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When Do Data-Driven Systems Exhibit the Capability to Infer?

Motivated by the regulatory ambiguities in the European AI Act regarding credit scoring systems, this paper proposes a framework grounded in statistical learning theory to grade and analyze the capability to infer across entire data processing workflows, demonstrating that regulatory classification depends on the holistic system design and human involvement rather than individual models alone.

Original authors: Maximilian Poretschkin, Tabea Naeven

Published 2026-06-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Maximilian Poretschkin, Tabea Naeven

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a judge in a courtroom. The European Union has passed a new law called the AI Act, which says, "If you are an Artificial Intelligence, you must follow strict rules." But the law has a tricky loophole: it doesn't clearly define what "AI" actually is.

The law says an AI is a system that can "infer." In plain English, this means the system can look at data and figure out how to make a decision on its own, rather than just following a rigid list of instructions written by a human.

The problem? There is a gray area. Many systems used for credit scoring (deciding if you get a loan) use statistical math. Are these "smart" enough to be called AI, or are they just "dumb" calculators? The authors of this paper, Maximilian and Tabea, decided to build a ladder to help us climb out of this gray area.

The "Inference Ladder"

The authors created a 5-step ladder to measure how much "thinking" a system does. The higher you climb, the more likely the system is to be considered AI under the new law.

Level 0: The Robot Butler (Fixed Mapping)
- The Metaphor: Imagine a robot that only does exactly what you tell it. "If the light is red, stop. If green, go."
- The Reality: The rules are written in stone by humans. The data doesn't change the rules; it just triggers them.
- AI Status: Not AI. Just a fancy calculator.
Level 1: The Tuning Knob (Parametric Adaptation)
- The Metaphor: Imagine a radio. The station (the structure) is fixed, but you can turn the volume knob (the parameters) up or down based on how loud the music is.
- The Reality: The system uses a fixed formula (like a standard math equation). It looks at data to adjust the numbers inside that formula, but the formula itself never changes.
- AI Status: This is the "gray area." The law's guidelines suggest this might not be AI because it's just "basic data processing."
Level 2: The Menu Selector (Structural Selection)
- The Metaphor: Imagine a chef who has a menu of 10 pre-written recipes. The chef looks at the ingredients you have (the data) and picks one recipe from the list to cook. The chef doesn't invent a new recipe; they just choose the best one from the list.
- The Reality: The system has a set list of possible structures. It uses data to pick which one to use (e.g., "Let's use Feature A and B, but ignore C").
- AI Status: This is a middle ground. It's more than just tuning knobs, but it's not inventing new logic.
Level 3: The Architect (Structural Construction)
- The Metaphor: Imagine a builder who is given a pile of bricks and a goal (build a house). The builder looks at the bricks and invents the blueprint on the spot. They decide where the walls go and how the roof is shaped based entirely on the materials they have.
- The Reality: The system doesn't just pick a recipe; it builds the logic from scratch using the data. It creates a decision tree or a complex pattern that no human explicitly wrote down.
- AI Status: This is definitely AI. The system is "deriving" its own logic.
Level 4: The Dreamer (Representational Construction)
- The Metaphor: Imagine an artist who not only paints a picture but also invents a new color to use in the painting because the old colors didn't fit the mood.
- The Reality: The system doesn't just build the logic; it invents a whole new way of seeing the data (new features) to solve the problem. This is what deep learning and modern AI do.
- AI Status: Definitely AI.

The Credit Scorecard Test

The authors tested this ladder on credit scoring, which is a high-risk area under the AI Act. They looked at how banks usually build these scores.

The "Old School" Way: Banks often take a list of variables (income, debt, etc.), chop them into buckets (binning), and plug them into a logistic regression equation.
- If the bank just adjusts the numbers in the equation? That's Level 1.
- If the bank uses data to decide which variables to keep and which to throw away? That's Level 2.
- The Verdict: The authors argue that even these "simple" systems often involve human experts making judgment calls during the setup (like deciding how to chop the buckets). Because humans are heavily involved in designing the structure, the system might not have enough "autonomy" to be considered a true AI under the law.
The "Smart" Way: If a system automatically builds the decision tree or the complex structure from the data without human intervention, it hits Level 3.
- The Verdict: This is clearly AI and must follow the strict rules.

The Big Takeaway

The paper concludes that we can't just look at the final math equation to decide if something is AI. We have to look at the whole process:

Did a human design the rules?
Did a human pick the variables?
Or did the data itself build the logic?

If a human expert is doing the heavy lifting of designing the system's structure, the system might be "dumb" enough to escape the strict AI Act regulations, even if it uses complex math. But if the system builds its own logic from the data, it is "smart" enough to be regulated as AI.

In short: The law is worried about systems that "learn" their own rules. This paper gives us a ruler to measure exactly how much learning is happening, helping banks and regulators know who needs to follow the new rules.

Technical Summary: When Do Data-Driven Systems Exhibit the Capability to Infer?

Problem Statement
The European AI Act establishes a comprehensive legal framework for artificial intelligence, defining an AI system primarily by its "capability to infer." However, the Act and its accompanying Commission Guidelines do not provide a precise technical definition of inference, creating regulatory ambiguity for data-driven systems that rely on classical statistical models rather than modern machine learning architectures. This uncertainty is particularly acute in the domain of credit scoring, which is explicitly listed as a high-risk application in Annex III of the AI Act. Industry practitioners and regulators face a dilemma: many credit scoring systems utilize logistic regression and statistical binning procedures. It remains unclear whether these systems, which often involve human expert intervention in model development, possess the "capability to infer" sufficient to classify them as AI systems under the Act, or if they fall outside the scope as "basic data processing."

Methodology
To address this ambiguity, the authors develop a graded framework for assessing the capability to infer, grounded in statistical learning theory. The methodology proceeds in three stages:

Theoretical Abstraction: The authors formalize the concept of inference by analyzing how data influences the formation of input-output mappings. Drawing on the distinction between parametric estimation (data modeling culture) and algorithmic construction (algorithmic modeling culture), they propose a five-level staged framework (Levels 0–4) that categorizes systems based on the extent to which data shapes the system's logic:
- Level 0 (Fixed Mapping): Fully specified ex ante by humans; data is processed but does not influence structure or parameters.
- Level 1 (Parametric Adaptation): The functional form is fixed; data determines only numerical parameters (e.g., coefficients in linear/logistic regression).
- Level 2 (Structural Selection): Data selects among a predefined set of admissible structures (e.g., stepwise feature selection, $L_1$ -regularization).
- Level 3 (Structural Construction): Data functionally constructs the input-output mapping, either explicitly (e.g., decision trees) or implicitly (e.g., $k$ -nearest neighbors).
- Level 4 (Representational Construction): Data determines the representational space itself (e.g., deep neural networks, representation learning).
Regulatory Mapping: The framework is applied to the text of the AI Act (Article 3, Recital 12) and the Commission Guidelines. The authors analyze the Guidelines' exclusion of systems that "improve mathematical optimization" or "accelerate traditional methods" to determine where the regulatory threshold for "capability to infer" lies. They explore two interpretations: one where Level 1 falls outside the AI definition, and an alternative where even parameter estimation constitutes inference.
Case Study Application: The framework is applied to two realistic credit scoring workflows using the "Give Me Some Credit" dataset. The authors dissect the end-to-end development process, including:
- Binning: Analyzing manual vs. data-driven binning (e.g., recursive binary splits optimizing Shannon entropy).
- Logistic Regression: Examining standard logistic regression versus versions employing stepwise feature selection.
- Human Involvement: Assessing how expert constraints (e.g., monotonicity requirements, regulatory rules) and manual shortlisting affect the system's inference capability.

Key Contributions

A Graded Inference Framework: The paper introduces a structured, five-level taxonomy that distinguishes between systems based on how data shapes input-output mappings. This moves beyond binary classifications to allow for granular analysis of hybrid systems.
Regulatory Clarification for Statistical Models: The authors demonstrate that common credit scoring techniques occupy different levels of the framework. Specifically, they show that while standard logistic regression with fixed features is Level 1, the addition of data-driven binning (Level 3a) or stepwise feature selection (Level 2) shifts the system's inference capability.
Workflow-Level Analysis: The paper argues that regulatory assessment cannot be limited to the final predictive model. Instead, the entire data processing workflow must be evaluated, as preprocessing steps like binning and variable selection can introduce inference capabilities that the final model alone might not possess.
Role of Human Expertise: The analysis highlights that human involvement during the development phase (e.g., defining constraints, selecting variables manually) can significantly influence whether a system is considered to have the capability to infer, potentially keeping a system within the "basic data processing" category even if it uses statistical models.

Results
Applying the framework to credit scoring workflows reveals that these systems are often composite:

Binning: Manual binning remains at Level 0 or 1. However, data-driven binning methods (like those optimizing entropy) constitute Level 3a (Explicit Structural Construction), as the partition structure is functionally constructed from data rather than selected from a fixed catalog.
Logistic Regression: A standard logistic regression model with pre-selected features is Level 1. However, when combined with stepwise feature selection, the system operates at Level 2 (Structural Selection).
Regulatory Threshold: The authors suggest that if the Commission Guidelines are interpreted strictly to exclude systems that merely "accelerate" traditional optimization, Level 1 systems (parametric adaptation) may fall outside the AI Act's scope. Conversely, systems exhibiting Level 2 or higher (structural selection or construction) align more closely with the Act's definition of deriving models from data.
Ambiguity Resolution: The study illustrates that a single credit scoring system may contain components at different levels. Consequently, the "capability to infer" is not an intrinsic property of the algorithm alone but a property of the specific implementation and workflow.

Significance
The paper claims that its primary significance lies in providing a technical tool to operationalize the legal concept of "capability to infer" for regulators and industry practitioners. By demonstrating that not all data-driven systems are equal in their inference capabilities, the framework offers a basis for consistent regulatory treatment of borderline cases, particularly in high-risk sectors like credit scoring. The authors emphasize that their work does not definitively resolve the legal status of logistic regression but rather clarifies the technical distinctions necessary for such a determination, highlighting that the involvement of human experts and the specific workflow design are critical factors in determining whether a system meets the AI Act's definition.

The "Inference Ladder"

The Credit Scorecard Test

The Big Takeaway

Technical Summary: When Do Data-Driven Systems Exhibit the Capability to Infer?

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