/https://piazza.com/class_profile/get_resource/ln18bjs43q41tr/ln18n411vo070m

Recall Kernel SVM

• for each pair of points, compute similarity (in a matrix)

• each data point votes w/ own label yi, and weight a_i

  

Mercer’s Condition

an m x m similarity matrix for k(xi, xj) must be PSD

• if satisfied: k is a kernel function
• another way to think about: there exists some way to expand the data s.t. the similarity function is just the dot product between the expanded data points

RBF Kernel

$$ \phi : R^d -> R^{ \infin} \\ s.t. \\ k(x, z) = \phi(x) * \phi(z) $$

• only matters that dot product exists at all

• can fit any boundary

  • why; its like a polynomial of arbitrarily high degree

  

• little data: just predict most likely label

• s → only gets the closest point to x, all other go to 0

• more data = decrease s