Feature Selection and Importance Overview
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Questions and Answers

What is the primary goal of feature selection in data mining?

  • To evaluate all available features
  • To choose a subset of relevant features (correct)
  • To increase model complexity
  • To strictly include all available variables

    • Which method treats feature selection as part of the training process?

  • Filter methods
  • Best subset selection
  • Wrapper methods
  • Embedded methods (correct)

    • Which of the following is NOT a benefit of feature selection?

  • Reducing computational cost
  • Making the model more complex (correct)
  • Enhancing interpretability
  • Avoiding overfitting

    • What distinguishes an irrelevant feature from a redundant feature?

    <p>Irrelevant features have weak relationships in isolation; redundant features have weak relationships conditional on others.</p> Signup and view all the answers

    What is a common limitation of feature screening?

    <p>It cannot identify redundant features.</p> Signup and view all the answers

    In best subset selection, how are features chosen?

    <p>By fitting all possible models and selecting the best according to criteria</p> Signup and view all the answers

    Which measure of dependence might be used in feature screening?

    <p>Mutual information</p> Signup and view all the answers

    Which statement accurately reflects feature selection?

    <p>Feature selection can aid in reducing computational costs.</p> Signup and view all the answers

    What is the total number of models that can be estimated with 3 predictors?

    <p>8</p> Signup and view all the answers

    What is a significant drawback of the brute-force search method in best subset selection?

    <p>It requires estimating a large number of models.</p> Signup and view all the answers

    Which of the following correctly describes forward stepwise selection?

    <p>It starts with a null model and adds one predictor at a time.</p> Signup and view all the answers

    What is a benefit of using best subset selection?

    <p>Higher predictive accuracy compared to full feature models.</p> Signup and view all the answers

    Which of the following statements about stepwise selection is true?

    <p>It dramatically reduces computational cost compared to brute-force search.</p> Signup and view all the answers

    What happens when the number of predictors p is large, such as 30?

    <p>It can lead to fitting over a billion models.</p> Signup and view all the answers

    What is a limitation of the best subset selection method mentioned in the content?

    <p>It may produce binary decisions not optimal in many cases.</p> Signup and view all the answers

    Which algorithmic process does forward selection employ?

    <p>Fit one model at each step by adding predictors sequentially.</p> Signup and view all the answers

    What does the variable λ balance in model selection methods?

    <p>Loss function and regularization</p> Signup and view all the answers

    Which part of the equation describes the loss function in supervised learning?

    <p>L(yi, f(xi; θ))</p> Signup and view all the answers

    In the context of linear regression, what is the purpose of the regulariser C(β)?

    <p>To discourage large parameter values</p> Signup and view all the answers

    What characteristic of ridge regression qualifies it as ℓ2 regularisation?

    <p>It imposes a penalty based on the squared Euclidean norm.</p> Signup and view all the answers

    What does the term argmin represent in the model equations?

    <p>The optimal parameter values</p> Signup and view all the answers

    In the ridge regression formula, what is being minimized?

    <p>The sum of squared residuals along with the model parameters</p> Signup and view all the answers

    Which of the following is NOT required to create a learning algorithm from the supervised learning equation?

    <p>A dataset D</p> Signup and view all the answers

    The regularised estimation problem in ridge regression includes which specific penalty term?

    <p>$eta_j^2$</p> Signup and view all the answers

    What happens to the coefficients in ridge regression as the value of λ increases?

    <p>They are decreased towards zero.</p> Signup and view all the answers

    Which statement correctly describes what occurs when λ equals 0 in ridge regression?

    <p>The method becomes equivalent to ordinary least squares (OLS).</p> Signup and view all the answers

    What kind of solution does lasso regularization favor?

    <p>Sparse solutions with many zero coefficients</p> Signup and view all the answers

    What form does the ridge regression estimator take?

    <p>βridge = (X⊤X + λI)^{-1} X⊤y</p> Signup and view all the answers

    What is the key difference in the constraint formulations between lasso and ridge regression?

    <p>Lasso imposes an L1 penalty, while ridge imposes an L2 penalty</p> Signup and view all the answers

    In ridge regression, what is the role of the regularizer?

    <p>To penalize large coefficients.</p> Signup and view all the answers

    Which of the following statements about the coefficient profiles for lasso is accurate?

    <p>The lasso shrinkage factor measures the relative size of coefficients.</p> Signup and view all the answers

    What happens to the model's coefficients when λ approaches infinity in ridge regression?

    <p>They all are set to zero.</p> Signup and view all the answers

    What is the implication of having a higher predictive accuracy with lasso compared to OLS?

    <p>Lasso reduces variance while maintaining low bias.</p> Signup and view all the answers

    How do orthonormal columns of the design matrix X affect ridge regression?

    <p>They simplify the understanding of coefficient interactions.</p> Signup and view all the answers

    In the context of the ridge penalty, how does it compare to the lasso penalty?

    <p>The ridge penalty does not promote sparsity.</p> Signup and view all the answers

    Which loss function is minimized in ridge regression?

    <p>The squared difference between predicted and observed values plus a penalty term.</p> Signup and view all the answers

    Which condition must be true for two vectors to be considered orthonormal?

    <p>They must be orthogonal and have norms equal to one.</p> Signup and view all the answers

    What characterizes the solutions of β = (0, 1) and β′ = (1/2, 1/2) in relation to the ridge penalty?

    <p>Both solutions have the same ridge penalty.</p> Signup and view all the answers

    How are the regions of constraints described for lasso and ridge regression?

    <p>Lasso constrains coefficients with linear boundaries, ridge with circular boundaries.</p> Signup and view all the answers

    Why is the lasso said to reduce variance?

    <p>It restricts the flexibility of the model to improve consistency.</p> Signup and view all the answers

    Study Notes

    Feature Selection

    • Involves choosing a subset of available features for model building, enhancing model performance.
    • Aims to avoid overfitting, improve interpretability, and reduce computational costs.
    • Three main methods:
      • Filter methods: Select features before applying learning algorithms.
      • Wrapper methods: Evaluate learning algorithms with various subsets of features.
      • Embedded methods: Perform feature selection during model training.

    Feature Importance

    • Distinction between irrelevant features (weak relationship with response) and redundant features (weak relationship when conditioned on other features).
    • Irrelevant features may seem independently unimportant but could play a role in combination with others.

    Feature Screening

    • Removes features with weak bivariate relationships using measures of dependence like mutual information or Pearson correlation.
    • Benefits: Low computational cost; effective in high-dimensional spaces.
    • Limitations: May exclude features that are significant in combination; does not address redundancy.

    Best Subset Selection

    • Involves fitting all possible models and selecting the best based on model selection criteria.
    • Faces combinatorial explosion issue: for 30 features, over a billion models can be needed, making it computationally impractical.

    Lasso vs. Ridge Regression

    • Lasso regression tends to yield sparse solutions by employing an L1 penalty, promoting feature selection by shrinking unnecessary coefficients to zero.
    • Ridge regression uses an L2 penalty, shrinking coefficients but typically retaining all features.
    • Lasso can outperform Ordinary Least Squares (OLS) in predictive accuracy by controlling variance without excessive bias.

    Supervised Learning Framework

    • The general formulation involves minimizing the loss function L with a regularization term C to balance fit and complexity.

    Regularization

    • Ridge regression penalizes the squared L2 norm of coefficients to prevent overfitting.
    • Ridge estimator formula: ( \hat{\beta}_{ridge} = (X^T X + \lambda I)^{-1} X^T y ).
    • As λ increases, coefficient shrinkage towards zero intensifies.

    Stepwise Selection Methods

    • Can add or remove features iteratively to find near-optimal subsets while reducing computational load compared to brute-force search.
    • Forward selection adds one predictor at a time, selecting the model with the lowest training error, which avoids exhaustive model fitting.

    Importance of Regularization Parameters

    • The selection of λ is critical for balancing model complexity and fit quality; a higher λ increases regularization, leading to simpler models with lower variance.

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    Description

    This quiz focuses on the concepts of feature selection and importance in model building, highlighting methods like filter, wrapper, and embedded techniques. Additionally, it discusses the distinction between irrelevant and redundant features and the process of feature screening. Enhance your understanding of how to improve model performance and interpretability.

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