arXiv subjects

Jiangkai Xiong

Publications and source records attributed to Jiangkai Xiong.

2 recordsLinked to original sources

arXiv2026

From Evaluated Models to Evaluation Aids: A Multi-Evidence Study of LLM-Based Difficulty Calibration for Programming Examinations

Difficulty differences across parallel-class programming examinations affect the fairness of course assessment. This study repositions large language models from benchmark evaluation targets to auxiliary evidence sources for interpreting exam difficulty, combining AI evidence with aggregated student performance, item exposure, online-judge process data, and teacher interpretation. First, ten models solved an eight-problem final exam synchronously with 120 students: AI pass rate correlated positively with student pass rate (Spearman rho = 0.866, exact p = 0.0119), and a solving-based composite difficulty index correlated negatively with it (rho = -0.905, exact p = 0.0046). A single structured reviewer was then run via auditable API calls on a third-party OpenAI-compatible endpoint whose model label (gpt-5.6-sol) cannot authenticate an official OpenAI upstream model; call metadata and raw responses are archived. Across 79 problems from 11 parallel-class final exams, AI overall difficulty correlated with problem-level pass rate at rho = -0.871 and with non-attempt rate at rho = 0.800; in a 26-problem longitudinal Data Structures and Algorithms B sample, the correlations were -0.829 and 0.883. A 106-problem introductory-course (CS101) sample marks the boundary: the problem-level correlation weakened to rho = -0.552, and the exam-level correlation across 16 exams was near zero, with cohort composition dominating exam-level outcomes. Exposure-discount (0-0.40) and duplicate-problem perturbation tests did not change these directions. AI evidence can thus serve as an external reference for problem validation, parallel-class fairness discussion, and longitudinal quality tracking, while the model-identity boundary, single-reviewer design, and review-output instability set explicit limits: AI difficulty scales must not be used for individual student evaluation or automatic grade adjustment.

cs.CY↗

arXiv2026

Calibrating an Imperfect Auxiliary Predictor for Unobserved No-Purchase Choice

Firms typically cannot observe key consumer actions: whether customers buy from a competitor, choose not to buy, or even fully consider the firm's offer. This missing outside-option information makes market-size and preference estimation difficult even in simple multinomial logit (MNL) models, and it is a central obstacle in practice when only transaction data are recorded. Existing approaches often rely on auxiliary market-share, aggregated, or cross-market data. We study a complementary setting in which a black-box auxiliary predictor provides outside-option probabilities, but is potentially biased or miscalibrated because it was trained in a different channel, period, or population, or produced by an external machine-learning system. We develop calibration methods that turn such imperfect predictions into statistically valid no-purchase estimates using purchase-only data from the focal environment. First, under affine miscalibration in logit space, we show that a simple regression identifies outside-option utility parameters and yields consistent recovery of no-purchase probabilities without collecting new labels for no-purchase events. Second, under a weaker nearly monotone condition, we propose a rank-based calibration method and derive finite-sample error bounds that cleanly separate auxiliary-predictor quality from first-stage utility-learning error over observed in-set choices. Our analysis also translates estimation error into downstream decision quality for assortment optimization, quantifying how calibration accuracy affects revenue performance. The bounds provide explicit dependence on predictor alignment and utility-learning error, clarifying when each source dominates. Numerical experiments demonstrate improvements in no-purchase estimation and downstream assortment decisions, and we discuss robust aggregation extensions for combining multiple auxiliary predictors.

cs.LG↗