在非 5 星评级系统中应用贝叶斯平均值

Question

我期待应用贝叶斯方法来优先考虑可以考虑喜欢、不喜欢和评论计数的列表。

here 中列出的方法依赖于贝叶斯平均值：

$bayesian_rating = ( ($avg_num_votes * $avg_rating) + ($this_num_votes * $this_rating) ) / ($avg_num_votes + $this_num_votes);

就我而言，没有$avg_rating，因为它不是一个 5 星级系统，它永远不会存在，喜欢、不喜欢和评论的数量总是在增加，因此我需要注意列表的真实表示.

here 中的解决方案不足以决定方法。

如果我想应用数学方法，最好的解决方案是什么？

编辑添加： 参考。 @Ina , 点赞数乘以 5 就可以体现五星系统, 是五星系统中的最高值。

回到代码，在添加了一些额外的变量来处理（喜欢、不喜欢、评论数量、添加到购物篮的次数）之后，我不确定我可以填写 $avg_rating 和 @ 987654327@与？

这是目前为止的代码：

// these values extracted from the database
    $total_all_likes = 10; //total likes of all the products
    $total_all_dislikes = 5; //total dislikes of all the products
    $total_all_reviews = 7; //total reviews of all the products
    $total_all_addedToBasket = 2; //total of products that has been added to basket for all the users
    $total_all_votes = ($total_all_likes *5) + $total_all_dislikes;  //total of likes and dislikes
    $total_all_weight = $total_all_votes + $total_all_reviews + $total_all_addedToBasket; //total interactions on all the products
    $total_all_products = 200; //total products count

    //Get the average
    $avg_like = ($total_all_likes*5)/$total_all_votes; //Average of likes of all the votes 
    $avg_dislike = $total_all_dislikes/$total_all_votes; //Average of dislikes of all the votes 
    $avg_reviews = $total_all_reviews/$total_all_products; //Average of reviews of all the products
    $avg_addedToBasket = $total_all_addedToBasket/$total_all_products; //Average of added to basket count of all the products
    $avg_weight = $avg_like + $avg_dislike + $avg_reviews + $avg_addedToBasket; //Total average weight

    //New product, it has not been liked, disliked, added to basket or reviewed 
    $this_like = 0 *5;
    $this_dislike = 0;
    $this_votes  = $this_like + $this_dislike;
    $this_review     = 0;
    $this_addedToBasket = 0;
    $this_weight = $this_votes + $this_review + $this_addedToBasket;

    //$avg_rating
    //$this_rating

    $bayesian_rating = (($avg_weight * $avg_rating) + ($this_weight * $this_rating) ) / ($avg_weight + $this_weight);   

Answer 1

你有一个二进制系统，而不是一个 5 星系统。人们要么“喜欢”，要么“不喜欢”。因此，评级自然是一个介于 0 和 1 之间的数字，计算方式如下：

likes / (likes + dislikes)

您无需乘以 5 即可模仿 5* 评级系统。

然后你的代码变成：

$avg_rating = $total_all_likes / ($total_all_likes + $total_all_dislikes)
$this_rating = $this_like / ($this_like + $this$total_num_positive_votes / $total_num_votes) // Check you're not dividing by 0
$bayesian_rating = (($avg_num_votes * $avg_rating) + ($this_num_votes * $this_rating) ) / ($avg_num_votes + $this_num_votes);

如果您还想考虑“篮子”和“评论”的数量，您可以简单地将它们视为更多的“重量”

$this_weight = $this_addedToBasket + $this_votes + $this_review;
$avg_votes = $total_all_votes / $total_all_products;
$avg_weight = $avg_addedToBasket + $avg_votews + $avg_reviews;
$bayesian_rating = (($avg_weight * $avg_rating) + ($this_weight * $this_rating) ) / ($avg_weight + $this_weight);    

这会给你一个很好的相对排名，但是如果你希望看到 0 到 1 之间有意义的分数，那么你可以通过除以篮子和评论增加的权重来标准化。