Definition
A model is considered linear when it is linear in its parameters, regardless of whether it’s linear in the inputs. Specifically, a model is linear if:
- It can be expressed as a linear combination of the parameters
- The output is a weighted sum of basis functions y(x) = Σ wⱼφⱼ(x)
Examples
- Simple linear regression: y(x) = w₀ + w₁x
- Linear in both parameters and input
- Polynomial regression: y(x) = w₀ + w₁x + w₂x² + … + wₙxⁿ
- Linear in parameters (w₀, w₁, w₂, …) but non-linear in input x