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.