A large tree will generally have trouble capturing the structure in the data, while a small tree will have high variance.

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BlackTom AI · Accepted Answer

The statement says: a large tree will generally have trouble capturing the structure in the data, while a small tree will have high variance.

First, consider the behavior of decision trees in terms of bias-variance tradeoff. A large (complex) tree tends to fit the training data very closely, which reduces bias but increases variance. This means it captures even noise as if it were signal, leading to overfitting rather than trouble capturing structure; it typically models complex structure well on training data, though it may fail to generalize.

Second, a small (simple) tree tends to underfit the data, resulting in high bias because it cannot capture the underlying relationships. However, its simplicity generally yields lower variance, since it does not react strongly to fluctuations in the training data.

Therefore, the claim that a large tree will generally have trouble capturing the structure in the data is inaccurate; the more common issue with large trees is overfitting and high variance, not underfitting. Conversely, the assertion that a small tree will have high variance is also incorrect because small trees typically exhibit lower variance due to their simplicity, even though they have higher bias.

In summary, both parts of the statement mischaracterize the usual bias-variance dynamics of decision trees, making the overall claim false.

QBUS6810 (ND) Week 9 Quiz

A large tree will generally have trouble capturing the structure in the data, while a small tree will have high variance.

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