Merge pull request #137 from CartoDB/adds-outlier-functions

Adds (nonspatial) outlier functions
2016-12-01 10:43:51 +01:00
parent 2547318f59 c7e690980f
commit b0dcd7f572
4 changed files with 346 additions and 0 deletions
@@ -0,0 +1,75 @@
+
+-- Find outliers using a static threshold
+--
+CREATE OR REPLACE FUNCTION CDB_StaticOutlier(column_value numeric, threshold numeric)
+RETURNS boolean
+AS $$
+BEGIN
+
+  RETURN column_value > threshold;
+
+END;
+$$ LANGUAGE plpgsql;
+
+-- Find outliers by a percentage above the threshold
+-- TODO: add symmetric option? `is_symmetric boolean DEFAULT false`
+
+CREATE OR REPLACE FUNCTION CDB_PercentOutlier(column_values numeric[], outlier_fraction numeric, ids int[])
+RETURNS TABLE(is_outlier boolean, rowid int)
+AS $$
+DECLARE
+  avg_val numeric;
+  out_vals boolean[];
+BEGIN
+
+  SELECT avg(i) INTO avg_val
+    FROM unnest(column_values) As x(i);
+
+  IF avg_val = 0 THEN
+    RAISE EXCEPTION 'Mean value is zero. Try another outlier method.';
+  END IF;
+
+  SELECT array_agg(
+           outlier_fraction < i / avg_val) INTO out_vals
+    FROM unnest(column_values) As x(i);
+
+  RETURN QUERY
+  SELECT unnest(out_vals) As is_outlier,
+         unnest(ids) As rowid;
+
+END;
+$$ LANGUAGE plpgsql;
+
+-- Find outliers above a given number of standard deviations from the mean
+
+CREATE OR REPLACE FUNCTION CDB_StdDevOutlier(column_values numeric[], num_deviations numeric, ids int[], is_symmetric boolean DEFAULT true)
+RETURNS TABLE(is_outlier boolean, rowid int)
+AS $$
+DECLARE
+  stddev_val numeric;
+  avg_val numeric;
+  out_vals boolean[];
+BEGIN
+
+  SELECT stddev(i), avg(i) INTO stddev_val, avg_val
+    FROM unnest(column_values) As x(i);
+
+  IF stddev_val = 0 THEN
+    RAISE EXCEPTION 'Standard deviation of input data is zero';
+  END IF;
+
+  IF is_symmetric THEN
+    SELECT array_agg(
+             abs(i - avg_val) / stddev_val > num_deviations) INTO out_vals
+      FROM unnest(column_values) As x(i);
+  ELSE
+    SELECT array_agg(
+             (i - avg_val) / stddev_val > num_deviations) INTO out_vals
+      FROM unnest(column_values) As x(i);
+  END IF;
+
+  RETURN QUERY
+  SELECT unnest(out_vals) As is_outlier,
+         unnest(ids) As rowid;
+END;
+$$ LANGUAGE plpgsql;
@@ -0,0 +1,23 @@
+SET client_min_messages TO WARNING;
+\set ECHO none
+is_outlier|rowid
+t|11
+t|16
+t|17
+(3 rows)
+is_outlier|rowid
+t|16
+t|17
+(2 rows)
+ERROR:  Standard deviation of input data is zero
+is_outlier|rowid
+t|8
+t|11
+t|16
+(3 rows)
+is_outlier|rowid
+t|8
+t|9
+t|11
+t|16
+(4 rows)
@@ -0,0 +1,85 @@
+SET client_min_messages TO WARNING;
+\set ECHO none
+\pset format unaligned
+
+--
+-- postgres=# select round(avg(i), 3) as avg,
+--                   round(stddev(i), 3) as stddev,
+--                   round(avg(i) + stddev(i), 3) as one_stddev,
+--                   round(avg(i) + 2 * stddev(i), 3) As two_stddev
+--            from unnest(ARRAY[1,3,2,3,5,1,2,32,12,3,57,2,1,4,2,100]) As x(i);
+--   avg   | stddev | one_stddev | two_stddev
+-- --------+--------+------------+------------
+--  14.375 | 27.322 |     41.697 |     69.020
+
+
+-- With an threshold of 1.0 standard deviation, ids 11, 16, and 17 are outliers
+WITH a AS (
+    SELECT
+      ARRAY[1,3,2,3,5,1,2,32,12, 3,57, 2, 1, 4, 2,100,-100]::numeric[] As vals, ARRAY[1,2,3,4,5,6,7, 8, 9,10,11,12,13,14,15, 16,  17]::int[] As ids
+), b As (
+  SELECT
+    (cdb_crankshaft.cdb_StdDevOutlier(vals, 1.0, ids)).*
+  FROM a
+  ORDER BY ids)
+SELECT *
+FROM b
+WHERE is_outlier IS TRUE;
+
+-- With a threshold of 2.0 standard deviations, id 16 is the only outlier
+WITH a AS (
+    SELECT
+      ARRAY[1,3,2,3,5,1,2,32,12, 3,57, 2, 1, 4, 2,100,-100]::numeric[] As vals,
+      ARRAY[1,2,3,4,5,6,7, 8, 9,10,11,12,13,14,15, 16,  17]::int[] As ids
+), b As (
+  SELECT
+    (cdb_crankshaft.CDB_StdDevOutlier(vals, 2.0, ids)).*
+  FROM a
+  ORDER BY ids)
+SELECT *
+FROM b
+WHERE is_outlier IS TRUE;
+
+-- With a Stddev of zero, should throw back error
+-- With a threshold of 2.0 standard deviations, id 16 is the only outlier
+WITH a AS (
+    SELECT
+      ARRAY[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]::numeric[] As vals,
+      ARRAY[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]::int[] As ids
+), b As (
+  SELECT
+    (cdb_crankshaft.CDB_StdDevOutlier(vals, 1.0, ids)).*
+  FROM a
+  ORDER BY ids)
+SELECT *
+FROM b
+WHERE is_outlier IS TRUE;
+
+-- With a ratio threshold of 2.0 threshold (100% above or below the mean)
+--  which is greater than ~21, which are values
+WITH a AS (
+    SELECT
+      ARRAY[1,3,2,3,5,1,2,32,12, 3,57, 2, 1, 4, 2,100,-100]::numeric[] As vals,
+      ARRAY[1,2,3,4,5,6,7, 8, 9,10,11,12,13,14,15, 16,  17]::int[] As ids
+), b As (
+  SELECT
+    (cdb_crankshaft.CDB_PercentOutlier(vals, 2.0, ids)).*
+  FROM a
+  ORDER BY ids)
+SELECT *
+  FROM b
+ WHERE is_outlier IS TRUE;
+
+-- With a static threshold of 11, what are the outliers
+WITH a AS (
+     SELECT
+       ARRAY[1,3,2,3,5,1,2,32,12, 3,57, 2, 1, 4, 2,100,-100]::numeric[] As vals,
+       ARRAY[1,2,3,4,5,6,7, 8, 9,10,11,12,13,14,15, 16,  17]::int[] As ids
+ ), b As (
+   SELECT unnest(vals) As v, unnest(ids) as i
+     FROM a
+ )
+SELECT cdb_crankshaft.CDB_StaticOutlier(v, 11.0) As is_outlier, i As rowid
+  FROM b
+WHERE cdb_crankshaft.CDB_StaticOutlier(v, 11.0) is True
+ORDER BY i;