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Distributionally robust chance constrained svm model with $\ell_2$-Wasserstein distance

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  • In this paper, we propose a distributionally robust chance-constrained SVM model with $ \ell_2 $-Wasserstein ambiguity. We present equivalent formulations of distributionally robust chance constraints based on $ \ell_2 $-Wasserstein ambiguity. In terms of this method, the distributionally robust chance-constrained SVM model can be transformed into a solvable linear 0-1 mixed integer programming problem when the $ \ell_2 $-Wasserstein distance is discrete form. The DRCC-SVM model could be transformed into a tractable 0-1 mixed-integer SOCP programming problem for the continuous case. Finally, numerical experiments are given to illustrate the effectiveness and feasibility of our model.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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  • Table 1.  Mean performance comparison

    AUC (S.E.)
    Classical SVM 0.9039 0.0046
    $ \ell_2 $-Wasserstein SVM 0.9105 0.0020
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    Table 2.  UCI Database

    Date set classification numbers feature
    Sonar 2 208 60
    Pima 2 267 22
    Heart 2 270 12
    BUPA Liver 2 345 6
    Ionosphere 2 351 34
    Australian 2 690 14
    Breast Cancer 2 699 13
    Bank 2 4521 16
     | Show Table
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    Table 3.   

    Classic SVM $ \ell_2 $-Wasserstein SVM Soft margin SVM
    Data set n Accuracy (S.E.) Accuracy (S.E.) Accuracy (S.E.)
    Sonar 50 0.814 0.0064 0.801 0.0050 0.799 0.0049
    Sonar 70 0.856 0.0045 0.851 0.0041 0.850 0.0040
    Sonar 100 0.872 0.0038 0.862 0.0033 0.860 0.0032
    Pima 50 0.732 0.0055 0.723 0.0048 0.722 0.0047
    Pima 70 0.745 0.0051 0.741 0.0043 0.741 0.0043
    Pima 100 0.751 0.0046 0.743 0.0034 0.743 0.0034
    Heart 50 0.791 0.0027 0.788 0.0025 0.787 0.0024
    Heart 70 0.821 0.0024 0.815 0.0020 0.814 0.0018
    Heart 100 0.833 0.0016 0.831 0.0011 0.827 0.0009
    BUPA Liver 50 0.773 0.0035 0.768 0.0033 0.765 0.0028
    BUPA Liver 70 0.789 0.0032 0.788 0.0031 0.788 0.0031
    BUPA Liver 100 0.801 0.0025 0.801 0.0024 0.799 0.0023
    Ionosphere 50 0.812 0.0054 0.810 0.0051 0.808 0.0050
    Ionosphere 70 0.834 0.0037 0.842 0.0035 0.832 0.0035
    Ionosphere 100 0.852 0.0033 0.848 0.0022 0.845 0.0020
    Australian 50 0.812 0.0022 0.810 0.0020 0.807 0.0015
    Australian 70 0.823 0.0019 0.832 0.0016 0.822 0.0015
    Australian 100 0.833 0.0015 0.830 0.0013 0.830 0.0013
    Breast Cancer 50 0.952 0.0023 0.951 0.0022 0.951 0.0022
    Breast Cancer 70 0.955 0.0020 0.955 0.0018 0.952 0.0017
    Breast Cancer 100 0.964 0.0016 0.969 0.0011 0.952 0.0009
     | Show Table
    DownLoad: CSV

    Table 4.   

    Data set n Classic SVM L2-Wasserstein SVM Soft-margin SVM
    Accuracy Accuracy (10% noise) Accuracy Accuracy (10% noise) Accuracy Accuracy (10% noise)
    Bank 100 0.8421 0.7870 0.8841 0.8842 0.8823 0.8743
    200 0.8377 0.7798 0.8844 0.8846 0.8823 0.8773
    300 0.8379 0.7785 0.8846 0.8845 0.8824 0.8768
    400 0.8377 0.7757 0.8850 0.8847 0.8821 0.8763
    500 0.8407 0.7735 0.8853 0.8854 0.8833 0.8765
    600 0.8389 0.7759 0.8855 0.8852 0.8831 0.8775
     | Show Table
    DownLoad: CSV
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