, it may lead to a loss of information from the majority class.\n",
    "\n",
    "2. **Synthetic Data Generation**:\n",
    "   - **SMOTE (Synthetic Minority Over-sampling Technique)**: SMOTE generates synthetic examples for the minority class by interpolating between existing minority class samples. It helps address class imbalance without duplicating data.\n",
    "   - **ADASYN (Adaptive Synthetic Sampling)**: Similar to SMOTE but adaptively generates synthetic samples based on the distribution of the data.\n",
    "\n",
    "3. **Cost-Sensitive Learning**:\n",
    "   - Modify the logistic regression algorithm to take into account class imbalance by assigning different misclassification costs to each class. Many machine learning libraries and frameworks, including scikit-learn, allow you to set class weights to penalize misclassification of the minority class more heavily.\n",
    "\n",
    "4. **Threshold Adjustment**:\n",
    "   - By default, logistic regression predicts a class based on a threshold of 0.5. Adjust the threshold to be more sensitive to the minority class if necessary. Lowering the threshold can increase the recall (true positive rate) for the minority class, but it may also increase false positives.\n",
    "\n",
    "5. **Evaluation Metrics**:\n",
    "   - Use appropriate evaluation metrics that focus on model performance for imbalanced datasets. Common metrics include precision, recall, F1-score, and the area under the Precision-Recall curve (AUC-PR). These metrics provide a more balanced view of performance than accuracy, which can be misleading with imbalanced data.\n",
    "\n",
    "6. **Resampling during Cross-Validation**:\n",
    "   - When performing cross-validation, ensure that oversampling or undersampling is done within each fold to prevent data leakage and more reliable model evaluation.\n",
    "\n",
    "7. **Ensemble Methods**:\n",
    "   - Consider using ensemble techniques like Random Forest, Gradient Boosting, or AdaBoost, which can handle imbalanced data more effectively than single models. Ensemble methods can weigh misclassifications differently and combine multiple models to improve performance.\n",
    "\n",
    "8. **Anomaly Detection**:\n",
    "   - Treat the minority class as anomalies and use anomaly detection techniques like One-Class SVM or Isolation Forest. These methods are designed for identifying rare instances in datasets.\n",
    "\n",
    "9. **Collect More Data**:\n",
    "   - If feasible, collect more data for the minority class to balance the dataset naturally. This may not always be possible but can be a highly effective strategy.\n",
    "\n",
    "10. **Feature Engineering**:\n",
    "    - Carefully select and engineer features that can improve the discrimination between classes. Feature engineering can help the model better capture the underlying patterns in imbalanced data."
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    "### Can you discuss some common issues and challenges that may arise when implementing logistic regression, and how they can be addressed? For example, what can be done if there is multicollinearity among the independent variables?\n",
    "\n",
    "Some common issues that may arise when implementing logistic regression and strategies to address them:\n",
    "\n",
    "1. **Multicollinearity**:\n",
    "   - **Issue**: Multicollinearity occurs when two or more independent variables in the model are highly correlated, making it challenging to determine each variable's individual impact on the target variable.\n",
    "   - **Solution**: \n",
    "     - Identify and assess the extent of multicollinearity using correlation matrices or variance inflation factors (VIF).\n",
    "     - Address multicollinearity by removing one of the correlated variables or using dimensionality reduction techniques like principal component analysis (PCA) to create uncorrelated variables.\n",
    "     - Domain knowledge can also help in selecting which variables to retain based on their importance.\n",
    "\n",
    "2. **Overfitting**:\n",
    "   - **Issue**: Overfitting happens when the model captures noise in the training data and does not generalize well to unseen data.\n",
    "   - **Solution**:\n",
    "     - Use regularization techniques like L1 (Lasso) or L2 (Ridge) regularization to penalize large weights and simplify the model.\n",
    "     - Limit the complexity of the model by reducing the number of features or using feature selection techniques.\n",
    "     - Ensure proper validation by using techniques like cross-validation to assess model performance on unseen data.\n",
    "\n",
    "3. **Imbalanced Datasets**:\n",
    "   - **Issue**: Imbalanced datasets can lead to biased models, particularly in binary classification problems where one class significantly outnumbers the other.\n",
    "   - **Solution**:\n",
    "     - Apply resampling techniques such as oversampling the minority class or undersampling the majority class to balance the dataset.\n",
    "     - Use cost-sensitive learning by assigning different misclassification costs to each class.\n",
    "     - Employ evaluation metrics like precision, recall, F1-score, and AUC-PR that are better suited for imbalanced datasets.\n",
    "\n",
    "4. **Non-Linear Relationships**:\n",
    "   - **Issue**: Logistic regression assumes a linear relationship between the independent variables and the log-odds of the target variable. If the relationship is non-linear, the model may not perform well.\n",
    "   - **Solution**:\n",
    "     - Transform features or engineer new features to capture non-linear relationships (e.g., polynomial features or interaction terms).\n",
    "     - Consider using more complex models like decision trees, random forests, or kernelized SVMs if linearity is not appropriate.\n",
    "\n",
    "5. **Outliers**:\n",
    "   - **Issue**: Outliers can disproportionately influence the coefficients in logistic regression and affect model performance.\n",
    "   - **Solution**:\n",
    "     - Detect and handle outliers using techniques such as trimming, capping, or transforming the data.\n",
    "     - Robust regression techniques like Huber or Tukey regression can also mitigate the impact of outliers.\n",
    "\n",
    "6. **Data Quality and Missing Values**:\n",
    "   - **Issue**: Incomplete or noisy data can lead to unreliable model results.\n",
    "   - **Solution**:\n",
    "     - Impute missing values using techniques like mean imputation, median imputation, or advanced imputation methods.\n",
    "     - Address data quality issues by cleaning, preprocessing, and validating the dataset.\n",
    "     - Be cautious about the implications of imputing missing data and consider whether it is appropriate for the problem at hand.\n",
    "\n",
    "7. **Interpretability**:\n",
    "   - **Issue**: Logistic regression models are relatively interpretable, but with many features or complex transformations, interpretation can become challenging.\n",
    "   - **Solution**:\n",
    "     - Prioritize feature selection and engineering to keep the model interpretable.\n",
    "     - Use model-agnostic interpretability techniques such as partial dependence plots, SHAP values, or LIME (Local Interpretable Model-agnostic Explanations).\n",
    "\n",
    "8. **Sample Size**:\n",
    "   - **Issue**: Logistic regression models may require a reasonably large sample size to provide stable and reliable estimates of coefficients.\n",
    "   - **Solution**:\n",
    "     - Ensure that the sample size is adequate for the number of features and the complexity of the problem.\n",
    "     - Consider using techniques like bootstrapping to estimate confidence intervals for coefficients.\n",
    "\n",
    "9. **Model Complexity**:\n",
    "   - **Issue**: Logistic regression may not capture complex, high-dimensional relationships in the data.\n",
    "   - **Solution**:\n",
    "     - If needed, explore more complex models like decision trees, random forests, or neural networks.\n",
    "     - Regularize the logistic regression model to prevent overfitting while still benefiting from its simplicity."
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