# Machine Learning Questions and Answers – Kernels

This set of Machine Learning Multiple Choice Questions & Answers (MCQs) focuses on “Kernels”.

1. The computational complexity challenge related to learning half-space in high dimensional feature spaces can be solved using the method of kernels.
a) True
b) False

Explanation: When the data is mapped into a high dimensional feature space, it extends the expressiveness of half-space predictors. And it raises both sample complexity and computational complexity challenges. And it can be solved using the method of kernels.

2. A kernel is a type of a similarity measure between instances.
a) True
b) False

Explanation: A kernel is a type of a similarity measure between instances. When we are embedding the data into a high dimensional feature space we introduce the idea of kernels. Mathematical meaning of a kernel is the inner product in some Hilbert space. So a standard interpretation of a kernel is the pair wise similarity between different samples.

3. Let the domain be the real line and consider the domain points {-10, -9, -8, …, 0, 1, …, 9, 10} where the labels are +1 for all x such that |x| > 2 and 1 otherwise. The given training set is separable by a half-space.
a) True
b) False

Explanation: The given training set is not separable by a half-space. Because the domain points are {-10, -9, -8, …, 0, 1, …, 9, 10} where the labels are +1 for all x such that |x| > 2 and 1 otherwise. Here the expressive power of half-spaces is rather restricted. So it is not separable by a half-space.

4. Which of the following is not true about making the class of half-spaces more expressive?
a) First map the original instance space into another high dimension space
b) Initially map the original instance space into another low dimension space
c) After mapping then learn a half-space in that space
d) Increasing expressive power is useful in separating the training set by a half-space

Explanation: Initially we are mapping the original instance space not into another low dimension space but to a higher dimension space. After the mapping then learns a half-space in that space. And it is useful in separating the training set by a half-space.

5. Polynomial-based classifiers yield much richer hypothesis classes than half-spaces.
a) False
b) True

Explanation: Polynomial-based classifiers yield much richer hypothesis classes than half-spaces. Consider the domain points {-6,…, 0, 1,…, 5, 6} where the labels are +1 for all x such that |x| > 2 and 1 otherwise. It is not separable by a half-space, but after the embedding x ↦ (x, x2) it is perfectly separable.

6. Which of the following statements is not true about Kernel methods?
a) It can be used for pattern analysis or pattern recognition
b) It maps the data into higher dimensional space
c) The data can be easily separated in the higher dimensional space
d) It only leads to finite dimensional space

Explanation: The kernel methods lead not only to finite dimensional space but also to infinite dimensional space as there are no constraints of this mapping. Because it maps the data into higher dimensional space by assuming that the data can be easily separated in the higher dimensional space. And it can be used for pattern analysis or pattern recognition.

7. Which of the following statements is not true about Kernel methods?
a) It works by embedding the input data to some high dimensional feature space
b) Embedding into feature space can be determined uniquely by specifying a kernel function that computes the dot product between data points in the feature space
c) It defines only the linear mapping to the feature space
d) Expensive computations in the high dimensional feature space can be avoided by evaluating the kernel function

Explanation: The kernel function not only defines the linear mapping to the feature space but also implicitly defines the non linear mapping to the feature space and expensive computations in the high dimensional feature space can be avoided by evaluating the kernel function. All other three statements are true about kernel methods.

Sanfoundry Global Education & Learning Series – Machine Learning.

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