Summary and Revision Notes
Key ideas
- A linear score is a weighted sum plus a bias.
- Weights control feature contribution.
- Bias shifts the score.
- Raw scores are not automatically probabilities.
- A score vector contains one score per class.
- A binary linear decision boundary is where
x . w + b = 0. - In two dimensions, that boundary is a line.
- Linear models are useful but limited by linear boundaries.
Notation
| Notation | Meaning |
|---|---|
x | input feature vector |
w | weight vector for one score |
b | bias |
x . w + b | one linear score |
xW + b | vector of scores |
Common mistakes
- Treating raw scores as probabilities.
- Forgetting the bias term.
- Confusing number of input features with number of classes.
- Assuming a linear model can represent every pattern if trained long enough.
Before moving on
You should be able to compute x . w + b, identify weights and bias, predict score shapes, and explain why nonlinear activations are needed after linear models.