Select Random Row from a Postgresql Table with Weighted Row Probabilities

Select random row from a PostgreSQL table with weighted row probabilities

This should do the trick:

WITH CTE AS (
    SELECT random() * (SELECT SUM(percent) FROM YOUR_TABLE) R
)
SELECT *
FROM (
    SELECT id, SUM(percent) OVER (ORDER BY id) S, R
    FROM YOUR_TABLE CROSS JOIN CTE
) Q
WHERE S >= R
ORDER BY id
LIMIT 1;

The sub-query Q gives the following result:

1  50
2  85
3  100

We then simply generate a random number in range [0, 100) and pick the first row that is at or beyond that number (the WHERE clause). We use common table expression (WITH) to ensure the random number is calculated only once.

BTW, the SELECT SUM(percent) FROM YOUR_TABLE allows you to have any weights in percent - they don't strictly need to be percentages (i.e. add-up to 100).

[SQL Fiddle]

Random row selection with weighted filters in SQL/PostgreSQL

Ok. Managed to solve it. Basically, used the strategy already outlined in the question and a little help from 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 but for multiple rows --, not needing to create the "bounds" by hand.

Let's try step-by-step:

Since the filters, with the weights, come from outside the schema, let's create a 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
)

Now, let's filter the rows, ignoring the weight (for now), so later we don't need to work with the whole 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')
)

The same question can be selected by multiple filters, increasing the chance of it being selected. We must update the weights to solve this.

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
)

Generating the bounds, like exposed 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
)

Generating the random series. Had to re-normalize (random() * (SELECT SUM(weight_sum)) because the weights were updated in a previous step. 10 is the number of rows that we want to return.

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

And finally:

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, '(]')

And we get the following distribution:

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  

Putting it all together:

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, '(]')

Weighted Random Selection

Given the small input dataset, it's straightforward to do this in pure SQL. Use CTEs to build lower & upper bound columns for each row in each of the common_FOO_name tables, then use generate_series() to generate sets of random numbers. Join everything together, and use the random value between the bounds as the WHERE clause.

with first_names_weighted as (
  select first_name,
    sum(ratio) over (order by first_name) - ratio as lower_bound,
    sum(ratio) over (order by first_name) as upper_bound
  from common_first_name
),
last_names_weighted as (
  select last_name,
    sum(ratio) over (order by last_name) - ratio as lower_bound,
    sum(ratio) over (order by last_name) as upper_bound
  from common_last_name
),
randoms as (
  select random() * (select sum(ratio) from common_first_name) as f_random,
         random() * (select sum(ratio) from common_last_name) as l_random
  from generate_series(1, 32)
)
select r, first_name, last_name
from randoms r
cross join first_names_weighted f
cross join last_names_weighted l
where f.lower_bound <= r.f_random and r.f_random <= f.upper_bound
  and l.lower_bound <= r.l_random and r.l_random <= l.upper_bound;

Change the value passed to generate_series() to control how many names to generate. If it's important that it be a function, you can just use a LANGAUGE SQL function definition to parameterize that number:

https://www.db-fiddle.com/f/mmGQRhCP2W1yfhZTm1yXu5/3

How to dynamically perform a weighted random row selection in PostgreSQL?

Here is a solution that works as follows:

• first compute the weight of each student
• sum the weight of all students and multiply if by a random seed
• then pick the first student above that target, random, weight

Query:

with 
    student_with_weight as (
        select 
            id,
            (
                extract(epoch from (now() - last_played_datetime)) / 60 * 0.75
                + total_play_duration * 0.5
                + total_points_earned * 0.25
            ) / 1.5 weight
        from student
    ),
    random_weight as (
        select random() * (select sum(weight) weight from student_with_weight ) weight
    )
select id 
from 
    student_with_weight s
    inner join random_weight r on s.weight >= r.weight
order by id
limit 1;

Infinite scroll algorithm for random items with different weight ( probability to show to the user )

The following are some ideas to implement the solution:

The database table should have a column where each entry is a number generated as follows:

• log(R) / W,

where—

• W is the record's weight greater than 0 (itself its own column), and
• R is a per-record uniform random number in (0, 1)

(see also Arratia, R., "On the amount of dependence in the prime factorization of a uniform random integer", 2002). Then take the records with the highest values of that column as the need arises.

However, note that SQL has no standard way to generate random numbers; DBMSs that implement SQL have their own ways to do so (such as RANDOM() for PostgreSQL), but how they work depends on the DBMS (for example, compare MySQL's RAND() with T-SQL's NEWID()).

quick random row in PostgreSQL: why time (floor(random()*N)) + (select * from a where id = const) 100 times less then select where id = random?

This is because random() is defined as volatile, so Postgres evaluates it for each and every row again - effectively going through all rows.

If you want to prevent that, "hide" it behind a (otherwise useless) subselect:

SELECT * 
FROM a 
where id = (select trunc(random ()*1000)::integer);

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