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An Autoencoder-Like Nonnegative Matrix Co-Factorization for Improved Student Cognitive Modeling
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Proposes AE-NMCF, an autoencoder-like nonnegative matrix co-factorization that embeds psychometric monotonicity into an encoder-decoder pipeline to improve knowledge proficiency estimation while keeping performance prediction accurate, optimized by projected gradient block coordinate descent with Lipschitz step sizes.
Problem
Student cognitive modeling needs both accurate prediction of student exercise performance and accurate estimation of knowledge proficiency, but matrix factorization methods predict well with uninterpretable latents while proficiency estimates are poor, especially under sparse response data.
Approach
Co-factorize the student response matrix and an exercise-knowledge association matrix sharing an exercise-characteristic factor, derive student knowledge proficiency as V^T U, and reconstruct responses through a probit link with exercise difficulty so that monotonicity between proficiency and success probability is enforced end-to-end.
Key results
- AE-NMCF attains top-2 ACC on all datasets except FrcSub, with average Friedman rank 1.33 on ACC and 1.67 on RMSE.
- On knowledge proficiency estimation (KRC rc), AE-NMCF rises above SNMCF on all datasets (Wilcoxon p = 0.031), e.g., 0.8738 vs. the best CDM on FrcSub.
- Ablation: removing the decoder degrades ACC substantially (e.g., SLP-Eng ACC 0.5511 vs. 0.7632 for full model).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use AE-NMCF instead of SNMCF | student performance prediction · Junyi-s | ACC: 0.6878±0.0192 -> 0.7065±0.0285 | Helped |
| Use AE-NMCF instead of SNMCF | student performance prediction · Quanlang-s | ACC: 0.7417±0.0051 -> 0.7531±0.0064 | Helped |
| Use AE-NMCF instead of SNMCF | student performance prediction · SLP-Bio-s | RMSE: 0.4236±0.0082 -> 0.3996±0.0060 | Helped |
| Use AE-NMCF instead of SNMCF | student performance prediction · FrcSub | RMSE: 0.3349±0.0029 -> 0.3476±0.0088 | Hurt |
| Use AE-NMCF instead of DeepCDF | student performance prediction · Junyi-s | RMSE: 0.3874±0.0036 -> 0.4514±0.0193 | Hurt |
| remove decoder (ablation) | AE-NMCF · FrcSub | ACC: 0.8267±0.0048 -> 0.7523±0.0118 | Hurt |
| remove decoder (ablation) | AE-NMCF · Junyi-s | ACC: 0.7065±0.0285 -> 0.6261±0.0524 | Hurt |
| remove decoder (ablation) | AE-NMCF · Quanlang-s | ACC: 0.7531±0.0064 -> 0.6187±0.0278 | Hurt |
| remove decoder (ablation) | AE-NMCF · SLP-Bio-s | ACC: 0.7553±0.0101 -> 0.6582±0.0099 | Hurt |
| remove decoder (ablation) | AE-NMCF · SLP-His-s | ACC: 0.8072±0.0019 -> 0.7224±0.0062 | Hurt |
| remove decoder (ablation) | AE-NMCF · SLP-Eng | ACC: 0.7632±0.0062 -> 0.5511±0.0184 | Hurt |
| remove encoder (ablation) | AE-NMCF · FrcSub | ACC: 0.8267±0.0048 -> 0.8156±0.0060 | Hurt |
Surprising findings
- Competing CDMs such as DINA and DeepCDF have strong RMSE on some datasets but poor ACC on others, indicating unstable performance across datasets.
- QRCDM gives good diagnostic results but its prediction performance suffers on several datasets.
Limitations
- Higher computational complexity than SNMCF (O(MNK^2) per block iteration).
- Diagnostic results for some knowledge concepts are overoptimistic because the model ignores knowledge prerequisite structure.
- Convergence guaranteed only to a critical point; global optimum not guaranteed from arbitrary initialization.
Experimental setup
Datasets: FrcSub Junyi-s Quanlang-s SLP-Bio-s SLP-His-s SLP-Eng
Benchmarks: FrcSub Junyi-s Quanlang-s SLP-Bio-s SLP-His-s SLP-Eng
Metrics: ACC RMSE KRC (rc)
Baselines: NMF MCF GNMF NMMF SNMCF DINA DIRT DeepCDF QRCDM
Builds on: nonnegative matrix factorization matrix co-factorization SNMCF DINA projected gradient method
Closest papers by meaning
- Towards Accurate and Fair Cognitive Diagnosis via Monotonic Data Augmentation (NeurIPS 2024 · similarity 0.85)
- Enhancing Cognitive Diagnosis Using Un-interacted Exercises: A Collaboration-Aware Mixed Sampling Approach (AAAI 2024 · similarity 0.85)
- EduLLM: Leveraging Large Language Models and Framelet-Based Signed Hypergraph Neural Networks for Student Performance Prediction (ICML 2025 · similarity 0.84)
- Collaborative Cognitive Diagnosis with Disentangled Representation Learning for Learner Modeling (NeurIPS 2024 · similarity 0.84)
- Toward Student-oriented Teacher Network Training for Knowledge Distillation (ICLR 2024 · similarity 0.84)
- Over-parameterized Student Model via Tensor Decomposition Boosted Knowledge Distillation (NeurIPS 2024 · similarity 0.84)
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