Project_15_9_Logistic Regression -3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ec2d0c35",
   "metadata": {},
   "source": [
    "## Q1. Explain the concept of precision and recall in the context of classification models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93fd4b9b",
   "metadata": {},
   "source": [
    "Precision and recall are two important performance metrics used to evaluate the quality of a classification model, particularly in binary classification tasks. These metrics focus on different aspects of a model's performance and are especially relevant when dealing with imbalanced datasets or when different types of errors have different implications.\n",
    "\n",
    "**Precision (Positive Predictive Value):**\n",
    "\n",
    "- **Definition:** Precision measures the accuracy of positive predictions made by the model. It quantifies the proportion of instances predicted as positive that are actually true positives. Precision is calculated as ***TP/(TP+FP)***.\n",
    "\n",
    "- **Interpretation:** Precision answers the question: \"Of all the instances that the model predicted as positive, how many were correctly classified?\" It is concerned with minimizing false positives. In other words, it assesses the model's ability to avoid making incorrect positive predictions. High precision indicates that when the model predicts a positive outcome, it's highly likely to be correct.\n",
    "\n",
    "- **Use Cases:** Precision is essential in scenarios where the cost of false positives is high, and you want to minimize the number of false alarms. Examples include medical diagnosis (avoiding incorrect disease diagnoses) and spam email detection (minimizing false positives by not classifying legitimate emails as spam).\n",
    "\n",
    "**Recall (Sensitivity, True Positive Rate):**\n",
    "\n",
    "- **Definition:** Recall measures the model's ability to identify all relevant positive instances from the total number of actual positive instances. It quantifies the proportion of true positives that were correctly classified by the model. Recall is calculated as ***TP/(TP+FN)***.\n",
    "\n",
    "- **Interpretation:** Recall answers the question: \"Of all the actual positive instances, how many did the model correctly classify?\" It is concerned with minimizing false negatives. Recall assesses the model's ability to capture all positive cases, even at the cost of a higher false positive rate. High recall indicates that the model is sensitive to identifying positive cases and aims to minimize missed positive instances.\n",
    "\n",
    "- **Use Cases:** Recall is crucial in scenarios where missing positive instances has significant consequences, and false negatives are costly. Examples include disease screening (ensuring all cases are identified, even at the risk of false alarms) and search and rescue operations (finding all missing persons).\n",
    "\n",
    "In summary:\n",
    "\n",
    "- **Precision** is about the accuracy of positive predictions and is concerned with minimizing false positives. It is useful when the cost of false alarms is high.\n",
    "\n",
    "- **Recall** is about the ability to capture all positive instances and is concerned with minimizing false negatives. It is essential when missing positive instances has significant consequences.\n",
    "\n",
    "Depending on your specific classification problem and the trade-offs between false positives and false negatives, you may need to optimize your model's performance with respect to precision, recall, or a balance between the two using techniques like threshold adjustment."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "779f1f38",
   "metadata": {},
   "source": [
    "## Q2. What is the F1 score and how is it calculated? How is it different from precision and recall?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aecc6c52",
   "metadata": {},
   "source": [
    "The F1 score is a single performance metric used to assess the quality of a binary classification model, particularly when dealing with imbalanced datasets or situations where both precision and recall are important. It combines both precision and recall into a single value, providing a balance between the two metrics.\n",
    "\n",
    "**Calculation of the F1 Score:**\n",
    "\n",
    "The F1 score is calculated using the formula: ***2(Precision*Recall) / (Precision+Recall)***\n",
    "\n",
    "- **Precision:** Precision is the proportion of true positive predictions (correct positive predictions) to the total number of positive predictions made by the model. It measures the accuracy of positive predictions and is calculated as ***TP/(TP+FP)***.\n",
    "\n",
    "- **Recall:** Recall is the proportion of true positive predictions to the total number of actual positive instances in the dataset. It measures the model's ability to identify all relevant positive instances and is calculated as ***TP/(TP+FN)***.\n",
    "\n",
    "The F1 score takes the harmonic mean of precision and recall, providing a balanced assessment of the model's performance. The harmonic mean gives more weight to lower values, making the F1 score sensitive to situations where either precision or recall is significantly lower than the other. As a result, the F1 score tends to penalize models that have a substantial imbalance between precision and recall.\n",
    "\n",
    "**Differences Between F1 Score, Precision, and Recall:**\n",
    "\n",
    "1. **F1 Score:** The F1 score combines precision and recall into a single metric. It balances the trade-off between precision and recall and is especially useful when you want to assess a model's overall performance without favoring one metric over the other.\n",
    "\n",
    "2. **Precision:** Precision measures the accuracy of positive predictions and is concerned with minimizing false positives. It answers the question: \"Of all the instances predicted as positive, how many were correctly classified?\"\n",
    "\n",
    "3. **Recall:** Recall measures the model's ability to identify all relevant positive instances and is concerned with minimizing false negatives. It answers the question: \"Of all the actual positive instances, how many did the model correctly classify?\"\n",
    "\n",
    "In summary, while precision and recall focus on specific aspects of a classification model's performance, the F1 score provides a balanced evaluation by considering both false positives and false negatives. The choice between using precision, recall, or the F1 score depends on the specific requirements and priorities of your classification problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3705a85a",
   "metadata": {},
   "source": [
    "## Q3. What is ROC and AUC, and how are they used to evaluate the performance of classification models?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c23bf0ce",
   "metadata": {},
   "source": [
    "**ROC (Receiver Operating Characteristic) Curve** and **AUC (Area Under the ROC Curve)** are widely used evaluation metrics for assessing the performance of binary classification models. They help visualize and quantify the model's ability to distinguish between the positive and negative classes, particularly when you vary the classification threshold.\n",
    "\n",
    "**ROC Curve:**\n",
    "- **Definition:** The ROC curve is a graphical representation of a classification model's performance across different threshold settings. It plots the True Positive Rate (Recall) against the False Positive Rate at various threshold values.\n",
    "- **Interpretation:** The ROC curve shows the trade-off between the model's sensitivity (the ability to correctly identify positive instances) and its specificity (the ability to correctly identify negative instances) across different threshold levels. The curve is typically ascending, with better models having curves that rise steeply toward the upper-left corner, indicating high sensitivity and low false positive rates.\n",
    "- **Usage:** You can visually assess a model's performance by examining its ROC curve. A curve closer to the upper-left corner indicates better discrimination ability, while a diagonal line (representing random guessing) indicates poor discrimination. Models with curves below the diagonal line are worse than random guessing.\n",
    "\n",
    "**AUC (Area Under the ROC Curve):**\n",
    "- **Definition:** The AUC is a numerical value that quantifies the overall performance of a classification model by measuring the area under its ROC curve. A perfect model has an AUC of 1, while a random model has an AUC of 0.5 (the diagonal line).\n",
    "- **Interpretation:** The AUC provides a single scalar value to assess the model's ability to distinguish between positive and negative instances. A higher AUC indicates better overall model performance. An AUC of 0.5 suggests that the model performs no better than random guessing, while an AUC greater than 0.5 indicates an improvement over random guessing.\n",
    "- **Usage:** Comparing the AUC values of different models allows you to determine which model has superior discrimination ability. Higher AUC values indicate better separation between the classes.\n",
    "\n",
    "**Key Points:**\n",
    "- ROC curves and AUC are particularly useful when you want to assess a model's performance across various threshold settings, especially when precision and recall may have trade-offs.\n",
    "- They are insensitive to class imbalance, making them suitable for imbalanced datasets.\n",
    "- ROC curves and AUC are not suitable for multi-class classification; they are primarily used for binary classification problems.\n",
    "\n",
    "In summary, ROC curves and AUC provide a comprehensive evaluation of a classification model's performance by visualizing its ability to discriminate between positive and negative classes at different thresholds and quantifying that performance as a single AUC value. They are valuable tools for comparing and selecting models, particularly when you need to balance sensitivity and specificity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4be7e138",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 1:Import modules and fit logistic regression model\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import metrics\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#import dataset from CSV file on Github\n",
    "url = \"https://raw.githubusercontent.com/Statology/Python-Guides/main/default.csv\"\n",
    "data = pd.read_csv(url)\n",
    "\n",
    "#define the predictor variables and the response variable\n",
    "X = data[['student', 'balance', 'income']]\n",
    "y = data['default']\n",
    "\n",
    "#split the dataset into training (70%) and testing (30%) sets\n",
    "X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.3,random_state=0) \n",
    "\n",
    "#instantiate the model\n",
    "log_regression = LogisticRegression()\n",
    "\n",
    "#fit the model using the training data\n",
    "log_regression.fit(X_train,y_train)\n",
    "\n",
    "#Step 2: Plot the ROC Curve\n",
    "#define metrics\n",
    "y_pred_proba = log_regression.predict_proba(X_test)[::,1]\n",
    "fpr, tpr, _ = metrics.roc_curve(y_test,  y_pred_proba)\n",
    "\n",
    "#create ROC curve\n",
    "plt.plot(fpr,tpr)\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.show()\n",
    "\n",
    "#Step 3: Calculate the AUC\n",
    "#define metrics\n",
    "y_pred_proba = log_regression.predict_proba(X_test)[::,1]\n",
    "fpr, tpr, _ = metrics.roc_curve(y_test,  y_pred_proba)\n",
    "auc = metrics.roc_auc_score(y_test, y_pred_proba)\n",
    "\n",
    "#create ROC curve\n",
    "plt.plot(fpr,tpr,label=\"AUC=\"+str(auc))\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72fde2b8",
   "metadata": {},
   "source": [
    "## Q4. How do you choose the best metric to evaluate the performance of a classification model?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34baa04a",
   "metadata": {},
   "source": [
    "Choosing the best metric to evaluate the performance of a classification model depends on the specific characteristics of your problem, your objectives, and the trade-offs you are willing to make.\n",
    "\n",
    "Some common evaluation metrics for classification models and guidelines on how to choose the most appropriate one:\n",
    "\n",
    "1. **Accuracy:**\n",
    "   - **When to Use:** Accuracy is suitable when the class distribution is balanced (approximately equal instances of each class). It measures the overall correctness of predictions.\n",
    "   - **Considerations:** Accuracy can be misleading when dealing with imbalanced datasets, where one class significantly outnumbers the other. In such cases, high accuracy can be achieved by simply predicting the majority class, even if the model fails to detect the minority class.\n",
    "\n",
    "2. **Precision and Recall:**\n",
    "   - **When to Use:** Use precision when minimizing false positives (Type I errors) is critical, and you want to assess the accuracy of positive predictions. Use recall when minimizing false negatives (Type II errors) is crucial, and you want to ensure that all relevant positive instances are captured.\n",
    "   - **Considerations:** Precision and recall are often used together to assess a model's ability to balance Type I and Type II errors. You may need to make a trade-off between precision and recall based on the problem's context.\n",
    "\n",
    "3. **F1-Score:**\n",
    "   - **When to Use:** The F1-score is useful when you want to balance precision and recall and obtain a single metric that combines both. It's particularly valuable in scenarios where precision and recall have trade-offs.\n",
    "   - **Considerations:** The F1-score can be a better choice than accuracy when dealing with imbalanced datasets, where one class is much smaller than the other.\n",
    "\n",
    "4. **ROC Curve and AUC:**\n",
    "   - **When to Use:** ROC curves and AUC are valuable when you want to assess a model's discrimination ability across various threshold settings and prioritize the trade-off between true positives and false positives.\n",
    "   - **Considerations:** These metrics are suitable for imbalanced datasets and help you choose an appropriate threshold based on your problem's requirements.\n",
    "\n",
    "5. **Specificity:**\n",
    "   - **When to Use:** Specificity measures a model's ability to correctly identify the negative class. It's useful when minimizing false positives in the negative class is essential.\n",
    "   - **Considerations:** Specificity is particularly relevant in applications where the cost of false negatives in the negative class is high.\n",
    "\n",
    "6. **Balanced Accuracy:**\n",
    "   - **When to Use:** Balanced accuracy is useful when the class distribution is imbalanced. It calculates the average of recall for each class, considering class-specific performance.\n",
    "   - **Considerations:** Balanced accuracy provides a fair evaluation when class sizes differ significantly.\n",
    "\n",
    "Ultimately, the choice of the best metric depends on the specific goals and priorities of your classification problem. It's essential to consider the class distribution, the relative costs of different types of errors, and the specific context of your application when selecting an appropriate evaluation metric or combination of metrics. In practice, it's often beneficial to use multiple metrics to gain a more comprehensive understanding of your model's performance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45fd4782",
   "metadata": {},
   "source": [
    "## Q5. What is multiclass classification and how is it different from binary classification?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f838f13",
   "metadata": {},
   "source": [
    "**Multiclass classification** and **binary classification** are two fundamental types of supervised machine learning tasks used to categorize data into different classes or categories. Here's an explanation of each and the key differences between them:\n",
    "\n",
    "**Binary Classification:**\n",
    "- **Definition:** Binary classification is a type of classification problem where the goal is to categorize data into one of two possible classes or categories: typically, positive (1) or negative (0). It involves determining a decision boundary that separates the two classes.\n",
    "- **Examples:** Spam detection (classifying emails as spam or not spam), medical diagnosis (distinguishing between diseased and healthy individuals), and sentiment analysis (categorizing sentiment as positive or negative) are common examples of binary classification tasks.\n",
    "- **Output:** The model produces a single output or probability score that indicates the likelihood of an instance belonging to the positive class.\n",
    "\n",
    "**Multiclass Classification:**\n",
    "- **Definition:** Multiclass classification, also known as multinomial classification, is a type of classification problem where there are more than two distinct classes or categories, and the goal is to assign each instance to one of these multiple classes.\n",
    "- **Examples:** Handwritten digit recognition (recognizing digits from 0 to 9), object recognition (classifying images into various objects or animals), and language identification (identifying the language of a text) are examples of multiclass classification problems.\n",
    "- **Output:** The model produces multiple class probabilities or labels, one for each class, and assigns an instance to the class with the highest probability or confidence score.\n",
    "\n",
    "**Key Differences:**\n",
    "1. **Number of Classes:**\n",
    "   - In binary classification, there are only two classes (positive and negative).\n",
    "   - In multiclass classification, there are three or more distinct classes.\n",
    "\n",
    "2. **Output Format:**\n",
    "   - In binary classification, the model typically produces a single output or probability score that indicates the likelihood of belonging to the positive class (e.g., a probability between 0 and 1).\n",
    "   - In multiclass classification, the model produces multiple class probabilities or labels, and each instance is assigned to one of the multiple classes.\n",
    "\n",
    "3. **Decision Boundary:**\n",
    "   - Binary classification seeks to find a decision boundary that separates two classes.\n",
    "   - Multiclass classification involves distinguishing between multiple classes, often requiring a more complex decision boundary.\n",
    "\n",
    "4. **Model Complexity:**\n",
    "   - Binary classification models are designed to address two-class problems and are often simpler.\n",
    "   - Multiclass classification models are typically more complex because they need to accommodate multiple classes and their relationships.\n",
    "\n",
    "5. **Evaluation Metrics:**\n",
    "   - In binary classification, common evaluation metrics include accuracy, precision, recall, F1-score, ROC-AUC, and others.\n",
    "   - In multiclass classification, similar metrics can be used, but they may be extended or modified to account for multiple classes, such as micro-averaging, macro-averaging, and confusion matrices for each class.\n",
    "\n",
    "In summary, the key distinction between binary and multiclass classification lies in the number of classes and the output format of the classification model. Binary classification deals with two classes, while multiclass classification involves three or more classes, making it suitable for problems with multiple categories or labels."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c67f50ea",
   "metadata": {},
   "source": [
    "## Q6. Explain how logistic regression can be used for multiclass classification."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ab9e859",
   "metadata": {},
   "source": [
    "Logistic regression is a binary classification algorithm, but it can be extended to handle multiclass classification problems through various techniques. One common approach is to use \"One-vs-All\" (also known as \"One-vs-Rest\") or \"One-vs-Rest\" (OvR) encoding. Here's how logistic regression can be adapted for multiclass classification using the OvR technique:\n",
    "\n",
    "**One-vs-Rest (OvR) Multiclass Classification:**\n",
    "\n",
    "1. **Data Preparation:**\n",
    "   - Given a multiclass classification problem with K classes, you prepare the dataset with K binary classification problems, one for each class.\n",
    "   - For each binary problem, you create a new target variable that represents whether an instance belongs to the current class (positive class) or not (negative class).\n",
    "\n",
    "2. **Training Multiple Binary Classifiers:**\n",
    "   - Train a separate logistic regression model for each of the K binary classification problems.\n",
    "   - In each model, you use the original feature set but modify the target variable to indicate whether an instance belongs to the current class (positive class) or any other class (negative class).\n",
    "\n",
    "3. **Predictions:**\n",
    "   - To make a multiclass prediction for a new instance, you apply all K trained models to it.\n",
    "   - Each model produces a probability score indicating the likelihood of the instance belonging to its respective class.\n",
    "   - The class with the highest probability score is assigned as the final predicted class for the instance.\n",
    "\n",
    "4. **Decision Threshold:**\n",
    "   - You can choose a decision threshold for each binary model to convert probability scores into class predictions. A common threshold is 0.5, but you can adjust it to control precision and recall trade-offs for individual models.\n",
    "\n",
    "**Advantages of OvR for Logistic Regression in Multiclass Classification:**\n",
    "\n",
    "- **Simplicity:** OvR is straightforward to implement and extends binary logistic regression naturally to multiclass problems.\n",
    "- **Interpretability:** Each binary model provides interpretable coefficients, making it easier to understand the impact of features on individual classes.\n",
    "- **Scalability:** OvR can handle multiclass problems with a large number of classes without significantly increasing model complexity.\n",
    "\n",
    "**Limitations of OvR:**\n",
    "\n",
    "- **Class Imbalance:** If the dataset is imbalanced (some classes have many more instances than others), OvR may lead to biased models, as models for minority classes may be undertrained.\n",
    "- **Dependencies:** OvR assumes that the classes are independent, which may not hold in some cases (e.g., if classes are hierarchical or have relationships).\n",
    "- **Complexity:** For a large number of classes, the number of binary models can become substantial, potentially leading to longer training times and increased storage requirements.\n",
    "\n",
    "Logistic regression can be adapted for multiclass classification using the OvR technique, which trains multiple binary models, one for each class. While it's a simple and interpretable approach, it may have limitations related to class imbalance and class dependencies in complex multiclass problems. Other advanced techniques like softmax regression (multinomial logistic regression) are also available for multiclass classification and may offer better performance in certain scenarios."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1d67f1d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.685\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Generate a random multiclass classification dataset\n",
    "X, y = make_classification(n_samples=1000, n_features=10, n_classes=3, n_informative=8)\n",
    "\n",
    "# Split the data into training and testing sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "# Train a logistic regression model using softmax regression\n",
    "lr = LogisticRegression(multi_class='multinomial', solver='lbfgs')\n",
    "lr.fit(X_train, y_train)\n",
    "\n",
    "# Predict the class labels for the test set\n",
    "y_pred = lr.predict(X_test)\n",
    "\n",
    "# Print the accuracy score\n",
    "accuracy = lr.score(X_test, y_test)\n",
    "print(\"Accuracy:\", accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bfb31c44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "import seaborn as sns\n",
    "cf = confusion_matrix(y_test,y_pred)\n",
    "sns.heatmap(cf,annot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9cfb8e7",
   "metadata": {},
   "source": [
    "## Q7. Describe the steps involved in an end-to-end project for multiclass classification."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8766ba6c",
   "metadata": {},
   "source": [
    "Steps involved in an end-to-end project for multiclass classification are :\n",
    "\n",
    "1. **Problem Definition and Data Collection:**\n",
    "   - Clearly define the multiclass classification problem you want to solve and understand the business or research objectives.\n",
    "   - Gather a labeled dataset that includes features (attributes) and class labels for each instance. Ensure the data is representative of the problem domain.\n",
    "\n",
    "2. **Data Preprocessing:**\n",
    "   - Explore and understand the dataset by performing data analysis and visualization to identify patterns, distributions, and outliers.\n",
    "   - Clean the data by handling missing values, outliers, and anomalies.\n",
    "   - Perform feature engineering, which may include feature selection, transformation, or creation of new features to improve model performance.\n",
    "\n",
    "3. **Data Splitting:**\n",
    "   - Split the dataset into three subsets: training, validation, and test sets. Common splits include 70-80% for training, 10-15% for validation, and 10-15% for testing.\n",
    "   - Ensure that class distributions are balanced across the splits to prevent bias.\n",
    "\n",
    "4. **Model Selection:**\n",
    "   - Choose an appropriate machine learning algorithm or model architecture for multiclass classification. Options include logistic regression, decision trees, random forests, support vector machines, neural networks, and more.\n",
    "   - Consider the characteristics of your data, model complexity, and interpretability when selecting the model.\n",
    "\n",
    "5. **Model Training:**\n",
    "   - Train the selected model using the training dataset. This involves feeding the features and corresponding class labels into the model and adjusting its parameters to minimize a loss function.\n",
    "   - Experiment with hyperparameter tuning and cross-validation to optimize the model's performance.\n",
    "\n",
    "6. **Model Evaluation:**\n",
    "   - Assess the model's performance using the validation dataset and appropriate evaluation metrics (e.g., accuracy, precision, recall, F1-score, ROC-AUC).\n",
    "   - Utilize techniques like a confusion matrix or ROC curves for a deeper analysis of model errors.\n",
    "   - Consider adjusting the model or features based on evaluation results.\n",
    "\n",
    "7. **Model Optimization:**\n",
    "   - Fine-tune the model by modifying hyperparameters, using different algorithms, or addressing issues like overfitting or underfitting.\n",
    "   - Continue iterating on the model and validation until you achieve satisfactory performance.\n",
    "\n",
    "8. **Final Model Testing:**\n",
    "   - Evaluate the final model's performance on the test dataset to estimate its generalization ability to new, unseen data.\n",
    "   - Ensure that the test dataset is completely separate from the training and validation datasets.\n",
    "\n",
    "9. **Model Deployment:**\n",
    "   - Deploy the trained multiclass classification model in a production environment, making it accessible for making predictions on new data.\n",
    "   - Implement robust and scalable deployment strategies, such as containerization, cloud deployment, or integration with existing systems.\n",
    "\n",
    "10. **Monitoring and Maintenance:**\n",
    "    - Continuously monitor the model's performance in production to detect any drift or degradation in accuracy.\n",
    "    - Implement regular model retraining or updates as new data becomes available or as business requirements change.\n",
    "\n",
    "11. **Documentation and Reporting:**\n",
    "    - Document all aspects of the project, including data preprocessing steps, model architecture, hyperparameters, and evaluation metrics.\n",
    "    - Create clear and concise reports or documentation to communicate results, findings, and recommendations to stakeholders.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3703639",
   "metadata": {},
   "source": [
    "## Q8. What is model deployment and why is it important?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31ecf070",
   "metadata": {},
   "source": [
    "Model deployment is the process of making a trained machine learning model operational and accessible for real-world use. It involves integrating the model into a production environment or system where it can receive input data, make predictions or classifications, and provide output to end-users or other downstream applications. \n",
    "\n",
    "Model deployment is a crucial step in the machine learning workflow for several reasons:\n",
    "\n",
    "1. **Realizing Value:** The primary goal of developing machine learning models is often to leverage them for decision-making, automation, or improving processes. Model deployment is the step where the model begins delivering value by making predictions on new, unseen data.\n",
    "\n",
    "2. **Scalability:** Deployed models can handle a high volume of data and predictions, making it possible to automate tasks that would be time-consuming or infeasible for humans to perform at scale.\n",
    "\n",
    "3. **Timeliness:** Deployed models can provide predictions in real-time or near real-time, enabling timely decision-making and responses to changing conditions.\n",
    "\n",
    "4. **Continuous Learning:** Deployment allows models to continuously learn and adapt to new data, improving their accuracy and relevance over time.\n",
    "\n",
    "5. **Integration:** Deployed models can be integrated into existing software systems, workflows, or applications, making them an integral part of an organization's operations.\n",
    "\n",
    "6. **Cost Efficiency:** By automating tasks through deployment, organizations can often reduce costs associated with manual labor or errors.\n",
    "\n",
    "7. **Accessibility:** Deployed models can be accessed by end-users, stakeholders, or other systems through various interfaces, such as APIs (Application Programming Interfaces), web applications, or batch processing.\n",
    "\n",
    "8. **Monitoring and Maintenance:** Once a model is deployed, it can be continuously monitored to ensure its performance and accuracy. If the model's performance degrades or drifts, adjustments or retraining can be initiated.\n",
    "\n",
    "\n",
    "Overall, model deployment bridges the gap between model development and real-world applications, allowing organizations to harness the predictive power of machine learning in a practical and scalable manner. It's a critical phase in the machine learning lifecycle that requires careful planning, implementation, and ongoing management to ensure successful and effective deployment."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b176b43",
   "metadata": {},
   "source": [
    "## Q9. Explain how multi-cloud platforms are used for model deployment."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b3cc903",
   "metadata": {},
   "source": [
    "Multi-cloud platforms can be used for model deployment in a variety of ways to enhance redundancy, performance, and flexibility. Here's how multi-cloud platforms are used for model deployment:\n",
    "\n",
    "1. **Redundancy and High Availability:**\n",
    "   - Deploying models on multiple cloud providers ensures redundancy and high availability. If one provider experiences downtime or issues, the model can continue to serve predictions from resources hosted on another provider's infrastructure.\n",
    "\n",
    "2. **Global Reach and Low Latency:**\n",
    "   - Multi-cloud deployment allows you to host models in data centers across different regions and countries. This reduces latency and provides a better user experience by allowing users to access the model from the nearest data center.\n",
    "\n",
    "3. **Cost Optimization:**\n",
    "   - Different cloud providers offer varying pricing structures and options. You can optimize costs by choosing the most cost-effective provider for each component of your model deployment, such as model serving, data storage, or scaling resources.\n",
    "\n",
    "4. **Vendor Diversification:**\n",
    "   - Using multiple cloud providers mitigates the risk of vendor lock-in, where you become overly dependent on a single provider's services. This approach allows you to maintain flexibility and switch providers if necessary.\n",
    "\n",
    "5. **Compliance and Data Residency:**\n",
    "   - Multi-cloud platforms enable compliance with data residency regulations by allowing you to store data and deploy models in specific regions that align with legal requirements.\n",
    "\n",
    "6. **Resource Scaling and Load Balancing:**\n",
    "   - You can dynamically scale resources up or down across different cloud providers based on demand. Load balancing and traffic management solutions distribute incoming requests intelligently to optimize resource utilization and response times.\n",
    "\n",
    "7. **Disaster Recovery and Failover:**\n",
    "   - Multi-cloud deployments enhance disaster recovery capabilities by replicating data and applications across cloud providers. In the event of a major outage with one provider, the model can still be accessed from another provider's infrastructure.\n",
    "\n",
    "8. **Security and Risk Mitigation:**\n",
    "   - Spreading data and model deployments across multiple cloud providers can help protect against security breaches or vulnerabilities associated with a single provider. It adds an extra layer of security.\n",
    "\n",
    "9. **Hybrid Cloud Integration:**\n",
    "   - Multi-cloud platforms can facilitate hybrid cloud deployments, allowing you to integrate on-premises resources or private clouds with public cloud deployments as needed.\n",
    "\n",
    "10. **Cross-Cloud Load Balancing:**\n",
    "    - Implementing a load balancer that spans multiple cloud providers helps distribute traffic and requests evenly, optimizing resource usage and ensuring high availability.\n",
    "\n",
    "11. **Cross-Cloud Traffic Routing:**\n",
    "    - Multi-cloud deployment allows you to route traffic intelligently based on factors such as geographic location, user load, or service health, providing a seamless and efficient user experience.\n",
    "\n",
    "12. **Cross-Cloud Disaster Recovery:**\n",
    "    - In the event of a catastrophic failure or outage in one cloud provider's region, you can failover to resources in another provider's region to maintain service continuity.\n",
    "\n",
    "In summary, multi-cloud platforms for model deployment offer robust solutions for improving availability, performance, cost-efficiency, and compliance while mitigating risks associated with single-cloud deployments. They allow organizations to leverage the strengths of different cloud providers and optimize their machine learning model deployments for various scenarios and regions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66384a20",
   "metadata": {},
   "source": [
    "## Q10. Discuss the benefits and challenges of deploying machine learning models in a multi-cloud environment."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3eb6c659",
   "metadata": {},
   "source": [
    "**Benefits of Multi-Cloud Model Deployment:**\n",
    "\n",
    "1. **Redundancy and High Availability:**\n",
    "   - **Benefit:** Multi-cloud deployment provides redundancy and high availability. If one cloud provider experiences downtime, the model can continue to function from resources on another provider's infrastructure.\n",
    "   - **Example:** An e-commerce platform ensures that its recommendation model remains available even if one cloud provider experiences an outage during a major shopping event.\n",
    "\n",
    "2. **Performance Optimization:**\n",
    "   - **Benefit:** By strategically placing model-serving resources in different regions, organizations can reduce latency and improve the user experience for a global audience.\n",
    "   - **Example:** A video streaming service uses multi-cloud deployment to ensure viewers in different countries experience minimal buffering and fast playback.\n",
    "\n",
    "3. **Cost Optimization:**\n",
    "   - **Benefit:** Organizations can choose the most cost-effective cloud provider for different components of model deployment, resulting in cost savings.\n",
    "   - **Example:** A data-intensive research project leverages one cloud provider's cost-effective storage solution while using another provider for GPU-accelerated model training.\n",
    "\n",
    "4. **Vendor Diversification:**\n",
    "   - **Benefit:** Multi-cloud deployment mitigates the risk of vendor lock-in, allowing organizations to maintain flexibility and switch providers if necessary.\n",
    "   - **Example:** An enterprise opts for multi-cloud to avoid being tied to a single cloud provider's ecosystem, enabling future migration or expansion options.\n",
    "\n",
    "5. **Compliance and Data Residency:**\n",
    "   - **Benefit:** Multi-cloud platforms facilitate compliance with data residency regulations by enabling data and model deployment in regions that align with legal requirements.\n",
    "   - **Example:** A healthcare provider deploys patient data analysis models in regions where data privacy regulations are strictly enforced.\n",
    "\n",
    "**Challenges of Multi-Cloud Model Deployment:**\n",
    "\n",
    "1. **Complexity and Management:**\n",
    "   - **Challenge:** Managing resources, security, and configurations across multiple cloud providers can be complex and require additional expertise.\n",
    "   - **Example:** Orchestrating deployments and ensuring consistent security measures across different cloud environments can be challenging.\n",
    "\n",
    "2. **Cost Tracking and Optimization:**\n",
    "   - **Challenge:** Cost tracking becomes more complex as resources are spread across multiple providers, making it essential to monitor and optimize costs effectively.\n",
    "   - **Example:** Keeping track of spending and optimizing resource allocation across multiple providers can require dedicated cost management efforts.\n",
    "\n",
    "3. **Interoperability and Compatibility:**\n",
    "   - **Challenge:** Ensuring compatibility and interoperability between different cloud providers' services and APIs may require extra effort and development.\n",
    "   - **Example:** Integrating services and data pipelines from different cloud providers while maintaining consistency can be challenging.\n",
    "\n",
    "4. **Data Synchronization and Consistency:**\n",
    "   - **Challenge:** Ensuring data consistency and synchronization across multiple cloud environments can be complex, especially for real-time applications.\n",
    "   - **Example:** A financial institution faces challenges in maintaining consistent transaction records when deploying financial fraud detection models on multiple clouds.\n",
    "\n",
    "5. **Security and Compliance:**\n",
    "   - **Challenge:** Implementing robust security measures and ensuring compliance with regulations across multiple providers demands careful planning and monitoring.\n",
    "   - **Example:** Meeting stringent security requirements while deploying sensitive customer data models across multiple cloud environments is a complex task.\n",
    "\n",
    "In summary, multi-cloud model deployment offers valuable benefits, including redundancy, performance optimization, cost savings, vendor diversification, and compliance support. However, it also introduces challenges related to complexity, cost tracking, interoperability, data management, and security. Organizations must carefully weigh these pros and cons when deciding to adopt a multi-cloud strategy for model deployment and implement appropriate strategies to mitigate challenges effectively."
   ]
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}