What are the core assumptions behind Linear Discriminant Analysis (LDA)?
mediumAnswer
- LDA assumes each class-conditional distribution is Gaussian with class-specific mean but a *shared* covariance matrix Σ.
- Under this assumption, the log-posterior is linear in x — the decision boundary between any two classes is a hyperplane.
- It also assumes features are continuous.
- When assumptions hold, LDA is close to Bayes-optimal and needs little data because it estimates fewer parameters than QDA (one Σ instead of one per class).
Check yourself — multiple choice
- LDA assumes each class has a different covariance matrix
- LDA assumes Gaussian classes with a shared covariance matrix
- LDA assumes features are categorical
- LDA is a tree-based method
LDA: Gaussian classes + shared covariance ⇒ linear decision boundary.
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