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?

  • 4
    $\begingroup$ It's not kernel. You just add nonlinear transformations of input variables to your existing input variables. $\endgroup$ – seanv507 Dec 10 '15 at 7:59

For others who have similar questions, I found this paper by Zhu and Hastie very helpful.

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 $p(x)=\frac{e^{f(x)}}{1+e^{f(x)}}$.

  • $\begingroup$ @user777 Thanks. I think I'm asking for RBF kernel. $\endgroup$ – qweruiop Jan 15 '16 at 21:27
  • $\begingroup$ Sorry, I see now that I misread your question. Withdrawn. $\endgroup$ – Sycorax says Reinstate Monica Jan 15 '16 at 21:29
  • $\begingroup$ @user777 Of course it's not. It's nothing. It's just a quote from the resource I linked. $\endgroup$ – qweruiop Jan 15 '16 at 21:31

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