The Kernel Trick Quiz

Answers and explanations appear as you take the quiz.

1. What does a kernel function replace in an algorithm using the kernel trick?
   • The loss function with a validation score
   • The fitted class labels with similarity ranks
   • Inner products between explicitly transformed examples
   • The need to evaluate pairs of examples
2. How can a linear SVM with a nonlinear kernel produce a curved boundary in input space?
   • The kernel converts the training labels into distances
   • It is linear in an implicit feature space
   • A curved input boundary requires a different classifier for each row
   • The kernel makes the original input representation linearly separable without a mapping
3. What does increasing RBF gamma generally do to similarity as input distance grows?
   • Makes similarity decay more slowly
   • Leaves similarity unchanged for all distances
   • Changes only the class priors
   • Makes similarity decay more rapidly
4. Why does feature scaling matter for an RBF kernel?
   • Its similarity depends on distances between feature vectors
   • Scaling sets the RBF's degree as in a polynomial kernel
   • Scaling removes the need to tune regularization
   • Scaling guarantees the same geometry for arbitrary feature units
5. What mathematical condition is typically required of a Gram matrix for standard kernel methods?
   • Strictly negative eigenvalues
   • A diagonal containing only zeros for every nonzero input
   • Positive semidefiniteness
   • A determinant fixed at one
6. A dense pairwise kernel matrix stores entries for each pair of n examples. How does its size grow?
   • Linearly in n
   • Quadratically in n
   • Logarithmically in n
   • Only with the number of output classes
7. Which kernel is commonly associated with interactions up to a chosen polynomial degree?
   • A radial basis kernel with no finite polynomial degree
   • A purely linear kernel limited to first-degree interactions
   • A constant kernel independent of input products
   • A polynomial kernel
8. How should kernel type and hyperparameters be selected?
   • Using validation within the training protocol
   • By choosing whichever yields the best final test score
   • By assuming the most flexible kernel will generalize best
   • By choosing a kernel before checking feature scales