A binary node has class proportions 0.5 and 0.5. Find Gini impurity.
Answer and explanation
0.5
1−0.25−0.25=0.5.
Subjects
Ml methods
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Sample exercises
A node contains only one class. Find its Gini impurity.
Answer and explanation
0
1−1²=0.
What is a leaf in a decision tree?
- A guaranteed causal rule
- A terminal prediction region
- A random test-set label
- Always the first input column
Answer and explanation
A terminal prediction region
Leaves end a branch and supply predictions.
Which can limit tree complexity?
- Deleting all validation data
- Increasing filename length
- Allowing every record its own leaf without validation
- A minimum number of examples per leaf
Answer and explanation
A minimum number of examples per leaf
A minimum leaf size discourages unsupported fine partitions.
Child impurities are 0.2 and 0.4 with equal numbers of examples. Find weighted average impurity.
Answer and explanation
0.3
Equal weights give (0.2+0.4)/2.
Why should child impurity be weighted by child size?
Answer and explanation
A split can make a tiny pure child while leaving most data poorly separated. Weighting reflects the fraction of examples affected.
Credit representativeness of the overall split.
Study notes
Decision trees, splits and ensembles
A decision tree partitions feature space using a sequence of tests. Leaf predictions summarize the training examples reaching them.
UniversityDecision trees, splits and ensembles · revision notes
A decision tree partitions feature space using a sequence of tests. Leaf predictions summarize the training examples reaching them.
UniversityClustering, distances and interpretation
Clustering groups examples according to a representation and similarity rule. The groups are not automatically true natural categories.
UniversityClustering, distances and interpretation · revision notes
Clustering groups examples according to a representation and similarity rule. The groups are not automatically true natural categories.
UniversityPCA, variance and dimensionality reduction
Principal component analysis finds orthogonal directions of high variance in centred data under its standard formulation.
UniversityPCA, variance and dimensionality reduction · revision notes
Principal component analysis finds orthogonal directions of high variance in centred data under its standard formulation.
UniversityExplained variance of the first principal component
Use covariance eigenvalues sorted in descending order and a positive total variance.
UniversityExplained variance of the first principal component · formula reference
Use covariance eigenvalues sorted in descending order and a positive total variance.
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