Answers.Body: <p><span class="math-container">$\text{rank}(f((r,e)|u))$</span> in <span class="math-container">$A_t(u)$</span> means to compute the value of scoring function <span class="math-container">$f$</span> for all pairs <span class="math-container">$(r,e)\in A_t$</span> which are conditioned by <span class="math-container">$u$</span>, then sort them in a descending order. The rank of the <span class="math-container">$f((r,e)|u)$</span> in this order is equal to <span class="math-container">$\text{rank}(f((r,e)|u))$</span>. Hence <span class="math-container">$\text{rank}(f((r,e)|u)) \leqslant \alpha$</span> means to select the <span class="math-container">$\alpha$</span> top most scored pairs.  </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-06-02T12:33:33.880Z
Answers.LastActivityDate: 2020-06-15T10:07:14.247Z
Answers.LastEditDate: 2020-06-15T10:07:14.247Z
Answers.UserDisplayName: OmG
Body: <p>I've been reading the paper <a href="https://arxiv.org/pdf/1906.05237.pdf" rel="nofollow noreferrer">Reinforcement Knowledge Graph Reasoning for Explainable Recommendation</a> (by Yikun Xian et al.) lately, and I don't understand a particular section:</p>
  <blockquote>
  <p>Specifically, the scoring function <span class="math-container">$f((r,e)|u)$</span> maps any edge <span class="math-container">$(r,e)$</span> to a real-valued score conditioned on user <span class="math-container">$u$</span>. Then, the user-conditional pruned action space of state <span class="math-container">$s_t$</span> denoted by <span class="math-container">$A_t(u)$</span> is defined as:</p>
  <p><span class="math-container">$A_t(u) = \{(r,e)| rank(f((r,e)|u))) \leq \alpha ,(r,e) \in A_t\} $</span></p>
  <p>where <span class="math-container">$\alpha$</span> is a predefined integer that upper bounds the size of the action space.</p>
  </blockquote>
  <p>Details about the scoring function can be found in the attached paper.</p>
  <p>What I don't understand is: <strong>What does rank mean, here? Is the thing inside of it a matrix?</strong></p>
  <p>It would be great if someone could explain the expression for the user conditional pruned action space in greater detail.</p>
  
Tags: <reinforcement-learning><papers><recommender-system><knowledge-graph><knowledge-graph-embeddings>
Title: What is meant by the rank of the scoring function here?
UserDisplayName: stoic-santiago
ThreadText: # What is meant by the rank of the scoring function here?
  
  (Asked by: username_0 on 2020-06-02)
  
  I've been reading the paper [Reinforcement Knowledge Graph Reasoning for Explainable Recommendation](https://arxiv.org/pdf/1906.05237.pdf) (by Yikun Xian et al.) lately, and I don't understand a particular section:
  
  > Specifically, the scoring function $f((r,e)|u)$ maps any edge $(r,e)$ to a real-valued score conditioned on user $u$. Then, the user-conditional pruned action space of state $s\_t$ denoted by $A\_t(u)$ is defined as:
  >
  > $A\_t(u) = \{(r,e)| rank(f((r,e)|u))) \leq \alpha ,(r,e) \in A\_t\} $
  >
  > where $\alpha$ is a predefined integer that upper bounds the size of the action space.
  
  Details about the scoring function can be found in the attached paper.
  
  What I don't understand is: **What does rank mean, here? Is the thing inside of it a matrix?**
  
  It would be great if someone could explain the expression for the user conditional pruned action space in greater detail.
  
  **Tags:** reinforcement-learning, papers, recommender-system, knowledge-graph, knowledge-graph-embeddings
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-06-02. Score: 1 | Accepted answer
  
  $\text{rank}(f((r,e)|u))$ in $A\_t(u)$ means to compute the value of scoring function $f$ for all pairs $(r,e)\in A\_t$ which are conditioned by $u$, then sort them in a descending order. The rank of the $f((r,e)|u)$ in this order is equal to $\text{rank}(f((r,e)|u))$. Hence $\text{rank}(f((r,e)|u)) \leqslant \alpha$ means to select the $\alpha$ top most scored pairs.
  
  
  ---
  
  