Results with minimal test RMSE for each kernel on dataset Asyclic

All 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	35.19	4.50	-	14.58"
Marginalized	18.02	6.29	p_quit = 0.1	4'19"
Path	14.00	6.94	-	37.58"
WL subtree	7.55	2.33	height = 1	0.84"
Treelet	8.31	3.38	-	49.58"

RMSE stands for arithmetic mean of the root mean squared errors on all splits.
STD stands for standard deviation of the root mean squared errors on all splits.
Paremeter is the one with which the kenrel achieves the best results.
k_time is the time spent on building the kernel matrix.
The targets of training data are normalized before calculating path kernel and treelet kernel.

Detailed results of each kernel

In each table below:

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.

shortest path kernel

  RMSE_test    std_test    RMSE_train    std_train    k_time
-----------  ----------  ------------  -----------  --------
     35.192     4.49577       28.3604      1.35718   14.5768

Marginalized kernel

The table below shows the results of the marginalized under different termimation probability.

  p_quit    RMSE_test    std_test    RMSE_train    std_train    k_time
--------  -----------  ----------  ------------  -----------  --------
     0.1      18.0243     6.29247       12.1863      7.03899   258.77
     0.2      18.3376     5.85454       13.9554      7.54407   256.327
     0.3      18.496      5.73492       13.9391      7.95812   255.614
     0.4      19.4491     5.3713        16.2593      6.69358   254.897
     0.5      19.7857     5.55054       17.0181      6.84437   256.757
     0.6      20.1922     5.59122       17.6618      6.56718   256.557
     0.7      21.6614     6.02685       20.5882      5.74601   254.953
     0.8      22.996      6.08347       23.5943      3.80637   252.804
     0.9      24.4241     4.95119       25.8082      3.31207   256.738

Path kernel

The targets of training data are normalized before calculating the kernel.

  RMSE_test    std_test    RMSE_train    std_train    k_time
-----------  ----------  ------------  -----------  --------
    14.0015     6.93602       3.76191     0.702594   37.5759

Weisfeiler-Lehman 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     15.6859      4.1392      17.6816       0.713183  0.360443
       1      7.55046     2.33179      6.27001      0.654734  0.837389
       2      9.72847     2.05767      4.45068      0.882129  1.25317
       3     11.2961      2.79994      2.27059      0.481516  1.79971
       4     12.8083      3.44694      1.07403      0.637823  2.35346
       5     14.0179      3.67504      0.700602     0.57264   2.78285
       6     14.9184      3.80535      0.691515     0.56462   3.20764
       7     15.6295      3.86539      0.691516     0.56462   3.71648
       8     16.2144      3.92876      0.691515     0.56462   3.99213
       9     16.7257      3.9931       0.691515     0.56462   4.26315
      10     17.1864      4.05672      0.691516     0.564621  5.00918

Treelet kernel