5
$\begingroup$

I would like to know, how probabilities are calculated in support vector machine.

I have used Iris data set and here is my decision values for three "SupportVectorMachine" (please find the PMML below to know the support vector and coefficient values) presented.

setosa/versicolor setosa/virginica versicolor/virginica
         1.196152         1.091757            0.6708810

Based on voting mechanism explained in "dmg.org" site, I obtained the result as "setosa"

I am so confused how the probability values are calculated ? and these are the probability parameters obtained from R.

model$probA
[1] -3.589058 -3.793546 -3.518305

model$probB
[1] -0.16396052 -0.04387233  0.13178304

The probabilities from the above decision function and probability parameters are as follows.

   setosa versicolor   virginica
0.9795937 0.01161942 0.008786859

More info:

Kernel type : RBF

Input record:

Sepal_Length Sepal_Width Petal_Length Petal_Width
         5.1         3.5          1.4         0.2 

Could you please explain, how the probabilities are being calculated?

PMML

<SupportVectorMachineModel
    modelName="C-SVC"
    functionName="classification"
    svmRepresentation="SupportVectors">
    <MiningSchema>
        <MiningField
            name="Sepal_Length"
            usageType="active"/>
        <MiningField
            name="Sepal_Width"
            usageType="active"/>
        <MiningField
            name="Petal_Length"
            usageType="active"/>
        <MiningField
            name="Petal_Width"
            usageType="active"/>
        <MiningField
            name="Species"
            usageType="predicted"/>
    </MiningSchema>
    <RadialBasisKernelType
        gamma="0.1"/>
    <VectorDictionary
        numberOfVectors="55">
        <VectorFields
            numberOfFields="4">
            <FieldRef
                field="Sepal_Length_scaled"/>
            <FieldRef
                field="Sepal_Width_scaled"/>
            <FieldRef
                field="Petal_Length_scaled"/>
            <FieldRef
                field="Petal_Width_scaled"/>
        </VectorFields>
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        <Extension
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                NonResponse="versicolor"/>
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                vectorId="vec3"/>
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                vectorId="vec4"/>
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                value="10"/>
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                value="10"/>
            <Coefficient
                value="9.19776233533869"/>
            <Coefficient
                value="1.79961796126222"/>
            <Coefficient
                value="-10"/>
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                value="-0.997380296600909"/>
            <Coefficient
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            <Coefficient
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            <Coefficient
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        </Coefficients>
    </SupportVectorMachine>
    <SupportVectorMachine>
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                NonResponse="virginica"/>
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                paramB="-0.161186331924648"/>
        </Extension>
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            numberOfAttributes="4"
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                vectorId="vec4"/>
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    </SupportVectorMachine>
    <SupportVectorMachine>
        <Extension
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            <ResponseCategory
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                NonResponse="virginica"/>
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                paramB="0.211406625456119"/>
        </Extension>
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            numberOfAttributes="4"
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            <Coefficient
                value="-10"/>
            <Coefficient
                value="-10"/>
            <Coefficient
                value="-10"/>
            <Coefficient
                value="-10"/>
            <Coefficient
                value="-10"/>
            <Coefficient
                value="-10"/>
        </Coefficients>
    </SupportVectorMachine>
</SupportVectorMachineModel>
$\endgroup$
0
$\begingroup$

Your SVM implementation is very likely based on the LibSVM library. Please refer to LibSVM's documentation (eg. this FAQ item) for an explanation how probabilities are calculated.

In brief, probability calculation is based on a separate procedure, which has nothing in common with the decision function. It is even possible that the decision function and calculated probabilities predict different class as winner.

The PMML specification does not support LibSVM's probability calculation procedure. Hence, you can't use the probability output feature with SVM models.

$\endgroup$
  • 1
    $\begingroup$ So, what's the procedure followed to calculate probability here ? $\endgroup$ – Ramkumar Nov 26 '15 at 9:34
  • 1
    $\begingroup$ Exact formula, will be more helpful. $\endgroup$ – Ramkumar Nov 26 '15 at 9:37
  • $\begingroup$ I have also tried following Platt scaling method to get the probability estimates: (1 / (1 + exp(a x + b))) But this doesn't works too. $\endgroup$ – Ramkumar Nov 26 '15 at 9:57
  • $\begingroup$ This is not an answer to the question 'How are probabilities calculated for SVM models?'. The link posted doesn't even contain the answer. $\endgroup$ – Michael Andrew Bentley Oct 27 '16 at 12:29

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