I made assumptions about the original data set. You should be able to adapt this to the revised dataset - although note that the solution using variables (instead of my self-join) is faster...
DROP TABLE IF EXISTS my_table;
CREATE TABLE my_table
(ID INT NOT NULL
,Date DATE NOT NULL
,UID INT NOT NULL PRIMARY KEY
);
INSERT INTO my_table VALUES
(1 ,'2012-01-01', 1002),
(1 ,'2012-01-24', 2005),
(1 ,'2012-02-15', 5152),
(2 ,'2012-01-01', 6252),
(2 ,'2012-01-19', 10356),
(3 ,'2013-01-06', 10989),
(3 ,'2013-03-25', 25001),
(3 ,'2014-01-14', 35798);
SELECT a.*
, SUM(b.count) cumulative
FROM
(
SELECT x.id,YEAR(date) year,MONTH(date) month, COUNT(0) count FROM my_table x GROUP BY id,year,month
) a
JOIN
(
SELECT x.id,YEAR(date) year,MONTH(date) month, COUNT(0) count FROM my_table x GROUP BY id,year,month
) b
ON b.id = a.id AND (b.year < a.year OR (b.year = a.year AND b.month <= a.month)
)
GROUP
BY a.id, a.year,a.month;
+----+------+-------+-------+------------+
| id | year | month | count | cumulative |
+----+------+-------+-------+------------+
| 1 | 2012 | 1 | 2 | 2 |
| 1 | 2012 | 2 | 1 | 3 |
| 2 | 2012 | 1 | 2 | 2 |
| 3 | 2013 | 1 | 1 | 1 |
| 3 | 2013 | 3 | 1 | 2 |
| 3 | 2014 | 1 | 1 | 3 |
+----+------+-------+-------+------------+
If you don't mind an extra column in the result, you can simplify (and accelerate) the above, as follows:
SELECT x.*
, @running:= IF(@previous=x.id,@running,0)+x.count cumulative
, @previous:=x.id
FROM
( SELECT x.id,YEAR(date) year,MONTH(date) month, COUNT(0) count FROM my_table x GROUP BY id,year,month ) x
,( SELECT @cumulative := 0,@running:=0) vals;