Machine Learning MCQ - Comparison of bias of shallow and deep decision trees

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Machine Learning MCQ - Bias of shallow decision tree is greater than the bias of deeper tree

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1. Consider T1, a decision stump (tree of depth 2) and T2, a decision tree that is grown till a maximum depth of 4. Which of the following is/are correct?

a) Bias(T1) < Bias(T2)

b) Bias(T1) > Bias(T2)

c) Variance(T1) > Variance(T2)

d) None of the above

Answer: (b) Bias(T1) > Bias(T2) A shallow (limited depth) decision tree like this (depth 2) has high bias (and low variance) because it makes very strong assumptions about the underlying data. It assumes that the data can be divided into very few classes, which usually too simplistic for many real-world problems. A tree with high bias and low variance will result in poor accuracy on the training and test data.   In simpler terms, if the tree is shallow then we are not checking a lot of conditions/constrains i.e., the logic is simple or less complex.   High bias means the model consistently makes inaccurate predictions by missing important patterns and relationships in the data, and this behavior leads to underfitting the data.   A decision tree that grows deeper will be a complex tree and will be overfitting with low bias (and high variance).   Model complexity Tree T1 which is a decision tree of depth 2 is relatively simple. It can only create at most 7 leaf nodes (depending on the data and splits), meaning it can model fewer decision boundaries. On the other hand, tree T2, a decision tree of depth 4 is more complex than T1. It can create up to 15 leaf nodes and can make more detailed splits than T1. Answer C is not correct because variance of decision trees with smaller depths will be smaller than the variance of decision trees with higher depths. Refer bias variance tradeoff (link1, link2) for more information.

 

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How does the depth of decision tree affect the accuracy of the model?

Decision tree with smaller depth will have high bias than the tree with low bias

Compare decision trees with high bias and low bias

bias (shallow tree) is greater than the bias (deeper tree). why?

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