SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 6: CCLMF results on MIRT and NCD.
Metrics	Model	no dropout	10% dropout	20% dropout	30% dropout	40% dropout	50% dropout
AUC	MIRT	0.6379	0.6412	0.6398	0.6399	0.6342	0.6363
CC-MIRT	0.7059 (+0.0680)	0.7025 (+0.0612)	0.6998 (+0.0600)	0.6998 (+0.0599)	0.6957 (+0.0615)	0.6918 (+0.0555)
ACC	MIRT	0.6832	0.7037	0.6869	0.6886	0.6889	0.6991
CC-MIRT	0.7854 (+0.1022)	0.7834 (+0.0797)	0.7826 (+0.0958)	0.7833 (+0.0947)	0.7822 (+0.0933)	0.7797 (+0.0806)
RMSE	MIRT	0.4902	0.4821	0.4884	0.4916	0.5013	0.4949
CC-MIRT	0.3948 (-0.0954)	0.3965 (-0.0856)	0.3973 (-0.0911)	0.3973 (-0.0943)	0.3983 (-0.1029)	0.3999 (-0.0950)
AUC	NCD	0.6885	0.6846	0.6797	0.6787	0.6736	0.6675
CC-NCD	0.7106 (+0.0221)	0.7061 (+0.0215)	0.7028 (+0.0231)	0.7007 (+0.0221)	0.6953 (+0.0216)	0.6895 (+0.0221)
ACC	NCD	0.7613	0.7662	0.7682	0.7606	0.7635	0.7640
CC-NCD	0.7859 (+0.0246)	0.7834 (+0.0172)	0.7819 (+0.0137)	0.7814 (+0.0208)	0.7812 (+0.0177)	0.7817 (+0.0177)
RMSE	NCD	0.4109	0.4095	0.4081	0.4127	0.4121	0.4133
CC-NCD	0.3966 (-0.0143)	0.3973 (-0.0122)	0.3981 (-0.0100)	0.3991 (-0.0136)	0.3998 (-0.0123)	0.4009 (-0.0124)
Pre-training stage. CCLMF aims to leverage valuable insights gleaned from the vast data in the source course. In the pre-training stage, a CDM is trained in the source course, generating an informative student representation  $\boldsymbol{u}^s$ . Specifically, our CCLMF can be employed on CDMs which characterize student proficiency as:
$$
\boldsymbol {u} _ {i} ^ {s} = H _ {\mathrm {C D M}} \left(s _ {i}; \boldsymbol {w} _ {h}\right), \tag {1}
$$
where  $\boldsymbol{w}_h$  denotes the parameters of  $H_{\mathrm{CDM}}$ , and  $H_{\mathrm{CDM}}$  is a function abstracted from CDM which can calculate each student's latent proficiency representation  $\boldsymbol{u}_i^s$ . The dimensionality of vector  $\boldsymbol{u}_i^s$  is  $d^s$  which is usually related to the number of knowledge concepts and the number of problems. The generated  $\boldsymbol{u}^s$  contains personalized and auxiliary information that can be utilized in the meta stage.
Meta stage. Due to individual differences, the relationships between student proficiency in the source and target courses can vary significantly from one student to another. Therefore we need to create personalized mapping functions for each student in order to retain students' individual characteristics. In the meta stage, we utilized a meta network to learn personalized mapping functions for each student. The meta network  $G(\cdot)$  is formulated as:
$$
\boldsymbol {w} _ {\boldsymbol {u} _ {i}} = G \left(\boldsymbol {u} _ {i} ^ {s}; \boldsymbol {w} _ {g}\right), \tag {2}
$$
where  $\pmb{w}_{g}$  is the parameters of  $G(\cdot)$  and  $\pmb{w}_{\pmb{u}_i}$  is used as the parameters of the mapping function. The personalized mapping function  $F_{\pmb{u}}(\cdot; \pmb{w}_{\pmb{u}})$  then produces personalized transformed student's representation in the target course as:
$$
\boldsymbol {u} _ {i} ^ {t} = F _ {\boldsymbol {u} _ {i}} \left(\boldsymbol {u} _ {i} ^ {s}; \boldsymbol {w} _ {\boldsymbol {u} _ {i}}\right). \tag {3}
$$
Instead of mapping-oriented optimization used by Man et al.[18], we directly used the performance of diagnostic tasks as our optimization goal to train the meta network. This task-oriented training procedure advances in making full use of the ground truth values rather than approximate intermediate results. Therefore, the meta network  $G(\cdot)$  as well as the mapping function  $F_{\mathbf{u}}(\cdot; \mathbf{w}_{\mathbf{u}})$  are trained together using data in the target course.
Given the ground truth value  $r$  from  $\mathcal{R}^t$  and the CC-CDM's final output  $\hat{r}_i$  which is generated based on  $\boldsymbol{u}_i^t$ , the task-oriented loss can be formulated as:
$$
\operatorname {l o s s} _ {\mathrm {C C - C D M}} = - \sum_ {i} \left(r _ {i} \log \hat {r} _ {i} + \left(1 - r _ {i}\right) \log \left(1 - \hat {r} _ {i}\right)\right). \tag {4}
$$
Inference. The goal of CCLMF is to accurately measure students' level of proficiency in the target course. During inference, for any student  $s_j$  who is new to the target course, their level of proficiency can be determined by their personalized transformation function  $\boldsymbol{u}_j^t = F_{\boldsymbol{u}_j}(\boldsymbol{u}_j^s; \boldsymbol{w}_{\boldsymbol{u}_j})$ .
The whole procedure of CCLMF is summarized in Algorithm 1. Detailed implementation of CCLMF on NCD [27] can be found in Appendix C.
4.3 Experiment Settings
We conducted CCLMF on a traditional cognitive diagnosis model MIRT [24] and a deep-learning-based model NCD [27], called CC-MIRT and CC-NCD respectively.
Datasets. We constructed the cross-course datasets based on the datasets shown in Table 4. As depicted in Figure 4(a), the correlation coefficient between students' performance in Python Programming (Python) and Java Programming (Java) is 0.65, indicating a relatively high correlation. This high correlation makes these two courses well-suited for addressing cold-start problems. Python Programming was chosen as the source course. To simulate cold-start scenarios, 332, 568 response logs (7% of each student's response logs) from Java Programming were selected to form the target course. We reserved 20% of response logs in the target course as the test set and then conducted experiments on sub-datasets with varying degrees of sparsity. Specifically, we randomly dropped 10%, 20%, 30%, 40%, and 50% of the remaining data and split the resulting data into 7/1 as train-valid set. To reduce the influence of randomness, we repeated the dropout process 10 times for each dropout ratio, then reported the average results across the 10 sets of data.
Settings and Metrics. The meta network was implemented as a two-layer perceptron with input-size  $K^s$ , output-size  $K^s \times K^t$  and hidden-size 100, where each linear layer was followed by a RELU activation function. The weights were initialized by Xavier [10]. The batch size and learning rate are 128 and  $1 \times 10^{-3}$ . All experiments were executed on a Linux server with two GeForce RTX 3090s. The evaluation metrics include Area Under the ROC Curve (AUC) [2], Prediction Accuracy (ACC) and Root Mean Square Error (RMSE).
4.4 Experimental Results and Analysis
Table 6 shows the superiority of CCLMF over baseline models. CCLMF has better performance on both NCD and MIRT models with different dropout ratios on all metrics. Specifically, CCLMF achieves an average improvement of  $4.2\%$  on AUC,  $5.5\%$  on Accuracy, and  $5.3\%$  on RMSE.
To investigate the performance of our model over students of different sparsity levels, we show the performance with respect to the number of response logs a student has in Figure 6. Note that we did not re-train the model with different sets of students, instead we divided the test set into different groups by the number of logs per student. We observe that the performance improvement of CCLMF is more significant for students with fewer response logs, highlighting the advantage of our model in cold-start scenarios.
groups of students with different number of logs
Figure 6: AUC on NCD and CC-NCD w.r.t. student groups with varying degrees of sparsity.
5 Experiments on CD and KT Tasks
To demonstrate PTADisc's support for CD and KT, we specifically selected four courses with varying response log scales, namely Probability and Statistics (Probability), Linux System (Linux), Database Technology and Application (DB), and Computational
Table 7: Datasets for CD and KT.
Course Name	Probability	Linux	DB	Comp
Students	557	4,398	12,646	45,329
Problems	1,054	2,678	3,616	8,399
Concepts	247	284	325	477
Response Logs	46,106	391,434	2,363,206	6,504,414
Logs per Student	82.78	89.00	186.87	143.49
Thinking (Comp), as seen in Table 7, which were also marked in Figure 4(b) with vertical dashes.
5.1 Baseline Models
For CD, we considered the following baseline methods: three traditional methods DINA [5, 26], IRT [6], and MIRT [24], deep-learning method NCD [27] and graph based method RCD [8]. For
KT, we considered the following baseline methods: deep sequential method DKT [21], memory augmented method DKVMN [32], attention-based methods AKT [9] and SAKT [20], graph based methods GIKT [30] and SGKT [29], and pre-training based method PEBG [16]. Due to the intensive computing resources required by RCD, we did not conduct RCD on two courses with relatively large-scale data, which are DB and Comp. Additional information of these baseline models can be found in Appendix D.
5.2 Experiment Settings and Metrics
For each baseline model, we employed the same parameter settings and optimization methods as described in their respective papers to ensure fairness in the comparison. The evaluation metrics used for CD included AUC, ACC, and RMSE, while for KT, the evaluation metrics were AUC and ACC, which are consistent with commonly used metrics in the literature.
5.3 Experimental Results and Analysis
The results of the CD and KT tasks have yielded notable findings, as shown in Table 8. Firstly, we observed that the dataset size has a significant influence on model performance, with higher prediction accuracy observed for larger datasets. Secondly, we noted in Table 8 that the MIRT model performance was generally higher than that of the NCD model; this contrasts with the findings in Table 6. We attribute this discrepancy to the cross-course dataset's lower average number of student response logs (i.e. approximately 10 logs per student), compared to the larger dataset with over 80 logs per student, as shown in Table 7. These results suggest that the number of logs per student significantly influences model performance, and that the NCD model may outperform the traditional MIRT model specifically in cases where there are fewer student logs on average. Thirdly, PEBG achieved the best AUC performance across all datasets in the KT task, which demonstrates the effectiveness of employing pre-training techniques to capture the heterogeneous educational data.
Table 8: Baselines of existing CD and KT models on PTADisc.
Dataset Name	Metric	DINA	IRT	MIRT	NCD	RCD	DKT	DKVMN	SAKT	AKT	GIKT	SGKT	PEBG
Probability	AUC	0.6569	0.7257	0.7324	0.7092	0.7485	0.6876	0.6815	0.6879	0.7123	0.7086	0.7079	0.7320
ACC	0.6121	0.7097	0.7112	0.6894	0.7196	0.7025	0.6961	0.6721	0.6978	0.6883	0.6938	0.6977
RMSE	0.5141	0.4490	0.4730	0.4590	0.4346	-	-	-	-	-	-	-
Linux	AUC	0.7577	0.8199	0.8168	0.8171	0.8318	0.7898	0.7856	0.7756	0.8074	0.8173	0.8156	0.8379
ACC	0.7053	0.7802	0.7799	0.7755	0.7860	0.7726	0.7713	0.7665	0.7849	0.7791	0.7801	0.8040
RMSE	0.4493	0.3900	0.4023	0.3934	0.3841	-	-	-	-	-	-	-
DB	AUC	0.7141	0.7901	0.8121	0.7901	-	0.7813	0.7635	0.7562	0.7956	0.8101	0.7996	0.8381
ACC	0.7856	0.8322	0.8424	0.8299	-	0.8312	0.8281	0.8181	0.8383	0.8353	0.8299	0.8373
RMSE	0.3934	0.3493	0.3407	0.3504	-	-	-	-	-	-	-	-
Comp	AUC	0.7137	0.7819	0.8096	0.7734	-	0.7978	0.7811	0.7717	0.8091	0.8091	0.8172	0.8281
ACC	0.7303	0.7929	0.8018	0.7880	-	0.8276	0.8234	0.8012	0.8283	0.8337	0.8274	0.8194
RMSE	0.4335	0.3808	0.3749	0.3849	-	-	-	-	-	-	-	-
Outlook: We describe concrete ongoing and future work based on PTADisc. Specifically,
- We will conduct research about adaptive learning and personalized educational planning, and incorporate them into a personalized learning system alongside the CCLMF model as shown in Figure 1(a). We will also analyze the group-level student learning behaviors.
- We will explore programming knowledge tracing based on PTADisc which contains a large amount of multi-round programming problem submission records and rich evaluation information.
Limitation: The original content text of the problems cannot be shared currently due to copyright constraints. We intend to disclose the content by extracting text features in the future.
Conclusion: PTADisc is a diverse, immense, student-centered and cross-course dataset that enables researchers to conduct previously infeasible cross-course studies. Based on PTADisc, we developed CCLMF to alleviate the difficulty of diagnosing student knowledge states in the cold-start scenario. Furthermore, we demonstrate the broad range of applications of our dataset by reporting on the performance of baseline models for CD and KT tasks over PTADisc.
The authors wish to acknowledge the generous support and contributions of Hangzhou PAT Education Technology Co. Ltd. for this research. This work was supported by the National Natural Science Foundation of China (No.62037001, No.62307032, No.62293550), Shanghai Rising-Star Program (23QA1409000), National Key R&D Program of China (No. 2022ZD0117104), and the Starry Night Science Fund at Shanghai Institute for Advanced Study (SN-ZJU-SIAS-0010).
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PTADisc: A Cross-Course Dataset Supporting Personalized Learning in Cold-Start Scenarios (Appendix)
A Related Work 2
A.1 Cognitive Diagnosis and Knowledge Tracing 2
A.2 Cross-Domain Recommendation 2
A.3 Other educational applications 2
B Dataset Statistics 3
C Implementation Details 4
D Baseline Model Details 5
E Supplementary Experiment Results 6
Our code, dataset, and detailed description for the dataset are available at https://github.com/wahr0411/PTADisc.git.
A.1 Cognitive Diagnosis and Knowledge Tracing
The goal of cognitive diagnosis (CD) is to assess students' level of proficiency of different knowledge concepts through the prediction process of student performance, given students' exercise records, aka response logs. Traditional psychometric-based methods include Item Response Theory (IRT) [18], MIRT [19] and DINA [4, 22]. These methods depend on manually designed functions and the effectiveness requires a large number of psychological experiments to verify, which are labor-intensive and lack of ability to capture complex relationships between students, problems, and knowledge concepts. Recent years, with the development of artificial intelligence [10], deep learning-based cognitive diagnosis models have been developed [23, 6, 9, 28]. Specifically, NCD [23] incorporates neural networks to learn the complex exercising interactions. And RCD [6] models the interactive and structural relations via a multi-layer student-problem-concept relation map.
The goal of knowledge tracing (KT) is to dynamically model students' knowledge proficiency through her historical learning records, so as to predict her performance to new problems. Traditional probabilistic KT models assume students' knowledge state as a set of binary variables where each variable represents whether a student masters an individual concept or not, such as Bayesian Knowledge Tracing (BKT) [3]. Recent years, deep learning-based KT models are proposed for learning valid representations especially when large amounts of data are available, such as DKT [21] and DKVMN [26]. Further, from the perspective of model structure, a few methods based on transformers (SAKT [15]), GNNs (SGKT [24]), and pre-training frameworks (PEBG [11]) are proposed.
A.2 Cross-Domain Recommendation
Cross-domain recommendation is a promising method to alleviate data sparsity and the cold-start problem [30, 27, 2]. Several models have been proposed, including CMF [20], which uses shared parameters for all domains, and CST [14], which transfers knowledge about users and items from auxiliary data sources. Mapping-based methods have been shown to be effective in solving cold-start recommendation problems [12], by learning a mapping function from the source domain to the target domain. However, these methods have limited generalization ability for cold-start items or users. To address this issue, TMCDR [29] introduces meta learning to improve the generalization ability and PTUPCDR [30] further improves TMCDR by learning personalized bridges for each user. While the cross-domain problem has been widely explored in the recommendation domain, there is limited research on cross-course learner modeling in personalized learning.
A.3 Other educational applications
Prerequisite discovery refers to the task of identifying and establishing the sequence or order in which concepts or topics should be learned or presented, ensuring that foundational concepts are understood before more advanced ones [13]. Suppose a MOOC corpus is composed by  $n$  courses in the same subject area, denoted as  $\mathcal{D} = \{\mathcal{D}_1,\dots ,\mathcal{D}_i,\dots ,\mathcal{D}_n\}$ , where  $\mathcal{D}_i$  signifies an individual course. Course concepts are subjects taught in the course, i.e., the concepts not only mentioned but also discussed and taught in the course. Let us denote the course concept set of  $\mathcal{D}$  as  $\mathcal{C} = \mathcal{C}_1\cup \dots \cup \mathcal{C}_n$ , where  $\mathcal{C}_i$  representing the concepts intrinsic to  $\mathcal{D}_i$ . Prerequisite relation learning in MOOCs is formally defined as follows. Given a MOOC corpus  $\mathcal{D}$  and its corresponding course concepts  $\mathcal{C}$ , the objective is to learn a function  $\mathcal{P}:\mathcal{C}^2\to \{0,1\}$  that maps a concept pair  $\langle a,b\rangle$ , where  $a,b\in \mathcal{C}$ , to a binary class that predicts whether  $a$  serves as a foundational prerequisite for concept  $b$ .
Computerized adaptive testing (CAT) is an emerging testing format in many standardized examinations, aiming to rapidly and accurately diagnose a candidate's level of knowledge mastery through personalized test items [1]. Let's conceptualize a set of students represented by  $\mathcal{S} = \{s_1,s_2,\dots ,s_N\}$ , a problem set represented by  $\mathcal{P} = \{p_1,p_2,\ldots ,p_M\}$  and a set of knowledge concepts represented by  $\mathcal{C} = \{c_{1},c_{2},\ldots ,c_{K}\}$  related to the problems. We denote the record of student  $s_i$  answering problem  $p_j$  as a triplet  $r_{ij} = \langle s_i,p_j,a_{ij}\rangle$ , where  $a_{ij}$  equals 1 if  $s_i$  answers  $p_j$  correctly, and 0 otherwise. Problem set  $\mathcal{P}$  is divided into a tested set  $\mathcal{P}_T$  and an untested set  $\mathcal{P}_U$ . When introduced to a novel student  $s_i\in S$ , a problem pool  $\mathcal{P}$  with knowledge concepts  $\mathcal{C}$ , the challenge is to architect a strategy  $\mathcal{A}$  to select a  $X$ -size question set  $\mathcal{P}_T = \{p_1^*,p_2^*,\dots ,p_X^*\}$  step by step that has the maximum quality and diversity. Prior to the testing phase, we set up an abstract cognitive diagnosis model  $\mathcal{M}$  with
parameters  $\theta$  capturing knowledge states. During testing, at step  $t(1\leq t\leq X)$ , we select one question  $p_t^* = \mathcal{A}(\mathcal{P}_U,\mathcal{M})$ , then observe a new interaction test record  $r_{it}^{*} = \langle s_i,p_t^*,a_{it}^*\rangle$  and update the knowledge states, i.e.,  $\theta$ , in  $\mathcal{M}$  instantly. After testing, we measure the effectiveness of  $\mathcal{A}$  by computing  $\operatorname{Inf}(\mathcal{A})$  and  $\operatorname{Cov}(\mathcal{A})$ , where  $\operatorname{Inf}(\mathcal{A})$  denotes the measurement of quality and  $\operatorname{Cov}(\mathcal{A})$  denotes the measurement of diversity.
Educational recommendation lies in constructing a recommend system that can process the interactions between students and questions. This system should be capable of making appropriate learning suggestions to students [8]. In the context of a digital educational platform, assume there are  $N$  students and  $P$  problems. We record the exercising process of a certain student  $n = \{(p_1,r_1),(p_2,r_2),\dots ,(p_t,r_t)\} ,n\in \mathcal{N}$  where  $p_t\in \mathcal{P}$  represents the problems that student  $n$  practices at her time step  $t$  , and  $r_t$  denotes the corresponding score. Conventionally, a correct response to problem  $p_t$  is denoted by  $r_t$  equals to 1, , and an incorrect response by  $r_t$  equals to 0. Each problem  $p\in \mathcal{P}$  is characterized by a triplet  $p = \{w,c,d\}$  . Specifically, the element  $w$  represents its text content as a word sequence  $p = \{w_{1},w_{2},\ldots ,w_{W}\}$  .  $c\in \mathcal{C}$  describes its knowledge concept coming from all  $K$  concepts. And  $d$  means its difficulty factor.
(d)
Figure 1: Distribution of the number of students, problems, concepts and non-programming logs over courses in PTADisc.
CCLMF is a model-agnostic framework that can be applied to various CD or KT models. Here, we take NCD as an example and showcase the implementation details of CCLMF based on NCD, namely CC-NCD. After pre-training the NCD model in the source course, the student's proficiency representation in the source course can be obtained by extracting the corresponding row from the
matrix  $\mathbf{A}^s$  given the student ID  $i$ :
$$
\boldsymbol {u} _ {i} ^ {s} = \mathbf {A} _ {\mathrm {N C D}} ^ {s} [ i ], \tag {1}
$$
where  $\mathbf{A}^s$  is the student representation matrix learned by NCD.
In the meta stage, we used a two-layer perceptron (MLP) as the meta network. This meta network then generates a transformation matrix for each student as the personalized mapping function:
$$
\boldsymbol {T} _ {K ^ {s} \times K ^ {t}} = \operatorname {M L P} \left(\boldsymbol {u} _ {i} ^ {s}; \theta\right), \tag {2}
$$