I try to predict temperatures values as function of time and different parameters. The temperature curve look like a ramp with some gauss peaks on regular intervals.So, I try to build a regression model for the following equation:$$\hat{T}_{a, \mu, \sigma, s, c, m, p}\left(t\right) = a \frac{1}{\sigma\sqrt{2 \pi}} e^{-\frac{\left(\sin\left(\frac{t-s}{c}\right) - \mu\right)^2}{2 \sigma^2}} + m t + p$$My goal is to establish the values of $a$, $\mu$, $\sigma$, $s$, $c$, $m$, $p$.My first intention was to use the gradient descent, but I'm pretty sure that the derivative of the RSS based cost function won't be convex, so I might get stuck at local mimina.I'm also wondering if there is no better alternative to solve that problem. It concerns especially methods not involving minimizing derivatives. I think (but not sure) that neuronal networks can help me with that.So, in short, how would you solve the following?\begin{equation} \left[\begin{array}{l}   a \\   \mu \\   \sigma \\   s \\   c \\   m \\   p \end{array}\right] \leftarrow \textrm{argmin}_{a, \mu, \sigma, s, c, m, p}\frac{1}{2N} \sum_{i=1}^N{\left(a \frac{1}{\sigma\sqrt{2 \pi}} e^{-\frac{\left(\sin\left(\frac{t_i-s}{c}\right) - \mu\right)^2}{2 \sigma^2}} + m t + p - T_i\right)^2}\end{equation}Thanks a lot for your help.P.S.: I'm using python 3 with scipy stack
Regression problem - too complex for gradient descent
predictive modeling;regression;optimization;gradient descent