For logistic regression, the Cost function is defined as: \begin{equation} Cost(h_{\theta}(x)-y) = -ylog(h_{\theta}(x))-(1-y)log(1-h_{\theta}(x)) \end{equation}

I now have a nonlinear function \begin{equation} h_{\theta}^{(i)}(x)=xe^{-j\theta_i|x|^2} \end{equation} where $i$ denotes the $i$th training sample. How should I define cost function for this particular nonlinear function?


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