Table 2 Functions used to generate artificial datasets for regression
Function | Exact derivatives | |
|---|---|---|
\({R}_{1}:\,y={x}_{1}^{4}+2{x}_{2}^{3}+3\sqrt{{x}_{3}}\) | \(\frac{\partial y}{\partial {x}_{1}}=4{x}_{1}^{3}; \frac{\partial y}{\partial {x}_{2}}=6{x}_{2}^{2}; \frac{\partial y}{\partial {x}_{3}}=\frac{3}{2\sqrt{{x}_{3}}}\) | |
\({R}_{2}:\,y=\mathrm{sin}(\pi {x}_{1})+{e}^{{x}_{2}}+{x}_{3}^{2}\): | \(\frac{\partial y}{\partial {x}_{1}}=\pi \mathrm{cos}\left(\pi {x}_{1}\right); \frac{\partial y}{\partial {x}_{2}}={e}^{{x}_{2}}; \frac{\partial y}{\partial {x}_{3}}=2{x}_{3}\) | |
\({R}_{3}:\,y=\mathrm{sin}(\pi {x}_{1})+{e}^{{x}_{2}}+{x}_{3}^{2}+0.00001{x}_{4}\) | \(\frac{\partial y}{\partial {x}_{4}}=1e-5\) | |