rdkit.ML.SLT.Risk

Package rdkit :: Package ML :: Package SLT :: Module Risk |
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# Module Risk

source code

    code for calculating empirical risk

Functions | [hide private]
log2(x) | source code
BurgesRiskBound(VCDim, nData, nWrong, conf) Calculates Burges's formulation of the risk bound | source code
CristianiRiskBound(VCDim, nData, nWrong, conf) the formulation here is from pg 58, Theorem 4.6 of the book "An Introduction to Support Vector Machines" by Cristiani and Shawe-Taylor Cambridge University Press, 2000 | source code
CherkasskyRiskBound(VCDim, nData, nWrong, conf, a1=1.0, a2=2.0) The formulation here is from Eqns 4.22 and 4.23 on pg 108 of Cherkassky and Mulier's book "Learning From Data" Wiley, 1998. | source code

Imports: math

Function Details | [hide private]

### BurgesRiskBound(VCDim, nData, nWrong, conf) | source code
    Calculates Burges's formulation of the risk bound

    The formulation is from Eqn. 3 of Burges's review
    article "A Tutorial on Support Vector Machines for Pattern Recognition"
     In _Data Mining and Knowledge Discovery_ Kluwer Academic Publishers
     (1998) Vol. 2

    **Arguments**

      - VCDim: the VC dimension of the system

      - nData: the number of data points used

      - nWrong: the number of data points misclassified

      - conf: the confidence to be used for this risk bound

    **Returns**

      - a float

    **Notes**

     - This has been validated against the Burges paper

     - I believe that this is only technically valid for binary classification

### CristianiRiskBound(VCDim, nData, nWrong, conf) | source code
    the formulation here is from pg 58, Theorem 4.6 of the book
    "An Introduction to Support Vector Machines" by Cristiani and Shawe-Taylor
    Cambridge University Press, 2000

    **Arguments**

      - VCDim: the VC dimension of the system

      - nData: the number of data points used

      - nWrong: the number of data points misclassified

      - conf: the confidence to be used for this risk bound

    **Returns**

      - a float

    **Notes**

      - this generates odd (mismatching) values

### CherkasskyRiskBound(VCDim, nData, nWrong, conf, a1=1.0, a2=2.0) | source code
    The formulation here is from Eqns 4.22 and 4.23 on pg 108 of
    Cherkassky and Mulier's book "Learning From Data" Wiley, 1998.

    **Arguments**

      - VCDim: the VC dimension of the system

      - nData: the number of data points used

      - nWrong: the number of data points misclassified

      - conf: the confidence to be used for this risk bound

      - a1, a2: constants in the risk equation. Restrictions on these values:

          - 0 <= a1 <= 4

          - 0 <= a2 <= 2

    **Returns**

      - a float

    **Notes**

     - This appears to behave reasonably

     - the equality a1=1.0 is by analogy to Burges's paper.