# Classification in Loan Application Process

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Case study background and problem formulations

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

PROBLEM 0: problem_Logexp_Sum (original untransformed features)
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
——————————————————————–————————————————

Dataset1 2012 4 380465 -0.238801512644 2.82 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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 -0.244676286 4.56
Dataset3 2014 Problem statement Data Solution 4 380465 -0.216362946 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

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Dataset1 DTI, 2012 20 380465 -0.441511982280 1.45 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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 -0.363102932 48.09
Dataset3 DTI, 2014 Problem statement Data Solution 20 380465 -0.321050341 81.66
Dataset4 EmpLen, 2012 Problem statement Data Solution 20 380465 -0.215776179 20.04
Dataset5 EmpLen, 2013 Problem statement Data Solution 20 380465 -0.225138264 52.72
Dataset6 EmpLen, 2014 Problem statement Data Solution 20 380465 -0.130285134 120.86
Dataset7 FICO, 2012 Problem statement Data Solution 20 380465 -0.283383677 49.90
Dataset8 FICO, 2013 Problem statement Data Solution 20 380465 -0.299431106 121.41
Dataset8 FICO, 2014 Problem statement Data Solution 20 380465 -0.251899113 293.00
PROBLEM 2: problem_Logexp_Sum (transformed features)
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

——————————————————————–————————————————

Dataset1 2012 4 380465 -0.17741580617 1.61 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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 -0.17389892 3.59
Dataset3 2014 Problem statement Data Solution 4 380465 -0.11140448 8.97
PROBLEM 3: minimizing buffered probability of exceedance (bPOE) with transformed features(equivalent to maximization of bAUC)
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

——————————————————————–————————————————

Dataset1 2012 4 380465 0.106004778111 7.47 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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 0.09195791 14.38
Dataset3 2014 Problem statement Data Solution 4 380465 0.04428154 105.65
PROBLEM 4: minimizing Probability of Exceedance using transformed features (equivalent to maximization of AUC)
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
——————————————————————–————————————————

Dataset1 2012 4 380465 0.045272219018 113.33 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data