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Questions and Answers
What is the primary goal when picking an attribute for splitting at a non-terminal node in a decision tree?
What is the primary goal when picking an attribute for splitting at a non-terminal node in a decision tree?
- To minimize the complexity of the tree
- To maximize information gain (correct)
- To balance the number of examples in each group
- To ensure unique attribute values
What is a potential disadvantage of decision trees mentioned in the content?
What is a potential disadvantage of decision trees mentioned in the content?
- They are ineffective with discrete attributes
- They always yield the global optimum
- They cannot handle missing values
- They may overfit the data if too large (correct)
How should continuous attributes be handled when constructing a decision tree?
How should continuous attributes be handled when constructing a decision tree?
- By averaging their values across examples
- By splitting based on a threshold to maximize information gain (correct)
- By treating them as discrete categorical variables
- By ignoring them completely
What characteristic is desirable in a good decision tree in terms of size and interpretability?
What characteristic is desirable in a good decision tree in terms of size and interpretability?
What advantage is noted for decision trees when there are a large number of attributes?
What advantage is noted for decision trees when there are a large number of attributes?
What role do internal nodes play in a decision tree?
What role do internal nodes play in a decision tree?
What is typically used to determine the leaf value $y_m$ in a classification tree?
What is typically used to determine the leaf value $y_m$ in a classification tree?
Which case allows decision trees to approximate any function arbitrarily closely?
Which case allows decision trees to approximate any function arbitrarily closely?
What is the challenge in constructing a decision tree?
What is the challenge in constructing a decision tree?
What does high entropy indicate about a variable's distribution?
What does high entropy indicate about a variable's distribution?
How is branching determined in a decision tree?
How is branching determined in a decision tree?
In the context of conditional entropy, if X and Y are independent, what can be said about H(Y|X)?
In the context of conditional entropy, if X and Y are independent, what can be said about H(Y|X)?
What is expressed by each path from the root to a leaf in a decision tree?
What is expressed by each path from the root to a leaf in a decision tree?
What is the unit of measurement for entropy?
What is the unit of measurement for entropy?
What methodology is employed when choosing a good split in decision trees?
What methodology is employed when choosing a good split in decision trees?
What does a regression tree typically output at its leaf nodes?
What does a regression tree typically output at its leaf nodes?
What is implied by low entropy in a variable's distribution?
What is implied by low entropy in a variable's distribution?
Which statement is true regarding information gain?
Which statement is true regarding information gain?
What is the primary purpose of entropy in decision tree algorithms?
What is the primary purpose of entropy in decision tree algorithms?
How does knowing variable X affect uncertainty about variable Y according to the chain rule of entropy?
How does knowing variable X affect uncertainty about variable Y according to the chain rule of entropy?
What is the significance of a flat histogram in terms of entropy?
What is the significance of a flat histogram in terms of entropy?
Study Notes
Decision Trees
- Decision trees make predictions by recursively splitting on different attributes according to a tree structure.
- Internal nodes test attributes.
- Branching is determined by attribute value.
- Leaf nodes are outputs (predictions).
Expressiveness
- Decision trees can express any function of the input attributes in the discrete-input, discrete-output case.
- Decision trees can approximate any function arbitrarily closely in the continuous-input, continuous-output case.
Learning Decision Trees
- Learning the simplest (smallest) decision tree is an NP complete problem.
- Greedy heuristics are used to construct a useful decision tree.
- The process starts with an empty decision tree and splits on the "best" attribute
- Recursion is used to continue this process.
Choosing a Good Split
- The idea is to use counts at leaves to define probability distributions, then use information theory techniques to measure uncertainty.
- Entropy is a measure of expected "surprise".
Quantifying Uncertainty
- Entropy measures the information content of each observation in bits.
- Entropy is high when a variable has a uniform distribution, a flat histogram and low predictability.
- Entropy is low when a variable has a distribution with many peaks and valleys, a histogram with many lows and highs, and high predictability.
Conditional Entropy
- Conditional entropy measures the entropy of a variable given knowledge about another variable.
Information Gain
- Information gain measures the informativeness of a variable.
- The higher the information gain, the more informative the variable.
Constructing Decision Trees
- The decision tree construction algorithm is simple, greedy, and recursive.
- The algorithm builds the tree node-by-node.
- The algorithm picks an attribute to split at a non-terminal node.
- Examples are split into groups based on attribute values.
What Makes a Good Tree?
- A good tree is not too small or too big.
- A good tree has informative nodes near the root.
Summary
- Decision trees are good for problems with lots of attributes and a few important attributes.
- Decision trees are good with discrete attributes.
- Decision trees easily deal with missing values.
- Decision trees are robust to the scale of inputs.
- Decision trees are fast at test time.
- Decision trees are interpretable.
Problems with Decision Trees
- There is exponentially less data at lower levels.
- Large trees can overfit the data.
- The greedy algorithms do not necessarily yield the global optimum.
- Continuous attributes are handled by splitting based on a threshold, chosen to maximize information gain.
- Decision trees can also be used for regression on real-valued outputs.
- Splits are chosen to minimize squared error rather than maximize information gain.
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Description
This quiz explores the fundamentals of decision trees, focusing on their structure, expressiveness, and learning algorithms. Test your understanding of how decision trees make predictions and the techniques used for efficient learning and splitting decisions.
