Interactive Unknowns Recommendation in E-Learning Systems
Shan-Yun Teng 1 , Jundong Li 2 , Lo Pang-Yun Ting 1 , Kun-Ta Chuang 1 , Huan Liu 2
1 Dept. of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan
2 School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, USA
I NTRODUCTION
x
Knowns Unknowns
User
c1 Number c2 Arithmetic c3 Quadratic
c4 Cube c5 Pyramid c6 Cylinder
Concept Prerequisite
Concept Closeness
E-learning systems should provide supple- mentary resources to enrich the knowledge of users’ personal unknowns. Unfortunately, according to our analysis on the real log of user learning process, most users are not aware of his/her personal unknowns.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 10 20 30 40 50 60 70 80 90 100
Known and Unknown Rate
User ID
Unknown Known
Solving questions which users already un- derstood cannot effectively enrich their knowledge because of the lack of unknowns exploration. There is no teacher for users to interact with, and users’ knowledge changes over time, which cannot easily be aware by themselves. Therefore, how to interactively exploring users’ unknowns will be the key to the success of learning new knowledge.
User Request User
Unknown Recommendation
User Feedback User
Improvement Suggestion
User Progress Learning
from
User Feedback
Hi, I want to do some test.
The answer is a.
Ok, got it!
The answer is (c). This question is about “common
factor”. You can watch an online course through the link “http://commonfactor
/course”.
What is the greatest common factor of 12 and
18? (a) 2 (b) 3 (c) 6
UrBot
User
C AG M AB F RAMEWORK
q3 q4
q5 q6 q1
q2 c2
c3 c4
c5 c6
c7
c1
Q C
c2
c10
c4 c3
c7 c6
c8 c5
c1
c9 c2 c1
c3 c4 c5
c6 c7 c8
c10
c9 Question-Concept Graph Concept Relational
Graph
Concept Progress Graph
User-Question Rating Matrix
d d d d
Arm at :
question selection Reward rt :
user feedback
User
1 1 1 1
1 1 1
1 1 ? -1
? -1
-1 -1
-1
? -1
?
?
?
? 1
1
-1 -1 -1
-1 1
?
u1 u2 u3 u4 u5
q1 q2 q3 q4 q5 q6 Multi-Armed Bandit
Concept-Aware Graph Embedding Latent Factor Vectors Learning
u2
u1
u7
u4
u8
u6 u3
u5
q4 q5 q6
q1
q2 User Affinity Graph
Contextual Contextual
q3 Question
Latent
Latent
In this paper, we propose the CagMab framework incorporating concept-aware graph em- bedding into the multi-armed bandit. We propose concept-aware graph embeddings to pre- serve the graph structures into matrix factorization (MF) model, which helps to capture the interactions between question-concept, concept closeness and concept prerequisite. Then, we are able to well optimize the latent factors of users and questions.
U ,Q,C
min β(O
uq) + γ(O
qc+ O
cr+ O
cp) = β 1 2
X
i,j
O
ij( R
ij− ~ u
i· ~ q
j)
2+ λ
u2 ||U||
2F+ λ
q2 ||Q||
2F− γ
X
eij ∈Eqc
w
ij(log p(c
j|q
i) + log p(q
i|c
j)) + X
eij ∈Ecr
w
ijlog p(c
i, c
j) + X
ci∈C,ck∈N2(ci)
w
iklog p(c
k|c
i)
+ X
eij ∈Ecp
r
1(c
i, c
j) log p(c
i, c
j) + X
pci→ck ∈P
r
2(c
i, c
k) log p(c
k|c
i)
(1)
We introduce both the latent factors and contextual factors of users and questions to the reward with user affinity graph in a multi-armed bandit framework.
r u
i,q
t= E[r u
i,q
t|~x u
i,q
t, ~ a u
i, ~ u i , ~ q t ] = ~ x T u
i,q
tΘ ~ a u
i| {z }
contextual term
+ ~ u i ~ q t
| {z }
latent term
+ε t .
(2)
P ROBLEM D EFINITION
Problem Statement: Let U = {u 1 , u 2 , ..., u n } be the set of n users, Q = {q 1 , q 2 , ..., q m } be the set of m questions, and C = {c 1 , c 2 , ..., c o } be the set of o concepts. For a user-question rating matrix R ∈ R n×m , R ij = 1 if user u i correctly answers question q j , R ij = −1 denotes u i gives wrong answer to q j , and R ij = ‘?’ means u i has not answered q j yet.
Also, we use A q ∈ R m×o , A r ∈ R o×o , and A p ∈ R o×o as the corresponding adjacency matrices of graphs G qc , G cr , and G cp , respec- tively.
Given: users U, questions Q, concepts C, user-question rating matrix R, and the pro- posed graphs G qc , G cr , and G cp ;
Select: a set of k questions (user un- knowns) for users by interactively exploring rating matrix R along with proposed graph structures encoded in the adjacency matrices A q , A r , and A p .
I NTERACTIVE R ECOMMENDATION PERFORMANCE
Metric Naïve -greedy TS UCB LinUCB COFIBA factorUCB GOBLin CagMab Precision@5 0.1420 0.1500 0.1320 0.1520 0.1300 0.1420 0.1360 0.1440 0.3319
Recall@5 0.1404 0.1329 0.1168 0.1470 0.1258 0.1099 0.1059 0.1343 0.2886 AUC@5 0.3310 0.3200 0.3160 0.3510 0.3200 0.3260 0.3060 0.3520 0.5810 Precision@10 0.1480 0.1440 0.1410 0.1460 0.1310 0.1340 0.1340 0.1470 0.2580 Recall@10 0.2727 0.2736 0.2800 0.2512 0.2296 0.2114 0.2178 0.2371 0.4084 AUC@10 0.4640 0.4570 0.4705 0.4630 0.4455 0.4270 0.4320 0.4535 0.5790
Table 1: Performance comparison in terms of Precision, Recall and AUC.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
greddy TS UCB Lin COFI factor GOB CagMab
Precision@5
Methods
(a) Precision@5.
0 0.05 0.1 0.15 0.2 0.25 0.3
greddy TS UCB Lin COFIBA factor GOB CagMab
Recall@5
Methods
(b) Recall@5.
0 0.05 0.1 0.15 0.2 0.25
greddy TS UCB Lin COFIBA factor GOB CagMab
Precision@10
Methods
(c) Precision@10.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
greddy TS UCB Lin COFIBA factor GOB CagMab
Recall@10
Methods
(d) Recall@10.
Figure 1: Performance comparison on dataset with 10% cold-start users in terms of Precision and Recall.
P ARAMETER SENSITIVITY
(a) w.r.t (β,γ) (b) w.r.t (β,d)
(c) w.r.t (γ,d)
Figure 2: Parameter sensitivity of CagMab.
C ASE S TUDIES
2.302 3.908
0 1 2 3 4 5 6 7 0
1 2 3 4 5 6 7
1 10 20 30 40 50 60 70 80 90 100
Richness
User ID
Richness Diversity Richness Max Diversity Max
Diversity
Figure 3: The richness and the diversity of recom- mended questions.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 10 20 30 40 50 60 70 80 90 100
Ratio of Unknowns
User ID
Unknown unknowns Known unknowns
