Project_13_4_Feature Engineering Assignment - 2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56f48d7a",
   "metadata": {},
   "source": [
    "## Q1. What is the Filter method in feature selection, and how does it work?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c58bdba",
   "metadata": {},
   "source": [
    "In feature selection, the Filter method is a technique used to select relevant features from a dataset before training a machine learning model. It is a type of feature selection that focuses on evaluating the characteristics of individual features independently of the chosen machine learning algorithm. The Filter method is called \"filter\" because it filters out irrelevant or redundant features based on their statistical properties and their relationship with the target variable, without considering the model's learning process.\n",
    "\n",
    "The Filter method typically involves the following steps:\n",
    "\n",
    "1. Scoring Features: Each feature in the dataset is scored or ranked based on some statistical measure, such as correlation, mutual information, chi-square test, variance, or information gain. The chosen measure depends on the nature of the data (e.g., numeric or categorical features) and the type of problem (classification or regression).\n",
    "\n",
    "2. Ranking Features: Features are then ranked based on their scores, from most relevant to least relevant. The higher the score, the more important the feature is considered in relation to the target variable.\n",
    "\n",
    "3. Selecting Top Features: After ranking the features, a predetermined number of top-ranked features are selected to be used for training the machine learning model and a threshold can be set, the features with scores above the threshold are selected.\n",
    "\n",
    "4. Feature Subset: The selected features form a subset of the original dataset, and this reduced feature subset is used for training the machine learning model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ff00f47",
   "metadata": {},
   "source": [
    "## Q2. How does the Wrapper method differ from the Filter method in feature selection?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec3474e7",
   "metadata": {},
   "source": [
    "The Wrapper method and the Filter method are two different approaches to feature selection in machine learning and they aim to select relevant features from a dataset to improve model performance and reduce overfitting.\n",
    "\n",
    "#### Filter Method:\n",
    "\n",
    "- Evaluates features independently of the machine learning model.\n",
    "- Relies on statistical measures or data characteristics to assess feature relevance.\n",
    "- Independent of the learning algorithm used for model training.\n",
    "- Computationally efficient as it doesn't involve model training.\n",
    "- Selects features based on computed scores or ranking.\n",
    "- Quick, simple, and suitable for early data preprocessing.\n",
    "\n",
    "\n",
    "#### Wrapper Method:\n",
    "\n",
    "- Involves the learning algorithm during feature evaluation.\n",
    "- Uses the model's performance to assess feature importance.\n",
    "- Model-dependent and considers the model's behavior.\n",
    "- More computationally expensive as it requires training and evaluating the model multiple times.\n",
    "- Searches through different feature combinations to find the optimal subset.\n",
    "- Considers feature interactions and may lead to better feature selection.\n",
    "\n",
    "\n",
    "The Filter method is computationally efficient and quick to implement but may not capture complex feature interactions. On the other hand, the Wrapper method considers the model's behavior and interactions but can be computationally expensive, especially for large datasets with many features.\n",
    "\n",
    "A combination of different feature selection techniques, including Filter and Wrapper methods, can be used to improve the overall model performance and generalization."
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "c58e2d4b",
   "metadata": {},
   "source": [
    "![84353IMAGE1.png](attachment:84353IMAGE1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f67e36cb",
   "metadata": {},
   "source": [
    "## Q3. What are some common techniques used in Embedded feature selection methods?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b74c0a4",
   "metadata": {},
   "source": [
    "Embedded feature selection methods are techniques that incorporate feature selection as an integral part of the model training process. These methods aim to identify the most relevant features while the model is being trained. \n",
    "\n",
    "Some common techniques used in Embedded feature selection methods include:\n",
    "\n",
    "**LASSO (Least Absolute Shrinkage and Selection Operator)**: LASSO is a linear regression technique that adds a penalty term to the model's objective function, forcing some coefficients to be exactly zero. This encourages sparsity in the feature space and automatically selects important features.\n",
    "\n",
    "**Ridge Regression**: Ridge regression also adds a penalty term to the objective function, but it uses the L2 regularization term. While LASSO can set coefficients to exactly zero, Ridge regression can shrink them towards zero, making it useful for feature selection and reducing multicollinearity.\n",
    "\n",
    "**Elastic Net**: Elastic Net combines the L1 (LASSO) and L2 (Ridge) regularization terms to achieve a balance between feature selection and avoiding multicollinearity.\n",
    "\n",
    "**Recursive Feature Elimination (RFE)**: RFE is an iterative technique that starts with all features and repeatedly trains the model, removing the least important feature(s) at each iteration. This process continues until the desired number of features is reached or until the model's performance stabilizes.\n",
    "\n",
    "**Tree-Based Methods**: Decision trees and ensemble methods like Random Forest and Gradient Boosting can implicitly perform feature selection by giving more importance to relevant features during the tree-building process.\n",
    "\n",
    "**Regularized Linear Models**: Various linear models like Logistic Regression and Linear Support Vector Machines can use regularization techniques like L1 or L2 regularization to promote feature selection.\n",
    "\n",
    "**Embedded Feature Importance**: Some algorithms, like Random Forest and Gradient Boosting, provide feature importance scores, which can be used for feature selection. Features with higher importance scores are considered more relevant.\n",
    "\n",
    "**Feature Selection with Support Vector Machines (SVM)**: SVM can use regularization parameters (C) to control the importance of features during the training process, thus performing embedded feature selection.\n",
    "\n",
    "**Genetic Algorithms**: Genetic algorithms can be used to search for the best subset of features that optimize the model's performance by selecting and combining features based on a fitness function.\n",
    "\n",
    "Embedded methods are particularly useful when there are many features and computational efficiency is a concern, as they perform feature selection directly within the model training process, leading to more compact and efficient models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3819099e",
   "metadata": {},
   "source": [
    "## Q4. What are some drawbacks of using the Filter method for feature selection?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b29ce33",
   "metadata": {},
   "source": [
    "The drawbacks of using Filter method in feature selection are :\n",
    "    \n",
    "**Independence from Model**: Since the Filter method evaluates features independently of the machine learning model, it may not capture complex relationships or feature interactions that are essential for the model's performance. It might select features that individually appear relevant but do not contribute much to the model's predictive power when combined.\n",
    "\n",
    "**Limited Model Adaptability**: The Filter method's feature selection is agnostic to the learning algorithm, which means it doesn't take into account how well the selected features suit the specific learning algorithm being used. Certain features might be more valuable for one algorithm but less useful for another.\n",
    "\n",
    "**No Optimization of Model Performance**: The Filter method solely relies on statistical measures or data characteristics to assess feature relevance. It doesn't optimize the model's performance directly, which might lead to suboptimal feature subsets for a particular machine learning problem.\n",
    "\n",
    "**Overlooking Feature Combinations**: The Filter method examines features in isolation and may overlook combinations of features that, when used together, can provide valuable information for the model.\n",
    "\n",
    "**Inability to Adapt During Model Training**: Once the features are selected using the Filter method, they remain fixed throughout the model training process. If the model's performance deteriorates over time or with changes in the dataset, the selected feature subset might not be optimal anymore.\n",
    "\n",
    "**Sensitivity to Data Preprocessing**: The performance of the Filter method can be sensitive to data preprocessing steps. Small variations in data scaling, normalization, or transformation may lead to different feature rankings and selections.\n",
    "\n",
    "**Loss of Contextual Information**: The Filter method doesn't consider the context or semantics of the features in the dataset, potentially leading to the exclusion of important domain-specific features.\n",
    "\n",
    "**Selection Bias**: Depending on the choice of the statistical measure used for feature scoring, the Filter method might introduce selection bias, favoring certain types of features over others"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b932530",
   "metadata": {},
   "source": [
    "## Q5. In which situations would you prefer using the Filter method over the Wrapper method for feature selection?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0be18c5e",
   "metadata": {},
   "source": [
    "\n",
    "The choice between the Filter method and the Wrapper method for feature selection depends on the specific characteristics of the data and the objectives of the machine learning task. \n",
    "\n",
    "\n",
    "Here are some situations in which you might prefer using the Filter method over the Wrapper method:\n",
    "\n",
    "**Large Datasets**: The Filter method is computationally efficient and does not involve model training for each feature evaluation. If you have a large dataset with a substantial number of features, the Filter method can be a quicker and more scalable approach for initial feature screening.\n",
    "\n",
    "**Quick Feature Selection**: If you need a fast and straightforward way to identify potentially relevant features early in the data preprocessing stage, the Filter method can be a suitable choice. It allows you to remove irrelevant or redundant features before diving into the more computationally expensive feature selection methods.\n",
    "\n",
    "**Exploratory Data Analysis**: During exploratory data analysis, you might use the Filter method to gain insights into the relationship between individual features and the target variable without committing to a specific learning algorithm or complex model training.\n",
    "\n",
    "**Feature Ranking**: The Filter method provides feature ranking or scoring, which can help you identify the most important features without going through the exhaustive search space of the Wrapper method.\n",
    "\n",
    "**Data Preprocessing**: The Filter method can be used as a preliminary step in data preprocessing to remove features with low variance or that are highly correlated with other features. This can help improve the efficiency of subsequent feature selection techniques.\n",
    "\n",
    "**Independence from Model Choice**: The Filter method is model-agnostic and doesn't depend on the choice of the learning algorithm. If you want to identify relevant features regardless of the model you plan to use, the Filter method can be beneficial.\n",
    "\n",
    "**Handling High-Dimensional Data**: In situations where the dimensionality of the data is high and computational resources are limited, the Filter method can be more feasible compared to the Wrapper method, which requires training multiple models.\n",
    "\n",
    "\n",
    "The Filter method is often used as a preliminary step or in situations where computational efficiency is crucial. For more accurate and robust feature selection, especially when considering feature interactions and the model's behavior, the Wrapper method or Embedded methods might be preferred."
   ]
  },
  {
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   "id": "ea730ab2",
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    "## Q6. In a telecom company, you are working on a project to develop a predictive model for customer churn. You are unsure of which features to include in the model because the dataset contains several different ones. Describe how you would choose the most pertinent attributes for the model using the Filter Method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "321782b1",
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   "source": [
    "To choose the most pertinent attributes for the predictive model of customer churn using the Filter Method, you can follow these steps:\n",
    "\n",
    "**Understand the Data and Domain**: Begin by gaining a comprehensive understanding of the dataset and the domain of the telecom industry. Identify the target variable, which in this case is likely to be a binary indicator representing whether a customer churned or not.\n",
    "\n",
    "**Preprocess the Data**: Handle missing values, encode categorical variables, and perform necessary data transformations to ensure the data is ready for analysis.\n",
    "\n",
    "**Select Appropriate Filter Metrics**: Choose appropriate statistical measures that are relevant for feature selection in the context of customer churn. Common filter metrics include correlation, information gain, chi-square test, and mutual information for categorical features, and variance for numeric features.\n",
    "\n",
    "**Compute Feature Scores**: Apply the chosen filter metrics to compute scores or rankings for each feature based on their relevance to customer churn. For example, you can compute correlations with the target variable or calculate the information gain for each feature.\n",
    "\n",
    "**Visualize Feature Importance**: Create visualizations, such as bar plots or heatmaps, to gain insights into the importance of individual features based on their computed scores. This can help you quickly identify potentially relevant features.\n",
    "\n",
    "**Set a Threshold or Select Top Features**: Based on the scores or rankings, set a threshold or select the top-ranked features that you believe are most pertinent for the customer churn prediction. You can use domain knowledge and data exploration insights to guide this decision.\n",
    "\n",
    "**Validate the Selection**: Split the data into training and validation sets to assess the model's performance on the selected features. Use appropriate evaluation metrics like accuracy, precision, recall, F1-score, and area under the ROC curve (AUC-ROC) to evaluate the model's performance.\n",
    "\n",
    "**Iterate and Refine**: If necessary, iterate the process by trying different filter metrics or threshold values and evaluating the model performance until you achieve a satisfactory result.\n",
    "\n",
    "**Interpret the Results**: Once you have selected the most pertinent attributes, interpret their importance and relationships with the target variable. This analysis can provide valuable insights into the factors driving customer churn in the telecom company."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a67947d",
   "metadata": {},
   "source": [
    "## Q7. You are working on a project to predict the outcome of a soccer match. You have a large dataset with many features, including player statistics and team rankings. Explain how you would use the Embedded method to select the most relevant features for the model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6968a670",
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   "source": [
    "Using the Embedded method for feature selection in a project to predict the outcome of a soccer match can help identify the most relevant features that contribute significantly to the model's performance. The Embedded method incorporates feature selection as part of the model training process. Here's how you can use the Embedded method to select the most relevant features for your soccer match prediction model:\n",
    "\n",
    "1. Preprocess the Data: Start by preprocessing the dataset, including handling missing values, encoding categorical variables, and normalizing or scaling numeric features as needed.\n",
    "\n",
    "2. Select a Suitable Model: Choose a machine learning model suitable for predicting soccer match outcomes. Common models for classification tasks like this include Logistic Regression, Random Forest, Gradient Boosting, or Support Vector Machines (SVM).\n",
    "\n",
    "3. Define the Evaluation Metric: Select an appropriate evaluation metric to assess the model's performance. For soccer match prediction, metrics like accuracy, precision, recall, F1-score, and area under the ROC curve (AUC-ROC) can be relevant.\n",
    "\n",
    "4. Train the Model with All Features: Initially, train the chosen model using all available features from the dataset. This will give you a baseline performance for reference.\n",
    "\n",
    "5. Model with Embedded Feature Selection: Depending on the selected model, it might offer built-in feature selection capabilities as part of the training process. For example:\n",
    "\n",
    "> **LASSO (Least Absolute Shrinkage and Selection Operator)**: Use LASSO if you are using Linear Regression. LASSO adds an L1 regularization term to the model, which leads to sparse coefficient values and naturally performs feature selection.\n",
    "\n",
    ">**Random Forest or Gradient Boosting**: These ensemble models provide feature importance scores as part of their training process. Features with higher importance scores are considered more relevant.\n",
    "\n",
    ">**Regularized Linear Models**: For models like Logistic Regression or Linear SVM, you can use regularization techniques like L1 or L2 regularization to promote feature selection.\n",
    "\n",
    ">**Recursive Feature Elimination (RFE)**: If the selected model doesn't provide built-in feature selection, you can use RFE as an embedded method. RFE is an iterative technique that repeatedly removes the least important features based on model coefficients or feature importance scores.\n",
    "\n",
    "6. Evaluate the Model: After training the model with embedded feature selection, evaluate its performance using the chosen evaluation metric. Compare the model's performance with the baseline model (trained with all features).\n",
    "\n",
    "7. Select Relevant Features: Based on the model's feature importances or coefficients, identify the most relevant features that contribute significantly to the model's predictive power. These features are the ones that the model considers the most important for predicting soccer match outcomes.\n",
    "\n",
    "8. Iterate and Refine: If necessary, experiment with different models or hyperparameters and evaluate their performance with embedded feature selection. Continue this process until you achieve satisfactory results.\n",
    "\n",
    "9. Interpretation and Validation: Interpret the results and the selected features to gain insights into the factors that are most influential in predicting soccer match outcomes. Validate the model's performance on a separate test dataset to ensure its generalization ability.\n",
    "\n",
    "Using the Embedded method allows you to perform feature selection within the model training process, which can lead to more accurate and interpretable models by focusing on the most relevant features for predicting soccer match outcomes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70104df1",
   "metadata": {},
   "source": [
    "## Q8. You are working on a project to predict the price of a house based on its features, such as size, location, and age. You have a limited number of features, and you want to ensure that you select the most important ones for the model. Explain how you would use the Wrapper method to select the best set of features for the predictor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41692aa8",
   "metadata": {},
   "source": [
    "To use the Wrapper method for feature selection in your project to predict the price of a house, you can follow these steps:\n",
    "\n",
    "1. Define the Model: Start by selecting a machine learning model suitable for regression tasks, as the goal is to predict the price of a house. Common models for regression include Linear Regression, Random Forest Regression, Gradient Boosting Regression, and Support Vector Regression.\n",
    "\n",
    "2. Split the Data: Divide your dataset into training and validation sets. The training set will be used for feature selection, while the validation set will be used to evaluate the model's performance.\n",
    "\n",
    "3. Feature Subset Search: The Wrapper method involves an exhaustive search or a heuristic algorithm to find the best subset of features that results in the most optimal model performance. You can use techniques like backward elimination, forward selection, or recursive feature elimination (RFE).\n",
    "\n",
    ">1. Backward Elimination: Start with all features, train the model, and iteratively remove the least significant feature (based on p-values or feature importance scores) until the desired model performance is achieved.\n",
    "\n",
    ">2. Forward Selection: Start with an empty set of features and add the most significant feature at each step until no improvement in model performance is observed.\n",
    "\n",
    ">3. Recursive Feature Elimination (RFE): Begin with all features and repeatedly eliminate the least important feature based on model coefficients or feature importance scores until the desired number of features is reached.\n",
    "\n",
    "4. Model Evaluation: At each iteration of feature selection, train the model using the selected subset of features on the training set and evaluate its performance on the validation set using appropriate regression evaluation metrics like mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), or R-squared (R2) coefficient.\n",
    "\n",
    "5. Select the Best Subset: Continue the feature subset search process, evaluating different subsets of features until you find the one that produces the best model performance on the validation set.\n",
    "\n",
    "6. Interpretation and Validation: Once you have selected the best set of features using the Wrapper method, interpret the results to gain insights into the most important factors influencing the house price prediction. Validate the final model's performance on a separate test dataset to ensure its generalization ability.\n",
    "\n",
    "\n",
    "The Wrapper method involves training and evaluating the model multiple times, making it more computationally expensive compared to the Filter method."
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