SQL/PostgreSQL 中带加权过滤器的随机行选择

Question

我有一道题 table，我需要做 X 道题来准备考试。问题需要根据多个标准（学科、机构、地区等）进行筛选，每个标准具有不同的权重。

过滤器权重是在查询之外动态设置和规范化的。例如：

主题 1 — 0.4
科目 2 — 0.1
科目 3 — 0.5
机构 1 — 0.2
机构 2 — 0.04
机构 3 — 0.76
区域 1 — 1

其他几点：

今天，我有 10 个不同的过滤器（主题、机构、区域等），但用户可以 select 以多种方式混合（例如：10 个主题、5 个机构、30 个区域等），如上例所示。
问题 table 有 ~500k 行；
过滤器是 N — N 个问题；
过滤后，我想限制return行；
如果某个过滤器不能提供更多的问题，则必须考虑其他的（记住：我想准备一个测试——如果我还有问题，必须使用它们）
我非常关心这个查询的性能。

为了说明，如果我不想对过滤器进行加权，我会这样做：

SELECT
    *
FROM
    public.questions q
    INNER JOIN public.subjects_questions sq ON q.id = sq.question_id
    INNER JOIN public.subjects s ON s.id = sq.subject_id
    INNER JOIN public.institutions_questions iq ON iq.question_id = q.id
    INNER JOIN public.institutions i ON i.id = iq.institution_id
    INNER JOIN public.areas_questions aq ON aq.question_id = q.id
    INNER JOIN public.areas a ON a.id = aq.area_id
WHERE
    s.id IN :subjects
    AND a.id IN :areas
    AND i.id IN :institutions
ORDER BY
    random() limit 200

期望的输出：

Question — Subject — Institution — Area

我的想法是这样的：

使用过滤器 return 编辑的问题创建 CTE；必须考虑到同一个问题可以 return 被多个过滤器编辑——我是否需要分开评估每个过滤器然后 UNION ALL 来解决这个问题？也必须分配问题来自哪个过滤器；
创建另一个具有权重和关联的相应过滤器的 CTE；
加入 CTE，但此时必须对问题进行分组并对权重求和；
应用 Window 函数和 return 结果，限于 X 行 (LIMIT X)。

你会如何编写这样的查询/解决这个问题？

Answer 1

像这样的事情呢。这只是为了演示这个想法，我会把细节留给你。如果您不熟悉这种随机选择方法，如果您随机生成一个介于 0 和 1 之间的数字，它有 40% 的机会小于 .4。所以 rand() <= .4 将 return 40% 的时间为真。

假设您已经或可以创建一个看起来有点像这样的 "Filters" 实体

CREATE TABLE Filters
  ( FieldName VARCHAR(100), 
    FieldValue VARCHAR(100),
    Prob Float -- probability of selection based on Name and Value
  );

SELECT DISTINCT TMP.* -- The fields you want. Distinct needed to get rid of 
                      -- records which pass multiple conditions.
  FROM (SELECT YRSWF.*,
               RAND() AS rnd
          FROM YourResultSetWithoutFilters YRSWF -- You can code the details
       ) TMP  
 INNER
  JOIN Filters F
    ON (
       TMP.Subject = F.FieldValue
   AND F.FieldName = 'Subject'
   AND TMP.rnd <= F.prob
       )
    OR (
       TMP.Institution = F.FieldValue
   AND F.FieldName = 'Institution'
   AND TMP.rnd <= F.prob
       )
    OR ( 
       TMP.Area = F.FieldValue
   AND F.FieldName = 'Area'
   AND TMP.rnd <= F.prob
       );

Answer 2

好的。设法解决了它。基本上，使用问题中已经概述的策略和 here -- I had already seen this post before, but I was (and still am) trying to solve in a more elegant way -- something like this 的一些帮助，但对于多行 --，不需要手动创建 "bounds"。

让我们逐步尝试：

由于具有权重的过滤器来自架构外部，让我们创建一个 CTE：

WITH filters (type, id, weight) AS (
    SELECT 'subject', '148232e0-dece-40d9-81e0-0fa675f040e5'::uuid, 0.5
    UNION SELECT 'subject', '854431bb-18ee-4efb-803f-185757d25235'::uuid, 0.4
    UNION SELECT 'area', 'e12863fb-afb7-45cf-9198-f9f58ebc80cf'::uuid, 1
    UNION SELECT 'institution', '7f56c89f-705e-45c7-98fb-fee470550edf'::uuid, 0.5
    UNION SELECT 'institution', '0066257b-b2e3-4ee8-8075-517a2aa1379e'::uuid, 0.5
)

现在，让我们过滤行，忽略权重（暂时），这样以后我们就不需要处理整个 table:

WITH filtered_questions AS (
    SELECT
        q.id,
        s.id subject_id,
        a.id area_id,
        i.id institution_id
    FROM
        public.questions q
        INNER JOIN public.subjects_questions sq ON q.id = sq.question_id
        INNER JOIN public.subjects s ON s.id = sq.subject_id
        INNER JOIN public.institutions_questions iq ON iq.question_id = q.id
        INNER JOIN public.institutions i ON i.id = iq.institution_id
        INNER JOIN public.areas_questions aq ON aq.question_id = q.id
        INNER JOIN public.areas a ON a.id = aq.area_id
    WHERE
        subject_id IN (SELECT id from filters where type = 'subject')
        and institution_id IN (SELECT id from filters where type = 'institution')
        and area_id IN (SELECT id from filters where type = 'area')
)

同一个问题可以被多个过滤器选中，增加被选中的几率。我们必须更新权重来解决这个问题。

WITH filtered_questions_weights_sum AS (
    SELECT
        q.id,
        SUM(filters.weight) weight_sum
    FROM filtered_questions q
    INNER JOIN filters
    ON (filters.type = 'subject' AND q.subject_id IN(filters.id))
    OR (filters.type = 'area' AND q.area_id IN(filters.id))
    OR (filters.type = 'institution' AND q.institution_id IN(filters.id))
    GROUP BY q.id
)

正在生成边界，如暴露 here。

WITH cumulative_prob AS (
    SELECT
        id,
        SUM(weight_sum) OVER (ORDER BY id) AS cum_prob
    FROM filtered_questions_weights_sum
),
cumulative_bounds AS (
    SELECT
        id,
        COALESCE( lag(cum_prob) OVER (ORDER BY cum_prob, id), 0 ) AS lower_cum_bound,
        cum_prob AS upper_cum_bound
    FROM cumulative_prob
)

正在生成随机序列。必须重新规范化 (random() * (SELECT SUM(weight_sum))，因为权重已在上一步中更新。 10 是我们想要 return.

的行数

WITH random_series AS (
    SELECT generate_series (1,10),random() * (SELECT SUM(weight_sum) FROM filtered_questions_weights_sum) AS R
)

最后：

SELECT
      id, lower_cum_bound, upper_cum_bound, R
FROM random_series
JOIN cumulative_bounds
ON R::NUMERIC <@ numrange(lower_cum_bound::NUMERIC, upper_cum_bound::NUMERIC, '(]')

我们得到以下分布：

id                                   lower_cum_bound upper_cum_bound r                   
------------------------------------ --------------- --------------- ------------------- 
380f46e9-f373-4b89-a863-05f484e6b3b6 0               2.0             0.41090718149207534 
42bcb088-fc19-4272-8c49-e77999edd01c 2.0             3.9             3.4483200465794654  
46a97f1d-789f-46e7-9d3b-bd881a22a32e 3.9             5.9             5.159445870062337   
46a97f1d-789f-46e7-9d3b-bd881a22a32e 3.9             5.9             5.524481557868421   
972d0296-acc3-4b44-b67d-928049d5e9c2 5.9             7.8             6.842470594821498   
bdcc26f7-ccaf-4f8f-9e0b-81b9a6d29cdb 11.6            13.5            12.207371663767844  
bdcc26f7-ccaf-4f8f-9e0b-81b9a6d29cdb 11.6            13.5            12.674184153741226  
c935e3de-f1b6-4399-b5eb-ed3a9194eb7b 15.5            17.5            17.16804686235264   
e5061aeb-53b7-4247-8404-87508c5ac723 21.4            23.4            22.622627633158118  
f8c37700-0c3a-457e-8882-7c65269482ea 25.4            27.3            26.841821723571048

综合起来：

WITH filters (type, id, weight) AS (
        SELECT 'subject', '148232e0-dece-40d9-81e0-0fa675f040e5'::uuid, 0.5
        UNION SELECT 'subject', '854431bb-18ee-4efb-803f-185757d25235'::uuid, 0.4
        UNION SELECT 'area', 'e12863fb-afb7-45cf-9198-f9f58ebc80cf'::uuid, 1
        UNION SELECT 'institution', '7f56c89f-705e-45c7-98fb-fee470550edf'::uuid, 0.5
        UNION SELECT 'institution', '0066257b-b2e3-4ee8-8075-517a2aa1379e'::uuid, 0.5
        )
    ,
    filtered_questions AS
    (
        SELECT
            q.id,
            SUM(filters.weight) weight_sum
        FROM
        public.questions q
        INNER JOIN public.subjects_questions sq ON q.id = sq.question_id
        INNER JOIN public.subjects s ON s.id = sq.subject_id
        INNER JOIN public.institutions_questions iq ON iq.question_id = q.id
        INNER JOIN public.institutions i ON i.id = iq.institution_id
        INNER JOIN public.activity_areas_questions aq ON aq.question_id = q.id
        INNER JOIN public.activity_areas a ON a.id = aq.activity_area_id
        INNER JOIN filters
            ON (filters.type = 'subject' AND s.id IN(filters.id))
            OR (filters.type = 'area' AND a.id IN(filters.id))
            OR (filters.type = 'institution' AND i.id IN(filters.id))
        WHERE
            s.id IN (SELECT id from filters where type = 'subject')
            and i.id IN (SELECT id from filters where type = 'institution')
            and a.id IN (SELECT id from filters where type = 'area')
        GROUP BY q.id
    )
    ,
    cumulative_prob AS (
        SELECT
            id,
            SUM(weight_sum) OVER (ORDER BY id) AS cum_prob
        FROM filtered_questions
    )
    ,
    cumulative_bounds AS (
        SELECT
            id,
            COALESCE( lag(cum_prob) OVER (ORDER BY cum_prob, id), 0 ) AS lower_cum_bound,
            cum_prob AS upper_cum_bound
        FROM cumulative_prob
    )
    ,
    random_series AS
    (
        SELECT generate_series (1,14),random() * (SELECT SUM(weight_sum) FROM filtered_questions) AS R
    )
SELECT id, lower_cum_bound, upper_cum_bound, R
FROM random_series
JOIN cumulative_bounds
ON R::NUMERIC <@ numrange(lower_cum_bound::NUMERIC, upper_cum_bound::NUMERIC, '(]')

SQL/PostgreSQL 中带加权过滤器的随机行选择

Random row selection with weighted filters in SQL/PostgreSQL

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random

postgresql

probability

window-functions