rdkit.ML.SLT.Risk module — The RDKit 2016.09.1 documentation

# rdkit.ML.SLT.Risk module

code for calculating empirical risk

`rdkit.ML.SLT.Risk.` `BurgesRiskBound`(VCDim, nData, nWrong, conf)

  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

`rdkit.ML.SLT.Risk.` `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.

  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.

`rdkit.ML.SLT.Risk.` `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

  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

`rdkit.ML.SLT.Risk.` `log2`(x)