SAP HANA Predictive Analysis Library (PAL)

PAL_KNN_RESULTS_TBL:
3.2.8 Logistic Regression (with Elastic Net Regularization)
Logistic regression models the relationship between a dichotomous dependent variable (also known as
explained variable) and one or more continuous or categorical independent variables (also known as
explanatory variables). It models the log odds of the dependent variable as a linear combination of the
independent variables.
This function can only handle binary-class classification problems. For multiple-class classification problems,
refer to Multi-Class Logistic Regression.
Considering a training data set with n samples and m explanatory variables, the logistic regression model is
made by:
h (θ0 ,θ)(x) = 1/(1 + exp(–(θ 0 +θ T x)))
Where θ 0 is the intercept, θ represents coefficients θ 1 , …, θ m and θ T x = θ 1 x 1 + … + θ m x m
Assuming that there are only two class labels, {0,1}, you can get the below formula:
P(y = 1 | x; (θ 0 ,θ)) = h (θ0 ,θ)(x)
P(y = 0 | x; (θ 0 ,θ)) = 1 – h (θ0 ,θ)(x)
And combine them into:
P(y | x;(θ 0 ,θ)) = h (θ0 ,θ)(x) y (1 – h (θ0 ,θ)(x)) 1-y
Here θ 0 , θ 1 , …, θ m can be obtained through the Maximum Likelihood Estimation (MLE) method.
The likelihood function is:
The log-likelihood function is:
SAP HANA Predictive Analysis Library (PAL)
PAL Functions P U B L I C 165