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Section 6.2: Generative models

(6.28)

We can define a kernel with the generative model p(x)

latex($k(\mathbf{x},\mathbf{x^p}) = p(\mathbf{x}) p(\mathbf{x^p}) $) (6.23)

is this valid?

We can interpret as an inner product in the p(x) map --> the inputs are similar if they both have high probability.

use (6.13) and (6.17) to extend it to sums of different distributions and weights,

ie. use latex($ ck_{1}(\mathbf{x},\mathbf{x^p}) $) and latex($ k_{1}(\mathbf{x},\mathbf{x^p}) + k_{2}(\mathbf{x},\mathbf{x^p} $)

• to form

i) p(\mathbf{x^p} (6.29)

we can consider (6.30) with a continuous latent variable.

Fisher kernel

Fisher score (6.32)

\mathbf{\theta}) $)

leads to the fisher kernel (6.33)

latex($k(\mathbf{x},\mathbf{x^p}) = g(\mathbf{\theta},\mathbf{x})^T \mathbf{F}^{-1} g(\mathbf{\theta},\mathbf{x^p})$)

F is the information matrix, can be approximated by the sample average, or ignore it to get (6.36)