Recovering Stranded Discrimination in Knowledge Tracing: Per-Item Bias Correction via Empirical-Bayes Shrinkage

Knowledge Tracing (KT) is fundamental to intelligent education systems, yet relies on educational logs that are selectively observed. The non-random nature of exercise recommendations and student choices inevitably induces severe selection bias. Most existing KT methods neglect this issue, training on observed logs using standard empirical risk, which yields biased mastery estimates and accumulates errors in subsequent recommendations. To address this, we introduce a doubly robust (DR) formulation for KT that integrates a propensity model with an error imputation model, theoretically guaranteeing unbiasedness if either model is accurate. Beyond unbiasedness, in the sequential setting of KT, we identify that the estimator's performance is compromised by variance-dependent stochastic deviations that accumulate over time, thereby causing training instability and limiting performance. To mitigate this, we derive a generalization bound that explicitly characterizes the impact of estimator variance and identifies temporal smoothness as a key factor in controlling it. Building on these theoretical insights, we propose the Temporal Smoothness Doubly Robust (TSDR) framework. TSDR jointly optimizes the KT predictor and the imputation model with a smoothness regularizer, effectively reducing variance while preserving the unbiasedness guarantee of DR. Experiments on multiple real-world benchmarks demonstrate that TSDR consistently enhances various state-of-the-art KT backbones, underscoring the vital role of principled bias correction in KT.

Scaling laws provide a fundamental framework for understanding the performance of Language Models (LMs), yet deriving them requires prohibitively expensive evaluations across thousands of checkpoints or millions of inference samples. To address this, we introduce Item Response Scaling Laws (IRSL), a unified framework that integrates Item Response Theory (IRT) within the scaling law framework. Unlike traditional approaches that treat each model-benchmark pair in isolation, IRSL disentangles latent model ability from question characteristics, factorizing the scaling law estimation for $M$ models and $N$ questions to significantly reduce parameter complexity from $O(M \times N)$ to $O(M + N)$. We instantiate IRSL with Beta-IRT, which leverages the empirical probability responses of LMs -- such as token probabilities in pre-training and pass rates in test-time sampling -- to capture richer signals than binary responses. We validate our approach across two prevalent scaling paradigms: (1) pre-training downstream scaling, using 6,612 LM checkpoints and 37,682 questions from 10 benchmarks; and (2) test-time scaling, using 12 LMs and 120 questions from 4 benchmarks with up to 2,500 samples per question. Given a one-time calibration on existing model responses, IRSL yields more reliable scaling estimates using only 50 questions per benchmark (a 99.9% reduction), achieving comparable or superior decision accuracy to traditional approaches. Furthermore, we show that the estimated latent model abilities are generalizable, enabling accurate performance forecasting across benchmarks that share the same measurement objective.

Different predictors often excel on different inputs, so picking the best one per instance promises higher accuracy than committing to a single model. In practice, selectors trained from logged data routinely fail to beat the strongest single predictor. Three causes typically go unseparated before more tuning is applied: a mismatched learner, a state that does not predict which model wins, or buffer-to-deployment label shift. A three-stage diagnostic rules them out on a shared buffer. Stage1 estimates a local ceiling on oracle recovery from $k$-NN label consistency. Stage2 asks whether paired BC and offline-RL learners (BC, DQN, and CQL across penalty weights) reach that ceiling. Stage~3 ablates the selector state to test whether richer features would raise it. The combined verdict points to the most promising next step: tuning the learner, redesigning the state, or collecting new data. We apply it to selecting among five dropout-prediction models on edX clickstream data. Across 16 windows, the oracle beats the strongest single base model by 9.7 accuracy points on average, yet BC, DQN, and CQL land in the same test-accuracy band below it (robust to a tenfold buffer sweep and $N{=}2{,}000$ held-out examples). The bottleneck is local representational ambiguity: CQL closes the imitation gap without a deployment gain (not conservatism), regret clusters tightly across learners (not tie-breaking), and the three learners converge on test accuracy (not shift). The next iteration should change the state or collect new data, not tune the offline learner further.