The unified model is a mathematical framework showing that many regression algorithms can be expressed in a single, general form.
Mathematical Formulation
Components
- : Basis functions (typically Gaussian/RBF)
- : Weight vectors for local linear models
- : Bias/offset terms
- : Number of local models
- : Parameters of basis functions (e.g., mean, variance)
Deconstructing the Model
For any given , the model calculates which expert is most relevant and gives its output more weight in the final sum.
Prediction from Expert This is the simple linear model ( ). Each of the “experts” is a linear model with its own weight vector and bias .
Weight for Expert This is the gating function . It calculates a value based on the input . Typically, these gating functions are designed to be high for some regions of the input space and low for others.