Table 3.
Comparison of average test errors (and corresponding standard errors in parentheses) for Example 3 with respect to circular and spherical implicit functional relationship and three distance measures. The results for naive method, SSANOVA, Random Forest, resolution-wise regression with fixed smoothness, and resolution-wise regression with CV are listed in the columns from left to right respectively.
| Example | Measure | Naive | SSANOVA | Random Forest | Fixed smoothness | CV |
|---|---|---|---|---|---|---|
| Circle | KS | 0.175 | 0.201 | 0.398 | 0.172 | 0.156 |
| (0.010) | (0.014) | (0.030) | (0.010) | (0.008) | ||
| KL | 0.378 | 0.436 | 4.180 | 0.264 | 0.404 | |
| (0.019) | (0.032) | (0.322) | (0.008) | (0.027) | ||
| L 1 | 0.677 | 0.761 | 1.384 | 0.515 | 0.535 | |
| (0.039) | (0.034) | (0.108) | (0.022) | (0.025) | ||
| Sphere | KS | 0.170 | 0.184 | 0.413 | 0.183 | 0.161 |
| (0.012) | (0.010) | (0.037) | (0.009) | (0.006) | ||
| KL | 0.369 | 0.411 | 4.553 | 0.310 | 0.339 | |
| (0.015) | (0.021) | (0.355) | (0.009) | (0.016) | ||
| L 1 | 0.664 | 0.735 | 1.439 | 0.580 | 0.570 | |
| (0.026) | (0.038) | (0.080) | (0.024) | (0.025) |