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Questions and Answers
What is the purpose of building a Huffman code in the context provided?
What is the purpose of building a Huffman code in the context provided?
- To combine the symbols with the highest probabilities first
- To create a binary tree based on symbol probabilities (correct)
- To rank all symbols in order of their length in bits
- To randomly assign binary values to each symbol
In the context of training sets for learning, what does an entropy value of 0 indicate?
In the context of training sets for learning, what does an entropy value of 0 indicate?
- Maximum information gain
- High impurity
- Minimum impurity (correct)
- Complete randomness
How is entropy calculated for a group with 50% of examples in each class?
How is entropy calculated for a group with 50% of examples in each class?
- -0.25 log2(0.25) - 0.75 log2(0.75) = 0.75
- -0.5 log2(0.5) - 0.5 log2(0.5) = 1 (correct)
- -1 log2(0.5) - 0 log2(0) = 0
- -0.5 log2(0.5) + 0.5 log2(0.5) = 0
What does the average message length approach over time when using the provided Huffman code for many messages?
What does the average message length approach over time when using the provided Huffman code for many messages?
In the context of information gain, what is the primary goal when determining the most useful attribute for discriminating between classes?
In the context of information gain, what is the primary goal when determining the most useful attribute for discriminating between classes?
What does the entropy of a group with completely random distribution of examples represent?
What does the entropy of a group with completely random distribution of examples represent?
What is the primary purpose of entropy in decision tree learning?
What is the primary purpose of entropy in decision tree learning?
Which of the following statements about information gain is correct?
Which of the following statements about information gain is correct?
What is the relationship between entropy and the efficiency of a coding scheme?
What is the relationship between entropy and the efficiency of a coding scheme?
In the context of decision tree learning, what does a group with minimum impurity or entropy imply?
In the context of decision tree learning, what does a group with minimum impurity or entropy imply?
What is the significance of the Huffman coding scheme in the context of entropy and data compression?
What is the significance of the Huffman coding scheme in the context of entropy and data compression?
What is the role of conditional entropy in decision tree learning?
What is the role of conditional entropy in decision tree learning?
What is the purpose of information gain in the context of decision trees?
What is the purpose of information gain in the context of decision trees?
What is the formula for calculating the information gain when splitting on a feature A for a target variable Y?
What is the formula for calculating the information gain when splitting on a feature A for a target variable Y?
What is the relationship between information gain and entropy?
What is the relationship between information gain and entropy?
Which of the following statements about conditional entropy is true?
Which of the following statements about conditional entropy is true?
In the context of decision trees, what does impurity refer to?
In the context of decision trees, what does impurity refer to?
What is the purpose of the weighted average entropy of children in the information gain calculation?
What is the purpose of the weighted average entropy of children in the information gain calculation?
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Study Notes
Decision Tree Splitting
- Splitting based on whether balance exceeds 50K or not, and whether applicant is employed or unemployed.
- Information Gain (IG) measures the level of impurity in a group of examples.
Impurity and Entropy
- Impurity measures the level of uncertainty or randomness in a group of examples.
- Entropy (H(X)) is a common way to measure impurity.
- Entropy calculates the expected number of bits needed to encode a randomly drawn value of X (under the most efficient code).
Entropy Calculation
- Entropy formula: H(X) = -∑(P(X=i) * log2(P(X=i)))
- Example: Huffman code, a optimal coding scheme devised by David Huffman in 1952.
Information Gain
- Information Gain (IG) tells us how important a given attribute of the feature vectors is.
- IG is used to decide the ordering of attributes in the nodes of a decision tree.
- IG formula: IG = H(X) - H(X|Y)
- IG calculates the expected reduction in entropy of the target variable Y for a data sample S, due to sorting on variable A.
Calculating Information Gain
- IG calculation: Parent Entropy - [Average Entropy of Children]
- Example: IG = 0.996 - 0.615 = 0.38
Entropy-Based Decision Tree Construction
- Training set X is used to construct a decision tree.
- Each node is a probability of all nodes beneath it.
Huffman Code
- A Huffman code can be built by ranking all symbols in order of probability of occurrence.
- The code is built by successively combining the two symbols of the lowest probability to form a new composite symbol.
- The code is used to encode messages with a given probability distribution.
2-Class Cases: Entropy
- Entropy formula for 2-class cases: H(X) = -∑(P(X=i) * log2(P(X=i)))
- Example: Entropy of a group with all examples belonging to the same class is 0 (minimum impurity).
- Example: Entropy of a group with 50% in either class is 1 (maximum impurity).
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