Question at position 30 Multiple choice question: Which of the following represents a scenario where entropy is zero? A dataset with 7 positive and 3 negative instances.A dataset with 5 positive and 5 negative instances.A dataset with 6 positive and 4 negative instances.None of the other choices are correct.A dataset with 10 positive instances.

Question

BlackTom AI · Accepted Answer

To determine where entropy is zero, we need a dataset that is perfectly pure, meaning all instances belong to the same class and there is no uncertainty.
Option 1: A dataset with 7 positive and 3 negative instances. This dataset contains two classes and is not pure; there is uncertainty about the class of an arbitrary instance, so the entropy is greater than zero.
Option 2: A dataset with 5 positive and 5 negative instances. This is a perfectly balanced binary case, but it is not pure either; there is still uncertainty about which class an instance belongs to, so the entropy is maximal for a 50-50 split and not zero.
Option 3: A dataset with 6 positive and 4 negative instances. Although skewed, it still contains both classes, so there is residual uncertainty and the entropy is greater than zero.
Option 4: None of the other choices are correct. This would be chosen only if none of the prior options could yield entropy zero, but at least one option does describe a pure set, so this statement is not accurate for the question asked.
Option 5: A dataset with 10 positive instances. Here, every instance is positive; there is no uncertainty about the class label for any instance. In information-theoretic terms, the class distribution is degenerate, and the entropy is zero because there is no randomness left to quantify.

类似问题

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let H denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let [math: H] denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let H denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z 0 | 0 | 0 0 | 1 | 1 1 | 0 | 0 1 | 1 | 1 2 | 0 | 1 2 | 1 | 1 [/table] Compute the entropy of [math: XYZ+1]\frac{XY}{Z+1}

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let [math: H] denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z 0 | 0 | 0 0 | 1 | 1 1 | 0 | 0 1 | 1 | 1 2 | 0 | 1 2 | 1 | 1 [/table] Compute the entropy of [math: XYZ+1]\frac{XY}{Z+1}

Question at position 33 True/False Question: The entropy of a homogeneous set (a set of instances with the same label) is not always zero. TrueFalse

Question at position 16 Multiple Choice Question: Entropy can be negativeis used to calculate information gainis a measure of information gainis a measure of correlation between numeric variables

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