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results with minimal test RMSE for each kernel on dataset Asyclic
-- All the kernels are tested on dataset Asyclic, which consists of 185 molecules (graphs).
-- The criteria used for prediction are SVM for classification and kernel Ridge regression for regression.
-- For predition we randomly divide the data in train and test subset, where 90% of entire dataset is for training and rest for testing. 10 splits are performed. For each split, we first train on the train data, then evaluate the performance on the test set. We choose the optimal parameters for the test set and finally provide the corresponding performance. The final results correspond to the average of the performances on the test sets.
summary
| Kernels | RMSE(℃) | std(℃) | parameter | k_time |
|---|---|---|---|---|
| shortest path | 36.40 | 5.35 | - | - |
| marginalized | 17.90 | 6.59 | p_quit = 0.1 | - |
| path | 14.27 | 6.37 | - | - |
| WL subtree | 9.00 | 6.37 | height = 1 | 0.85" |
In each line, paremeter is the one with which the kenrel achieves the best results.
In each line, k_time is the time spent on building the kernel matrix.
detailed results of WL subtree kernel.
The table below shows the results of the WL subtree under different subtree heights.
height RMSE_test std_test RMSE_train std_train k_time
-------- ----------- ---------- ------------ ----------- --------
0 36.2108 7.33179 141.419 1.08284 0.392911
1 9.00098 6.37145 140.065 0.877976 0.812077
2 19.8113 4.04911 140.075 0.928821 1.36955
3 25.0455 4.94276 140.198 0.873857 1.78629
4 28.2255 6.5212 140.272 0.838915 2.30847
5 30.6354 6.73647 140.247 0.86363 2.8258
6 32.1027 6.85601 140.239 0.872475 3.1542
7 32.9709 6.89606 140.094 0.917704 3.46081
8 33.5112 6.90753 140.076 0.931866 4.08857
9 33.8502 6.91427 139.913 0.928974 4.25243
10 34.0963 6.93115 139.894 0.942612 5.02607
The unit of the RMSEs and stds is ℃, The unit of the k_time is s.
k_time is the time spent on building the kernel matrix.