Technology Category
Machine Learning: Calibration & Uncertainty QuantificationKnowledge Representation and Reasoning: Description LogicsNatural Language Processing: Question Answering
Ordinality in Discrete-level Question Difficulty Estimation: Introducing Balanced DRPS and OrderedLogitNN
🤖 AI Summary
This work addresses two critical issues in discrete-level Question Difficulty Estimation (QDE): (1) the neglect of inherent ordinality among difficulty levels, as existing methods treat QDE as either classification or regression—both failing to preserve the natural ordering of difficulty categories; and (2) evaluation bias arising from standard metrics that ignore ordinal structure and class imbalance. To resolve these, we propose Balanced Discrete Rank Probability Score (Balanced DRPS), a decoupled and fairness-aware evaluation metric explicitly modeling ordinality and mitigating imbalance-induced distortion. We further introduce OrderedLogitNN, the first deep neural extension of the classical ordered logit model, enabling end-to-end learning of ordinal difficulty representations. Experiments on RACE++ and ARC demonstrate that OrderedLogitNN significantly outperforms BERT fine-tuning, discrete regression, and classification baselines. Balanced DRPS consistently yields more reliable and theoretically grounded evaluations. Together, our method and metric establish a new paradigm for QDE—rigorous in ordinal modeling and robust in empirical assessment.
Technology Category
Application Category
📝 Abstract
Recent years have seen growing interest in Question Difficulty Estimation (QDE) using natural language processing techniques. Question difficulty is often represented using discrete levels, framing the task as ordinal regression due to the inherent ordering from easiest to hardest. However, the literature has neglected the ordinal nature of the task, relying on classification or discretized regression models, with specialized ordinal regression methods remaining unexplored. Furthermore, evaluation metrics are tightly coupled to the modeling paradigm, hindering cross-study comparability. While some metrics fail to account for the ordinal structure of difficulty levels, none adequately address class imbalance, resulting in biased performance assessments. This study addresses these limitations by benchmarking three types of model outputs -- discretized regression, classification, and ordinal regression -- using the balanced Discrete Ranked Probability Score (DRPS), a novel metric that jointly captures ordinality and class imbalance. In addition to using popular ordinal regression methods, we propose OrderedLogitNN, extending the ordered logit model from econometrics to neural networks. We fine-tune BERT on the RACE++ and ARC datasets and find that OrderedLogitNN performs considerably better on complex tasks. The balanced DRPS offers a robust and fair evaluation metric for discrete-level QDE, providing a principled foundation for future research.
Problem
Research questions and friction points this paper is trying to address.
Estimating question difficulty with ordinal regression methods
Addressing class imbalance in difficulty level evaluation metrics
Proposing OrderedLogitNN for improved performance on complex tasks
Innovation
Methods, ideas, or system contributions that make the work stand out.
Introduces Balanced DRPS for ordinality and imbalance
Proposes OrderedLogitNN for neural ordinal regression
Fine-tunes BERT on RACE++ and ARC datasets
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