# Use RBF kernel with logistic regression?

There are some resources online (e.g. this one) on logistic regression with polynomial kernels, such as

$$h_\theta(x)=logistic(\theta_0 + \theta_1x1+ \theta_3x_1^2 + \theta_4x_2^2)$$

I'm wondering if it's possible to use RBF kernel $K_r(x,x')=\exp(-\frac{\|x-x'\|^2}{r})$ here. If so, what would $h_\theta(x)$ looks like?

• It's not kernel. You just add nonlinear transformations of input variables to your existing input variables. – seanv507 Dec 10 '15 at 7:59

By the representer theorem, $f_\theta(x)$ has the form:
$$f_\theta(x)=b + \sum_i ^ N a_i K(x, x_i)$$
So the probability is $p(x)=\frac{e^{f(x)}}{1+e^{f(x)}}$.