Case study background and problem formulations
Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.
Maximize logexp_sum (log-likelihood function applied to original untransformed features)
Calculate:
pr_pen(difference of losses) (Probability of Exceedance applied to difference of losses based on original untransformed features )
——————————————————————–————————————————
logexp_sum = Logarithms Exponents Sum = log-likelihood function
pr_pen = Probability of Exceedance
——————————————————————–————————————————
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 2012 | 4 | 380465 | -0.238801512644 | 2.82 | |||
---|---|---|---|---|---|---|---|
Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50 GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset2 2013 | Problem statement | Data | Solution | 4 | 380465 | -0.244676286732 | 4.56 |
Dataset3 2014 | Problem statement | Data | Solution | 4 | 380465 | -0.216362946123 | 11.89 |
PROBLEM 1: problem_Logexp_Sum (for spline transformation of features)
Maximize logexp_sum(spline_sum) (log-likelihood function applied to spline function)
Calculate:
logistic(spline_sum) (calculation of Logistic to get transformed feature)
——————————————————————–————————————————
logexp_sum = Logarithms Exponents Sum = log-likelihood function
logistic = Logistic calculate values of logistic function of spline approximation for every scenario
spline_sum = Spline Sum calculates spline value depending upon regression variables for every scenario
——————————————————————–————————————————
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 DTI, 2012 | 20 | 380465 | -0.441511982280 | 1.45 | |||
---|---|---|---|---|---|---|---|
Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset2 DTI, 2013 | Problem statement | Data | Solution | 20 | 380465 | -0.363102932426 | 48.09 |
Dataset3 DTI, 2014 | Problem statement | Data | Solution | 20 | 380465 | -0.321050341841 | 81.66 |
Dataset4 EmpLen, 2012 | Problem statement | Data | Solution | 20 | 380465 | -0.215776179308 | 20.04 |
Dataset5 EmpLen, 2013 | Problem statement | Data | Solution | 20 | 380465 | -0.225138264176 | 52.72 |
Dataset6 EmpLen, 2014 | Problem statement | Data | Solution | 20 | 380465 | -0.130285134598 | 120.86 |
Dataset7 FICO, 2012 | Problem statement | Data | Solution | 20 | 380465 | -0.283383677945 | 49.90 |
Dataset8 FICO, 2013 | Problem statement | Data | Solution | 20 | 380465 | -0.299431106338 | 121.41 |
Dataset8 FICO, 2014 | Problem statement | Data | Solution | 20 | 380465 | -0.251899113731 | 293.00 |
Maximize logexp_sum (log-likelihood function applied to transformed features)
Calculate:
pr_pen(difference of losses) (Probability of Exceedance applied to difference of losses based on transformed features )
——————————————————————–————————————————
logexp_sum = Logarithms Exponents Sum = log-likelihood function
pr_pen = Probability of Exceedance
——————————————————————–————————————————
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 2012 | 4 | 380465 | -0.17741580617 | 1.61 | |||
---|---|---|---|---|---|---|---|
Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset2 2013 | Problem statement | Data | Solution | 4 | 380465 | -0.17389892051 | 3.59 |
Dataset3 2014 | Problem statement | Data | Solution | 4 | 380465 | -0.111404489632 | 8.97 |
Minimize bPOE (Buffered Probability of Exceedance applied to transformed features)
subject to
linear = const (linear constraint)
Calculate:
pr_pen(difference of losses) (Probability of Exceedance applied to difference of losses based on transformed features )
——————————————————————–————————————————
bPOE = Buffered Probability of Exceedance
pr_pen = Probability of Exceedance
——————————————————————–————————————————
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 2012 | 4 | 380465 | 0.106004778111 | 7.47 | |||
---|---|---|---|---|---|---|---|
Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset2 2013 | Problem statement | Data | Solution | 4 | 380465 | 0.09195791885 | 14.38 |
Dataset3 2014 | Problem statement | Data | Solution | 4 | 380465 | 0.044281544942 | 105.65 |
Minimize pr_pen(difference of losses) (Probability of Exceedance applied to difference of losses based on transformed features)
subject to
linear = const (linear constraint)
——————————————————————–————————————————
pr_pen = Probability of Exceedance
——————————————————————–————————————————
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 2012 | 4 | 380465 | 0.045272219018 | 113.33 | |||
---|---|---|---|---|---|---|---|
Environments | |||||||
Run-File | Problem Statement | Data | Solution | ||||
Matlab Toolbox | Data | ||||||
Matlab Subroutines | Matlab Code | Data | |||||
R | R Code | Data |
Instructions for importing problems from Run-File to PSG MATLAB.
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset2 2013 | Problem statement | Data | Solution | 4 | 380465 | 0.039795749026 | 450.90 |
Dataset3 2014 | Problem statement | Data | Solution | 4 | 380465 | 0.017920403518 | 1691.12 |
CASE STUDY SUMMARY
Problem 0 is the standard logistic regression. Features transformation is done using cubic splines (Problem 1). Splines transform one dimension observation data. Input data for building a spline are data of independent variables (features), dependent variables, and parameters defining number of knots and smoothing degree of the spline. Splines were built by minimizing log-likelihood logistic regression function (logexp_sum). Problem 2 is the logistic regression with transformed features. Problem 3 maximizes Buffered AUC (bAUC) by minimizing buffered probability of exceedance (bPOE). Problem 4 maximizes AUC by minimizing Probability of Exceedance (PSG function pr_pen).