Concept - Decision Boundary

Logistic regression (s.270): decide by comparing probabilities: $p(y=1\mid \mathbf{x})>p(y=-1\mid \mathbf{x})\iff \frac{p(y=1\mid \mathbf{x})}{p(y=-1\mid \mathbf{x})}>1$. Taking the log gives $\ln \frac{p(y=1\mid \mathbf{x})}{p(y=-1\mid \mathbf{x})}={\mathbf{w}}^{\top }\mathbf{x}+b$.

• Boundary is linear: ${\mathbf{w}}^{\top }\mathbf{x}+b=0$.
• $y=+1$ if ${\mathbf{w}}^{\top }\mathbf{x}+b>0$, else $-1$. The threshold is tunable.
• Figure: 2-D scatter (red crosses vs blue circles) with straight green and purple lines.

Related

Concept - Logistic Regression

Sources: 03 Text Classification - Chunk 09 (s.241-270)