6.3.13. Home Equity (HMEQ)#

6.3.13.1. Summary#

Baseline and loan performance information for 5,960 recent home equity loans, from the book Credit Risk Analytics [1]. A bank’s consumer credit department wants to automate the approval of home equity lines of credit, and the task is to predict which applicants eventually default or become seriously delinquent.

Unlike most public credit scoring data, it records the amount each applicant asked for, which is what an instance-dependent cost matrix needs. Ballegeer et al. [2] use it with the cost matrix of Bahnsen et al. [3], which Empulse follows.

Classes	2
Defaulters	1189
Non-defaulters	4771
Samples	5960
Features	12

6.3.13.2. Using the Dataset#

The dataset is fetched through fetch_home_equity. It is downloaded from OpenML on first use and cached under ~/empulse_data (override with $EMPULSE_DATA_HOME or the data_home argument), so later calls work offline.

It returns a Dataset object with the following attributes:

data: the feature matrix
target: the target vector
cost_matrix: a CostMatrix with default values pre-filled
instance_costs: a dict of per-instance cost drivers ('cl', 'fp_cost')
feature_names: the feature names
target_names: the target names
DESCR: the full description of the dataset

import pandas as pd
from empulse.datasets import fetch_home_equity

dataset = fetch_home_equity(backend=pd)
X, y = dataset.data, dataset.target

The backend argument selects the dataframe library used for data and target. Pass the module itself — backend=pd for pandas or backend=pl for polars.

Most variables have missing values, so the data needs imputation before a linear model can use it. Pass the cost matrix to the model as a Metric loss, and hand it the instance costs at fit time:

from empulse.metrics import Metric, Cost
from empulse.models import CSLogitClassifier
from sklearn.compose import ColumnTransformer
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline, make_pipeline
from sklearn.preprocessing import OneHotEncoder, StandardScaler

numeric = X.select_dtypes(include=['number']).columns
categorical = X.select_dtypes(exclude=['number']).columns

pipeline = Pipeline([
    ('preprocessor', ColumnTransformer([
        ('num', make_pipeline(SimpleImputer(strategy='median'), StandardScaler()), numeric),
        ('cat', make_pipeline(
            SimpleImputer(strategy='constant', fill_value='missing'),
            OneHotEncoder(handle_unknown='ignore', sparse_output=False),
        ), categorical),
    ])),
    ('model', CSLogitClassifier(loss=Metric(dataset.cost_matrix, Cost()))),
])
pipeline.fit(
    X,
    y,
    model__cl=dataset.instance_costs['cl'],
    model__fp_cost=dataset.instance_costs['fp_cost'],
)

6.3.13.3. Cost Matrix#

	Actual positive $y_i = 1$	Actual negative $y_i = 0$
Predicted positive $\hat{y}_i = 1$	`tp_cost` $= 0$	`fp_cost` $= r_i + -\bar{r} \cdot \pi_0 + \bar{Cl} \cdot L_{gd} \cdot \pi_1$
Predicted negative $\hat{y}_i = 0$	`fn_cost` $= Cl_i \cdot L_{gd}$	`tn_cost` $= 0$

with

$Cl_i$ : the loan amount requested (loan_amount)
$r_i$ : the profit lost by rejecting what would have been a good loan
$\bar{r}$ : the average profit lost by rejecting a good loan
$\pi_0$ : the share of non-defaulters
$\pi_1$ : the share of defaulters
$\bar{Cl}$ : the average loan amount
$L_{gd}$ : the fraction of the loan amount lost when the borrower defaults

Rejecting a good applicant costs the profit their loan would have made, less what lending the money to an average alternative applicant would have earned instead [3]. The profit is computed with an interest rate of 4.79%, a cost of funds of 2.94% and a term of 24 months, and is baked into 'fp_cost'.

The loss given default stays symbolic, with the default $L_{gd} = 0.75$ of Ballegeer et al. [2]. Override it by passing its alias loss_given_default when evaluating the metric:

y_score = pipeline.predict_proba(X)[:, 1]

cost = Metric(dataset.cost_matrix, Cost())
default_lgd = cost(y, y_score, **dataset.instance_costs)
higher_lgd = cost(y, y_score, loss_given_default=0.9, **dataset.instance_costs)

6.3.13.4. Data Description#

The original column name is given in brackets.

Feature	Description	Type
`loan_amount` (`LOAN`)	Amount of the loan requested	numeric
`mortgage_due` (`MORTDUE`)	Amount due on the existing mortgage	numeric
`property_value` (`VALUE`)	Value of the current property	numeric
`reason` (`REASON`)	`DebtCon` (debt consolidation) or `HomeImp` (home improvement)	categorical
`job` (`JOB`)	Occupational category	categorical
`years_at_job` (`YOJ`)	Years at the present job	numeric
`n_derogatory_reports` (`DEROG`)	Number of major derogatory reports	numeric
`n_delinquent_credit_lines` (`DELINQ`)	Number of delinquent credit lines	numeric
`oldest_credit_line_age` (`CLAGE`)	Age of the oldest credit line, in months	numeric
`n_recent_credit_inquiries` (`NINQ`)	Number of recent credit inquiries	numeric
`n_credit_lines` (`CLNO`)	Number of credit lines	numeric
`debt_to_income` (`DEBTINC`)	Debt-to-income ratio	numeric
default (target)	Whether the applicant defaulted or was seriously delinquent (1 = yes, 0 = no)	binary

	Actual positive \(y_i = 1\)	Actual negative \(y_i = 0\)
Predicted positive \(\hat{y}_i = 1\)	`tp_cost` \(= 0\)	`fp_cost` \(= r_i + -\bar{r} \cdot \pi_0 + \bar{Cl} \cdot L_{gd} \cdot \pi_1\)
Predicted negative \(\hat{y}_i = 0\)	`fn_cost` \(= Cl_i \cdot L_{gd}\)	`tn_cost` \(= 0\)

6.3.13. Home Equity (HMEQ)#

6.3.13.1. Summary#

6.3.13.2. Using the Dataset#

6.3.13.3. Cost Matrix#

6.3.13.4. Data Description#

6.3.13.5. References#