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阅读本paper之前，强烈建议先参考 Dempster–Shafer theory

（本paper有些公式的表述不是很清楚，存在歧义。注意，在表示近邻用户index时，i其实是没有意义的，关于文中相关符号的详细妙处见http://nuoku.vip/users/2/articles/167）

本文所谓的提高用户对推荐系统的信任度的道理在于，提供了推荐结果的支持证据。（这个证据来源于相似近邻，每个近邻提供一组证据，综合近邻集合，提供最终证据）

Dempster-shafer thery (DS证据理论)的核心步骤是：确定多个基本概率分配m_i (BBA, Basic belief assignment) ; 然后后将这些概率分配组合起来确定最后的概率分配，就可以做出决定了。（一般有固定的计算方法，可以通过调整这些步骤的表达，去拟合自己的问题域）

本文的要点（item-based CF）是如何根据近邻物品确定m函数以及如何组合这些m函数。过程如下表，其中对于m的定义用到了物品之间的距离，以及同一分值下的（例如该用户所有5分物品）距离分布。所以，本文应该会为每个用户的每一个未访问的items定制出一个m分配表，如下。

其中有意思的一点是：用户的 $r_{ρ}$ 越小，即同一评分的物品之间的距离越小（物品越集中），将目标物品也确定为该评分的置信度越小，即m出的值越小；另外，距离越大，置信度也会越小。

注意：本paper中，每列只有近邻物品对应的rating 行和最后一行有数值，其他为0.（模型可以修改为每行都有值），另外，可以通过理解表的个数，来理解算法。

根据用户u选择目标物品x，和对应的近邻物品y，计算 $r_{ρ}$ ，最终根据m_{x}做决策		m_{x,y1}	m_{x,y2}	m_{x,y3}	m_{x,y4}	m_{x,y}	m_{x}
	rating	m_{1,1}	m_{1,2}	m_{1,3}	m_{1,4}	m_{1,i}	m_{1}
$r_{ρ 1}$	1
$r_{ρ 2}$	2
$r_{ρ 3}$	3
$r_{ρ 4}$	4
$r_{ρ 5}$	5
	{1,2,3,4,5}

另外，建议：可以根据历史数据，建立objective function去学习各个证据的可靠性。

(1) SMONE: A Session-based Recommendation Model based on Neighbor Sessions with Similar Probabilistic Intentions

(2) Discrete Listwise Personalized Ranking for Fast Top-N Recommendation with Implicit Feedback

(3) MLP4Rec: A Pure MLP Architecture for Sequential Recommendations

(4) Self-supervised Graph Neural Networks for Multi-behavior Recommendation

(5) Collaborative Self-Attention Network for Session-based Recommendation

(6) Measuring the Popularity of Job Skills in Recruitment Market: A Multi-Criteria Approach

(7) Discrete Embedding for Latent Networks

(8) Exploiting the Dynamic Mutual Influencefor Predicting Social Event Participation

(9) Improving Sequential Recommendation with Knowledge-Enhanced Memory Network

(10) Next-item Recommendation with Sequential Hypergraphs

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文献基本信息

文献题目			去谷歌学术搜索
Improving the Trustworthiness of Recommendations in Collaborative Filtering under the Belief Function Framework
文献作者			Raoua Abdelkhalek
文献发表年限			2017
文献关键字
Dempster–Shafer theory; DS证据理论；证据合成规则
摘要描述
Collaborative Filtering (CF) consists of filtering data, predicting users’ preferences and providing recommendations accordingly. Commonly, neighborhood-based CF methods predict the future ratings based on similar users (user-based) or similar items (item- based) to perform recommendations. However, the reliability of the information provided by these pieces of evidence as well as the final predictions cannot be fully trusted. Incorporating trust in the recommendation process can be argued to be an important challenge in Recommender Systems (RSs). To tackle these issues, we propose new CF approaches under the belief function framework. The final prediction is obtained by fusing evidences from similar items or similar users using Dempster’s rule of combination. The prediction process of our evidential approaches is able to provide the users with a global overview of their possible preferences. This would lead to increase their confidence towards the system as well as their satisfaction. In this paper, we mainly highlight the benefits of incorporating uncertainty in CF approaches using the belief function theory. We present the preliminary results and also discuss our ongoing works, as well as the challenges in the future.