Learning-Oriented Question Recommendation Using Bloom’s Learning Taxonomy and Variable Length Hidden Markov Models - Transactions on Large-Scale Data-and Knowledge-Centered Systems - page 35

The Recommendation Model. Based on the learned model P , we define the
learning-oriented recommender (LoR). For each user with history log s ∈Q ∗ ,we

want to recommend a set R ( s ) ↆQ of N questions that satisfies the following:

N
arg max
q∈Q and q∈s

R ( s )= P ( q | s ) (9)

where arg max N returns the first N maximal arguments with respect to the given
function. In other words, the learning oriented recommender tries to recommend
the first N best questions that maximize the user's utility. In this case, the utility
is dependent on the learned model P .
P is learned according to a probabilistic graphical model based on hidden
VLMCs: one with hidden states T and then, for each ˄

a VLMC with hidden
states L . The observation states are given by Q over the question space

∈T

Q (see

Figure 4 ).

Fig. 4. The learning-oriented recommender

To learn such a model, first, the training sequences are projected on the topic
space using p ˄ and a VLMC over T is trained on them. As a result, the transition
model P ( T ( t +1) T (1: t ) ) is obtained.

Then, for each topic ˄ , a transition probability P ˄ ( L ( t +1)

|

L (1: t ) ) is learned
by training a VLMC over L on the projections of the question sub-sequences
within topic ˄ , using the learning objective projection function p ˆ .
We define the observation model P ( Q ( t +1)

|

T ( t +1) ,L ( t +1) ,Q (1: t ) ) as the prob-
ability of randomly sampling an unvisited question corresponding to topic
T ( t +1) = ˄ t +1 and learning objective L ( t +1) = ˆ t +1

|

˄ t +1 ,ˆ t +1 ,q 1 )= 0

if

( q t +1 ,˄ t +1 )

∈M ˄ ∨

( q t +1 ,ˆ t +1 )

∈M ˆ

P ( q t +1 | ,

1
S

otherwise

(10)

where S =

{ q ∈Q\{ q 1 ,...,q t }|

( q ,˄ t +1 )

∈M ˄ ∧

( q ,ˆ t +1 )

∈M ˆ }

.