MLS-C01 Curse of Dimensionality Practice Question
A team is building a regression model to predict house prices. The dataset includes a column 'zip_code' with 100 unique values. The data scientist one-hot encodes this column, resulting in 100 new binary columns. The model shows poor performance on a validation set. What is the most likely cause?
⚠ Common exam trap
Candidates often underestimate the impact of one-hot encoding high-cardinality categorical variables. While the features are binary and not collinear, the sheer number of new features can cause the curse of dimensionality, leading to overfitting and poor generalization.
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
The model suffers from the curse of dimensionality due to the large number of features.
One-hot encoding 'zip_code' with 100 unique values creates 100 binary features. When combined with other features, the total number of features can be large relative to the number of training samples, leading to the curse of dimensionality. This causes the model to overfit the training data and generalize poorly to the validation set. While multicollinearity among one-hot encoded columns is often low due to their binary nature, the primary issue here is the high dimensionality relative to sample size. Option D correctly identifies this as the most likely cause.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
One-hot encoding introduced multicollinearity among the binary columns.
Why it's wrong here
While one-hot encoded columns are linearly dependent, this is typically handled by dropping one level; multicollinearity is not the main cause of poor performance.
- ✗
One-hot encoding reduced the number of features, causing underfitting.
Why it's wrong here
One-hot encoding increases the number of features, not reduces.
- ✗
The one-hot encoding introduced high variance, but the validation set has low variance.
Why it's wrong here
The issue is not about variance in the target but the high-dimensional feature space.
- ✓
The model suffers from the curse of dimensionality due to the large number of features.
Why this is correct
With 100 additional sparse features, the model may overfit and not generalize well.
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