Exploratory Data Analysis — Glossary · Certificate in Credit Risk Analytics in Python

Aggregated Default Rate #

Aggregated Default Rate

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Default rate, portfolio aggregation, exposure at default. The aggregated default rate is the overall proportion of borrowers who default across a combined set of loan segments, calculated by summing defaults and dividing by total exposures. Portfolio‑level insight helps risk managers benchmark performance. Example: A bank merges retail and corporate loan data, finds an aggregated default rate of 2.3 %. Challenge: Heterogeneity in loan terms can mask segment‑specific risks.

Bagging #

Bagging

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Bootstrap aggregating, ensemble methods, random forest. Bagging creates multiple training datasets via bootstrapping, fits a model to each, and averages predictions to reduce variance. In credit risk, bagging of decision trees stabilizes default probability estimates. Example: Using scikit‑learn’s BaggingClassifier on a dataset of 10,000 loan applications improves AUC from 0.71 To 0.75. Challenge: Increased computational cost and difficulty interpreting individual trees.

Balance Sheet Ratio #

Balance Sheet Ratio

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Liquidity ratio, leverage ratio, financial statement analysis. Balance sheet ratios compare items such as total assets to total liabilities, indicating a firm’s solvency. The debt‑to‑asset ratio, for example, is used to flag high‑risk corporate borrowers. Example: A company with a debt‑to‑asset ratio of 0.85 May be classified as high risk. Challenge: Ratios can be distorted by accounting policies, requiring careful normalization.

Boxplot #

Boxplot

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Whisker plot, five‑number summary, outlier detection. A boxplot visualizes the median, quartiles, and extreme values of a numeric variable, highlighting potential outliers. In credit risk, a boxplot of loan‑to‑value ratios quickly reveals extreme LTV values that may need capping. Example: A boxplot shows LTV outliers above 95 %. Challenge: Interpreting skewed distributions where the median may not represent the central tendency.

Bootstrap Sampling #

Bootstrap Sampling

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Resampling, Monte Carlo simulation, confidence intervals. Bootstrap sampling repeatedly draws random samples with replacement from the original dataset to assess the stability of statistics. Credit analysts use bootstrapping to estimate confidence intervals for loss‑given‑default. Example: 1,000 Bootstrap samples produce a 95 % CI for LGD of [0.35, 0.42]. Challenge: Computational intensity for large credit datasets.

Bucket #

Bucket

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Bin, segmentation, scorecard band. A bucket groups continuous variables into discrete intervals for analysis, often used in scorecard development. For instance, applicants’ ages may be bucketed into 20‑29, 30‑39, etc., To compute default rates per bucket. Example: The 30‑39 bucket shows a 1.2 % Default rate versus 3.5 % For 50‑59. Challenge: Choosing bucket boundaries that balance granularity and statistical significance.

Correlation Matrix #

Correlation Matrix

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Pearson correlation, heatmap, multicollinearity. A correlation matrix displays pairwise correlation coefficients between variables, helping detect multicollinearity before modeling. In credit risk, high correlation between income and debt‑to‑income may suggest redundant predictors. Example: A heatmap reveals a 0.88 Correlation between total assets and equity. Challenge: Linear correlation ignores non‑linear relationships, requiring alternative measures.

Credit Bureau Data #

Credit Bureau Data

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External data, credit report, scorecard inputs. Credit bureau data provides historical credit behavior, such as payment history, outstanding balances, and inquiries. Incorporating bureau data into EDA can dramatically improve predictive power. Example: Adding bureau‑derived “number of past due accounts” reduces model Brier score by 0.02. Challenge: Data privacy regulations limit sharing and require anonymization.

Credit Conversion Factor (CCF) #

Credit Conversion Factor (CCF)

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Exposure at default, utilization rate, off‑balance‑sheet exposure. CCF estimates the proportion of undrawn credit lines that will be drawn at default, converting commitments into exposure. For a revolving credit line, a typical CCF might be 0.5. Example: A $100 k undrawn line with a CCF of 0.5 Implies $50 k exposure at default. Challenge: CCF varies across industries and economic cycles, needing periodic recalibration.

Cross‑Validation #

Cross‑Validation

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K‑fold, train‑test split, model validation. Cross‑validation partitions data into k subsets, iteratively training on k‑1 folds and testing on the remaining fold to assess model generalizability. In credit risk, 5‑fold cross‑validation helps avoid overfitting to a particular loan cohort. Example: Cross‑validated AUC stabilizes around 0.78 Across folds. Challenge: Time‑ordered credit data may violate independence assumptions, requiring rolling‑window validation.

Cumulative Accuracy Profile (CAP) #

Cumulative Accuracy Profile (CAP)

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ROC curve, lift chart, model discrimination. CAP plots cumulative proportion of defaults captured against the proportion of the portfolio examined, visualizing model effectiveness. A steeper CAP curve indicates better discrimination. Example: A CAP curve captures 80 % of defaults in the top 30 % of scores. Challenge: Interpreting CAP for imbalanced datasets where defaults are rare.

Data Imputation #

Data Imputation

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Missing value handling, mean substitution, multiple imputation. Data imputation fills gaps in datasets where observations are missing, preserving sample size for analysis. Simple imputation (e.G., Median income) is fast but may bias results; multiple imputation preserves variability. Example: Using IterativeImputer to estimate missing credit scores improves model stability. Challenge: Improper imputation can create artificial patterns that mislead risk assessment.

Data Leakage #

Data Leakage

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Target leakage, information leakage, over‑optimistic performance. Data leakage occurs when information from the test set unintentionally influences model training, inflating performance metrics. In credit risk, using “account closed date” that occurs after default can leak future information. Example: A model trained with leakage reports an AUC of 0.92, But real‑world performance drops to 0.68. Challenge: Detecting subtle leakage during EDA requires rigorous feature provenance checks.

Decile Analysis #

Decile Analysis

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Quantile, performance bucket, lift table. Decile analysis divides a scored population into ten equal parts to compare observed default rates across score bands. It provides a quick sanity check for scorecard monotonicity. Example: The top decile (best scores) shows a 0.2 % Default rate, while the bottom decile shows 7.5 %. Challenge: Small sample sizes in some deciles can produce unstable rates, necessitating smoothing.

Distribution Skewness #

Distribution Skewness

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Asymmetry, kurtosis, normality test. Skewness measures the asymmetry of a variable’s distribution; positive skew indicates a long right tail. Credit variables such as loan amount often exhibit right skew. Example: Loan amount skewness of 2.3 Suggests log‑transformation may improve model linearity. Challenge: Extreme skew can mask outliers that need separate handling.

Empirical Cumulative Distribution Function (ECDF) #

Empirical Cumulative Distribution Function (ECDF)

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Cumulative distribution, quantile plot, non‑parametric estimator. ECDF plots the proportion of observations less than or equal to each value, providing a complete view of a variable’s distribution without assuming a parametric form. In credit risk, an ECDF of credit scores helps assess coverage across the score range. Example: The ECDF shows 60 % of borrowers have scores above 650. Challenge: Visual clutter with large datasets; sampling may be required.

Feature Engineering #

Feature Engineering

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Variable transformation, interaction term, domain knowledge. Feature engineering creates new predictors from raw data to capture underlying risk drivers, such as debt‑to‑income ratio or log‑transformed loan amount. Example: Combining “number of open lines” and “total credit limit” yields a utilization metric that improves model AUC. Challenge: Excessive engineered features can increase multicollinearity and overfitting risk.

Gini Coefficient #

Gini Coefficient

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Gini index, discrimination measure, AUC. The Gini coefficient is twice the area between the ROC curve and the diagonal, ranging from 0 (no discrimination) to 1 (perfect). In credit risk, a Gini of 0.45 Indicates moderate predictive power. Example: A logistic regression model attains a Gini of 0.48 After feature selection. Challenge: Gini is sensitive to class imbalance; reporting both Gini and KS may be advisable.

Histogram #

Histogram

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Bar chart, frequency distribution, binning. A histogram visualizes the frequency of numeric values across bins, revealing shape, central tendency, and outliers. For credit risk, a histogram of loan amounts can highlight clustering around typical loan sizes. Example: A histogram shows a bimodal distribution with peaks at $5 k and $20 k. Challenge: Choosing appropriate bin width; too many bins obscure trends, too few hide details.

Imbalanced Classification #

Imbalanced Classification

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Minority class, oversampling, SMOTE. Imbalanced classification occurs when default events constitute a small fraction of the dataset, leading to biased models that favor the majority class. Techniques such as Synthetic Minority Over‑sampling Technique (SMOTE) rebalance training data. Example: Applying SMOTE raises recall for defaults from 0.32 To 0.58. Challenge: Synthetic samples may not reflect real‑world default patterns, potentially inflating performance.

Kolmogorov‑Smirnov (KS) Statistic #

Kolmogorov‑Smirnov (KS) Statistic

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KS test, separation measure, model validation. KS measures the maximum distance between cumulative distributions of goods and bads, indicating discriminatory power. A KS of 0.30 Is considered acceptable in many banking contexts. Example: After variable selection, the model’s KS improves from 0.22 To 0.31. Challenge: KS does not account for calibration; a model can have high KS but poor probability estimates.

Kurtosis #

Kurtosis

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Peakedness, tail weight, normality. Kurtosis quantifies the heaviness of distribution tails relative to a normal distribution; high kurtosis indicates more extreme outliers. Credit variables like loss given default often exhibit high kurtosis. Example: LGD kurtosis of 7.5 Suggests heavy tails, prompting robust modeling techniques. Challenge: Extreme kurtosis can destabilize variance‑based methods, requiring transformation or trimming.

Lag Feature #

Lag Feature

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Time series, rolling window, temporal variable. A lag feature captures a variable’s value from a previous time period, useful for modeling borrower behavior over time. Example: “Previous month’s payment delinquency count” serves as a lag feature predicting next‑month default risk. Challenge: Aligning lags with varying payment cycles can create missing data that need careful imputation.

Leverage Ratio #

Leverage Ratio

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Debt‑to‑equity, financial leverage, solvency metric. The leverage ratio compares total debt to equity, indicating a firm’s financial risk. Higher leverage often correlates with higher default probability. Example: A corporate borrower with a leverage ratio of 4.2 May be flagged for higher risk pricing. Challenge: Industry‑specific norms require contextual benchmarks.

Logistic Regression #

Logistic Regression

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Logit model, binary classification, odds ratio. Logistic regression models the log‑odds of default as a linear combination of predictors, providing interpretable coefficients. In credit risk, it forms the basis of many scorecards. Example: A coefficient of 0.45 For “credit utilization” translates to an odds increase of 1.57 Per unit rise. Challenge: Linearity assumption may not capture complex interactions, prompting the use of non‑linear extensions.

Loss Distribution #

Loss Distribution

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Probability of loss, expected loss, tail risk. The loss distribution describes the probability of various loss amounts across a loan portfolio, integrating default probability, exposure, and loss‑given‑default. Example: Monte‑Carlo simulation produces a loss distribution with a 99 % VaR of $12 M. Challenge: Accurate estimation requires robust joint modeling of PD, EAD, and LGD, each with its own uncertainty.

Missing Not At Random (MNAR) #

Missing Not At Random (MNAR)

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Missing data mechanisms, non‑ignorable missingness, data bias. MNAR occurs when the probability of missingness depends on the unobserved value itself, complicating imputation. In credit risk, borrowers with high debt may omit income fields, leading to MNAR. Example: Ignoring MNAR can underestimate default risk for high‑debt applicants. Challenge: Diagnosing MNAR often requires external validation data or sensitivity analysis.

Multicollinearity #

Multicollinearity

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Variance inflation factor, correlated predictors, redundancy. Multicollinearity arises when predictors are highly correlated, inflating coefficient variance and reducing interpretability. Example: “Total assets” and “equity” show VIF > 10, indicating multicollinearity. Challenge: Dropping variables may lose information; regularization (e.G., Lasso) can mitigate the issue.

Outlier Detection #

Outlier Detection

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Anomaly detection, robust statistics, influence point. Outlier detection identifies observations that deviate markedly from the bulk of data, which may indicate data entry errors or genuine high‑risk cases. Example: A loan amount of $5 M in a consumer loan dataset is flagged as an outlier. Challenge: Distinguishing true outliers from legitimate high‑risk borrowers requires domain expertise.

Partial Dependence Plot (PDP) #

Partial Dependence Plot (PDP)

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Model interpretability, marginal effect, feature influence. PDPs show the average predicted response as a single feature varies, holding other features constant, helping interpret complex models. Example: A PDP for “credit score” reveals a steep decline in default probability below 600. Challenge: PDP assumes feature independence, which may not hold in correlated credit variables.

Performance Dashboard #

Performance Dashboard

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KPI, monitoring, visual analytics. A performance dashboard aggregates key metrics such as default rate, PD distribution, and model drift, providing real‑time oversight for credit risk teams. Example: A dashboard displays a sudden rise in “bad‑rate” for a new product line, prompting investigation. Challenge: Over‑loading dashboards with too many metrics can obscure critical signals.

Principal Component Analysis (PCA) #

Principal Component Analysis (PCA)

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Dimensionality reduction, eigenvectors, variance explained. PCA transforms correlated variables into orthogonal components that capture maximal variance, often used to reduce dimensionality before modeling. Example: The first three principal components explain 78 % of variance in a 25‑variable credit dataset. Challenge: Components lack direct economic interpretation, limiting regulatory acceptance.

Probability of Default (PD) #

Probability of Default (PD)

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Default likelihood, credit scoring, risk rating. PD quantifies the likelihood that a borrower will default within a specified horizon, typically one year. It is a core input for capital allocation under Basel regulations. Example: A borrower with a PD of 0.015 Receives a risk‑adjusted interest rate. Challenge: PD models must be calibrated to reflect changing macro‑economic conditions.

Quantile‑Quantile (Q‑Q) Plot #

Quantile‑Quantile (Q‑Q) Plot

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Normality check, distribution comparison, residual analysis. A Q‑Q plot compares the quantiles of a variable to those of a theoretical distribution, revealing deviations from normality. Example: A Q‑Q plot of residuals shows heavy tails, indicating the need for robust regression. Challenge: Interpreting slight deviations can be subjective; formal tests may be needed.

Random Forest #

Random Forest

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Ensemble learning, bagging, decision trees. Random forest builds many decision trees on bootstrapped samples and aggregates their predictions, reducing overfitting and improving accuracy. In credit risk, random forests capture non‑linear relationships between borrower characteristics and default. Example: A random forest model yields an AUC of 0.81 Versus 0.73 For logistic regression. Challenge: Reduced interpretability compared to linear models; feature importance must be communicated carefully.

Recall (Sensitivity) #

Recall (Sensitivity)

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True positive rate, detection rate, classification metric. Recall measures the proportion of actual defaults correctly identified by the model. High recall is crucial for risk‑averse institutions. Example: A model with recall 0.68 Captures 68 % of defaults but may increase false positives. Challenge: Balancing recall with precision to avoid excessive credit rejections.

Receiver Operating Characteristic (ROC) Curve #

Receiver Operating Characteristic (ROC) Curve

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AUC, discrimination, threshold analysis. The ROC curve plots true positive rate against false positive rate across classification thresholds, visualizing trade‑offs. Example: The ROC curve of a gradient‑boosted model dominates that of a logistic model, indicating better discrimination. Challenge: ROC can be overly optimistic with heavily imbalanced credit datasets; precision‑recall curves may be more informative.

Regression Diagnostics #

Regression Diagnostics

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Residual analysis, leverage points, heteroscedasticity. Regression diagnostics assess model assumptions and identify problematic observations. Tools include residual plots, Cook’s distance, and Breusch‑Pagan test. Example: Residuals versus fitted values reveal heteroscedasticity, prompting a log‑transform of the target. Challenge: Diagnosing issues in large credit datasets requires automated scripts.

Risk‑Weighted Asset (RWA) #

Risk‑Weighted Asset (RWA)

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Capital requirement, Basel III, asset risk weighting. RWA adjusts asset values by risk weights reflecting credit quality, forming the basis for regulatory capital calculations. Example: A $10 M loan with a risk weight of 100 % contributes $10 M to RWA. Challenge: Accurate PD and LGD estimates are essential to assign appropriate risk weights.

Sample Weighting #

Sample Weighting

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Importance sampling, stratified sampling, survey weights. Sample weighting assigns different importance to observations, often to correct for class imbalance or to reflect population proportions. Example: Weighting defaults higher improves model focus on rare events. Challenge: Improper weights can bias model coefficients and inflate variance.

Segmentation #

Segmentation

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Clustering, cohort analysis, market segmentation. Segmentation groups borrowers into homogeneous clusters based on characteristics such as income, geography, or product type, facilitating targeted risk analysis. Example: K‑means clustering yields three segments with distinct default rates. Challenge: Ensuring segments are statistically significant and not artefacts of random variation.

Shapley Additive Explanations (SHAP) #

Shapley Additive Explanations (SHAP)

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Model interpretability, feature importance, game theory. SHAP values attribute the contribution of each feature to an individual prediction, based on cooperative game theory. In credit risk, SHAP explains why a particular applicant received a high default probability. Example: SHAP analysis shows “recent missed payment” contributed +0.12 To the predicted risk. Challenge: Computational cost for large datasets; aggregating SHAP values for portfolio‑level insight can be non‑trivial.

Significance Testing #

Significance Testing

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P‑value, hypothesis test, statistical inference. Significance testing evaluates whether observed relationships could arise by chance. In EDA, chi‑square tests assess independence between categorical variables like loan purpose and default. Example: A chi‑square test yields p‑value = 0.004, Indicating a statistically significant association. Challenge: Large sample sizes can produce significant p‑values for trivial effects; effect size should also be considered.

Smoothing #

Smoothing

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Kernel density, moving average, loess. Smoothing techniques reduce noise in data visualizations, revealing underlying trends. A loess curve over a scatter plot of credit score versus default rate clarifies non‑linear patterns. Example: Applying a Gaussian kernel to the loan amount distribution uncovers a subtle secondary mode. Challenge: Over‑smoothing may hide important local variations.

Standardization #

Standardization

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Z‑score, scaling, normalization. Standardization rescales variables to have zero mean and unit variance, facilitating algorithms that assume comparable feature scales. Example: Standardizing “annual income” before feeding data into a support vector machine improves convergence. Challenge: Applying standardization to test data must use training‑set parameters to avoid data leakage.

Stratified Sampling #

Stratified Sampling

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Stratified split, proportional allocation, class balance. Stratified sampling ensures each class (e.G., Defaults vs. Non‑defaults) is represented proportionally in training and test sets, preserving the original distribution. Example: A 70/30 split with stratification maintains a 2 % default rate in both subsets. Challenge: Small minority classes may still suffer from insufficient samples for robust validation.

Target Variable #

Target Variable

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Response, dependent variable, label. In credit risk modeling, the target variable is typically binary (default = 1, no default = 0) or a continuous loss amount. Correctly defining the target is critical for model alignment with business objectives. Example: Using “30‑day delinquency” as the target instead of “full default” changes the modeling horizon. Challenge: Target definition may affect regulatory acceptability and operational feasibility.

Temporal Drift #

Temporal Drift

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Concept drift, model decay, data shift. Temporal drift occurs when relationships between predictors and the target evolve over time, reducing model performance. Monitoring drift metrics such as population stability index (PSI) helps detect degradation. Example: A PSI of 0.25 Over six months signals moderate drift, prompting model retraining. Challenge: Distinguishing genuine drift from seasonal effects requires careful analysis.

Time‑Series Split #

Time‑Series Split

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Rolling window, forward chaining, sequential validation. Time‑series split respects chronological order by training on earlier periods and testing on later periods, preventing look‑ahead bias. Example: A rolling 12‑month window evaluates model stability across successive years. Challenge: Limited data in early periods may reduce training set size, affecting model robustness.

Trimming #

Trimming

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Outlier removal, winsorization, robust statistics. Trimming removes extreme values beyond a specified percentile, reducing the influence of outliers on statistical estimates. Example: Trimming the top 1 % of loan amounts stabilizes mean calculations. Challenge: Aggressive trimming may discard genuine high‑risk cases, biasing risk assessments.

Variance Inflation Factor (VIF) #

Variance Inflation Factor (VIF)

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Multicollinearity diagnostic, eigenvalue, tolerance. VIF quantifies how much variance of a regression coefficient is inflated due to correlation with other predictors. VIF > 10 often signals problematic multicollinearity. Example: “Total debt” exhibits VIF = 12, suggesting removal or combination with “income”. Challenge: VIF does not capture non‑linear dependencies, requiring complementary diagnostics.

Variable Importance #

Variable Importance

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Feature ranking, information gain, permutation importance. Variable importance measures the contribution of each predictor to model performance, guiding feature selection and interpretation. Example: Permutation importance shows “credit utilization” as the top predictor in a gradient‑boosted model. Challenge: Importance scores can be biased toward variables with many categories or higher cardinality.

Winsorization #

Winsorization

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Capping, outlier treatment, robust scaling. Winsorization caps extreme values at chosen percentiles, preserving data size while limiting outlier influence. Example: Capping loan amounts at the 99th percentile reduces skew without discarding observations. Challenge: Selecting appropriate caps requires domain knowledge to avoid masking legitimate high‑risk loans.

Zero‑Inflated Model #

Zero‑Inflated Model

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Count data, hurdle model, overdispersion. Zero‑inflated models handle datasets with excess zeros, such as the number of missed payments where many borrowers have none. They combine a binary component (zero vs. Non‑zero) with a count component. Example: A zero‑inflated Poisson model better fits delinquency counts than a standard Poisson. Challenge: Model complexity increases, and interpretation of two components can be non‑intuitive.

Z‑Score Normalization #

Z‑Score Normalization

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Standard score, scaling, mean centering. Z‑score normalization converts values to the number of standard deviations from the mean, facilitating comparison across variables. Example: A borrower’s income with a z‑score of –1.2 Indicates below‑average earnings. Challenge: Outliers can distort mean and standard deviation, leading to misleading z‑scores; robust scaling may be preferable.