Instance Based Learning

Locally Weighted Regression

  1. We can minimize the squared error over $k$ nearest neighbors \[E_{1}(x_q) \equiv \frac{1}{2} \sum_{x \in k nearest nbrs of x_q} (f(x) - \hat{f}(x))^2 \]
  2. We can minimize the instance-weighted squared error over all neighbors \[E_{2}(x_q) \equiv \frac{1}{2} \sum_{x \in D} (f(x) - \hat{f}(x))^2 K(d(x_{q}, x)) \]
  3. Or, we can combine these two \[E_{2}(x_q) \equiv \frac{1}{2} \sum_{x \in k nearest nbrs of x_q} (f(x) - \hat{f}(x))^2 K(d(x_{q}, x)) \]

José M. Vidal .

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