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You have poured your savings into your startup idea. You have customers waiting, and you just need $40,000 to bridge the gap between now and profitability. Imagine sitting across from a loan officer as they review your application for a small business loan.

The loan officer types something into their computer, waits, then looks with a polite smile that could mean anything.

“I am sorry, but we won’t be able to approve your application at this time.”

What just happened? What invisible calculation decided your fate in those few seconds? And more importantly, was it right? This isn’t a hypothetical scenario, it plays out thousands of times every day across the world. Behind each decision is a credit risk model, a mathematical framework trying to answer one of the hardest questions in finance, will this person pay us back? In lending, approving one bad loan can erase the profit from dozens of good ones, so the cost of mistakes is a asymmetric.

Credit risk modeling isn’t just crunching numbers, it’s about protecting livelihoods, enabling opportunities, transparency, and keeping our financial system stable. When a financial institution decides whether to approve your mortgage or a small business gets the loan it needs to expand, credit scoring models are working behind the scenes making those critical decisions possible. The decision is not about who you are as a person, but how your financial profile aligns with patterns learned from past borrowers who did or did not repay.

In this and the following article, we will walk through how modern machine learning fits into credit risk assessment, with a focus on probability of default. Starting with interpretable models like logistic regression and gradually moving towards more powerful techniques. In lending, the goal isn’t just to predict defaults but also to make decisions that are accurate, fair and explainable.

The Gap in Traditional Approaches:

Financial and accounting models have been the backbone of credit risk assessment for decades. They’re sophisticated, well-tested, and built in economic theory but they share a common limitation. They rely on predefined rules and assumptions that struggle to capture the full complexity of human financial behavior.

Think about it: a traditional model might use a fixed set of predefined formulas to calculate default probability based on debt-to-income ratio and credit score. But what about the subtle patterns in how someone manages their accounts over time? Or the non-linear relationships between dozens of variables that might signal risk? These nuances slip through the cracks of rule based system.

This is where machine learning enters the picture, not to replace traditional methods but to enhance them.

Why Machine Learning Transformed Everything

Machine learning models excel at finding patterns in complexity. They can analyze a vast amount of data, identify non-linear relationships, and adapt to changing market conditions in ways that traditional models simply cannot. Most importantly, they learn from outcomes, continuously refining their predictions as they process more information.

Here we will explore the intersection of traditional finance and modern ML by building a loan default model. The model predicts whether the applicant will default in their loan given their information. I will present two different approaches: Logistic Regression and Regularized Logistic. Each brings something unique to the table.

For technical reader, you may explore the complete code (From data ingestion to model benchmarking), results and detail quantitative explanations in https://github.com/sudkc37/Risk-Modeling

Starting Simple: Logistic Regression

Let us begin with logistic regression, the classic workhorse of binary classification. It is essentially a sophisticated way to answer yes or no questions. Imagine that you are trying to predict whether someone will repay a loan. You look at various factors like their income, employment history, existing debts, etc and you need to arrive at a simple answer: approve or deny?

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Logistic regression does exactly the same, but in a clever way. Instead of forcing a hard yes or no, it calculates the probability of repayment. Think of it like a confidence score. I am 85% confident this person will repay versus I am only 40% confident. This gives lenders much more flexibility in decision making. They might auto approve anyone above 40%, and manually review the cases in between. Mathematically, logistic regression calculates the probability of repayment using the logit function:

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Here’s what makes it powerful: the model weights each factor appropriately. For example, someone’s income matters more than their age, or their payment history matters more than their job title. The model learns these weights from thousands of past loans, figuring out which factors were most predictive of who actually repaid and who defaulted. It learns the weight by minimizing the log loss.

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When tested with this approach on 8,726 loan application datasets, it predicted 7,787 instance correctly and 939 wrong. That’s nearly 90% accuracy and 89% Receiver Operating Characteristic (ROC) value which is pretty good for a relatively simple model. But more importantly, it showed that even straightforward statistical methods can be remarkably effective when performed with proper feature transformation.

But could we do better? That’s where regularization comes in.

Adding Sophistication: Elastic Net Regularization

Here’s a problem every data scientist faces. Sometimes a model can become too good at predicting the data it was trained on. For example, a student who memorized practice problems perfectly but fails the actual test because they haven’t learned the underlying concepts. They have just memorized specific examples. In machine learning, we call this “overfitting”, and it’s a serious issue. A model might achieve 99% accuracy on historical data but perform terribly on new loan applications because it learned quirks and noise in the training data rather than true patterns.

Regularization is like adding guardrails to prevent this. Think of it as teaching the model to focus on what truly matters while ignoring the noise. Elastic Net, the technique I used and it does this in two complementary ways:

The first approach (called L1 or Lasso) which forces the model to be picky. Imagine you have 50 different factors you could use to predict the loan repayment, everything from credit score to what kind of phone someone has. L1 regularization says “You can’t use all of these, pick only the factors that really matter and ignore the rest”. It automatically zeroes out the less important factors, making the model simpler and more focused.

The second approach (called L2 or Ridge) is gentler. Instead of eliminating factors entirely, it says penalize the features with heavy weight. This prevents the model from being overly dependent on any piece of information, as a result it becomes more stable and reliable when it encounters unusual cases.

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Elastic Net combines both approaches. It is selective about which factors to use and careful about how much weight to give each one. It’s like having both a minimalist mindset (use only what you need) and a balance portfolio strategy (don’t put all your eggs in one basket). In this project, the improvements were not dramatic because the dataset was relatively straightforward. But in real-world credit assessment regularization becomes absolutely critical because you might be analyzing hundreds of variables across millions of borrowers.

What We’ve Learned

Logistic regression and its regularized variants represents the foundation of modern credit risk modeling. They are transparent, interpretable, and surprisingly powerful. When a loan officer needs to explain a decision to an applicant, these models make it possible to say “Here are the three to five important factors that influenced this decision, and here’s how much each one mattered”.

In this project, logistic regression achieved nearly 89% ROC score which is impressive, but it has limitations. It assumes relationships between variables are linear and additive. In reality, it rarely that straightforward. Sometimes factors interact in complex ways. For example, a high income matters more for someone with unstable employment, or perhaps payment history becomes more critical above certain debt levels. These non-linear patterns and interactions are where the ensemble models truly shine. They can capture the messy, complicated reality of financial behavior in ways that traditional regression cannot.

In next article, we will explore tree-based approaches and see how they unlock new levels of predictive power. We will also tackle one of the biggest challenges in modern AI: the “black box” problem. How do we make sophisticated models explainable when their decisions affect people’s lives? How do we ensure fairness and accountability when algorithms are making the calls?

Code & Resources:

GitHub : https://github.com/sudkc37/Risk-Modeling