ClickHouse/docs/en/query_language/agg_functions/reference.md

Function Reference

count

Counts the number of rows or not-NULL values.

ClickHouse supports the following syntaxes for count:

• count(expr) or COUNT(DISTINCT expr).
• count() or COUNT(*). The count() syntax is ClickHouse-specific.

Parameters

The function can take:

• Zero parameters.
• One expression.

Returned value

• If the function is called without parameters it counts the number of rows.
• If the expression is passed, then the function counts how many times this expression returned not null. If the expression returns a Nullable-type value, then the result of count stays not Nullable. The function returns 0 if the expression returned NULL for all the rows.

In both cases the type of the returned value is UInt64.

Details

ClickHouse supports the COUNT(DISTINCT ...) syntax. The behavior of this construction depends on the count_distinct_implementation setting. It defines which of the uniq* functions is used to perform the operation. The default is the uniqExact function.

The SELECT count() FROM table query is not optimized, because the number of entries in the table is not stored separately. It chooses a small column from the table and counts the number of values in it.

Examples

Example 1:

SELECT count() FROM t

┌─count()─┐
│       5 │
└─────────┘

Example 2:

SELECT name, value FROM system.settings WHERE name = 'count_distinct_implementation'

┌─name──────────────────────────┬─value─────┐
│ count_distinct_implementation │ uniqExact │
└───────────────────────────────┴───────────┘

SELECT count(DISTINCT num) FROM t

┌─uniqExact(num)─┐
│              3 │
└────────────────┘

This example shows that count(DISTINCT num) is performed by the uniqExact function according to the count_distinct_implementation setting value.

any(x)

Selects the first encountered value. The query can be executed in any order and even in a different order each time, so the result of this function is indeterminate. To get a determinate result, you can use the 'min' or 'max' function instead of 'any'.

In some cases, you can rely on the order of execution. This applies to cases when SELECT comes from a subquery that uses ORDER BY.

When a SELECT query has the GROUP BY clause or at least one aggregate function, ClickHouse (in contrast to MySQL) requires that all expressions in the SELECT, HAVING, and ORDER BY clauses be calculated from keys or from aggregate functions. In other words, each column selected from the table must be used either in keys or inside aggregate functions. To get behavior like in MySQL, you can put the other columns in the any aggregate function.

anyHeavy(x)

Selects a frequently occurring value using the heavy hitters algorithm. If there is a value that occurs more than in half the cases in each of the query's execution threads, this value is returned. Normally, the result is nondeterministic.

anyHeavy(column)

Arguments

• column – The column name.

Example

Take the OnTime data set and select any frequently occurring value in the AirlineID column.

SELECT anyHeavy(AirlineID) AS res
FROM ontime

┌───res─┐
│ 19690 │
└───────┘

anyLast(x)

Selects the last value encountered. The result is just as indeterminate as for the any function.

##groupBitAnd

Applies bitwise AND for series of numbers.

groupBitAnd(expr)

Parameters

expr – An expression that results in UInt* type.

Return value

Value of the UInt* type.

Example

Test data:

binary     decimal
00101100 = 44
00011100 = 28
00001101 = 13
01010101 = 85

Query:

SELECT groupBitAnd(num) FROM t

Where num is the column with the test data.

Result:

binary     decimal
00000100 = 4

##groupBitOr

Applies bitwise OR for series of numbers.

groupBitOr(expr)

Parameters

expr – An expression that results in UInt* type.

Return value

Value of the UInt* type.

Example

Test data:

binary     decimal
00101100 = 44
00011100 = 28
00001101 = 13
01010101 = 85

Query:

SELECT groupBitOr(num) FROM t

Where num is the column with the test data.

Result:

binary     decimal
01111101 = 125

##groupBitXor

Applies bitwise XOR for series of numbers.

groupBitXor(expr)

Parameters

expr – An expression that results in UInt* type.

Return value

Value of the UInt* type.

Example

Test data:

binary     decimal
00101100 = 44
00011100 = 28
00001101 = 13
01010101 = 85

Query:

SELECT groupBitXor(num) FROM t

Where num is the column with the test data.

Result:

binary     decimal
01101000 = 104

groupBitmap

Bitmap or Aggregate calculations from a unsigned integer column, return cardinality of type UInt64, if add suffix -State, then return bitmap object.

groupBitmap(expr)

Parameters

expr – An expression that results in UInt* type.

Return value

Value of the UInt64 type.

Example

Test data:

UserID
1
1
2
3

Query:

SELECT groupBitmap(UserID) as num FROM t

Result:

num
3

min(x)

Calculates the minimum.

max(x)

Calculates the maximum.

argMin(arg, val)

Calculates the 'arg' value for a minimal 'val' value. If there are several different values of 'arg' for minimal values of 'val', the first of these values encountered is output.

Example:

┌─user─────┬─salary─┐
│ director │   5000 │
│ manager  │   3000 │
│ worker   │   1000 │
└──────────┴────────┘

SELECT argMin(user, salary) FROM salary

┌─argMin(user, salary)─┐
│ worker               │
└──────────────────────┘

argMax(arg, val)

Calculates the 'arg' value for a maximum 'val' value. If there are several different values of 'arg' for maximum values of 'val', the first of these values encountered is output.

sum(x)

Calculates the sum. Only works for numbers.

sumWithOverflow(x)

Computes the sum of the numbers, using the same data type for the result as for the input parameters. If the sum exceeds the maximum value for this data type, the function returns an error.

Only works for numbers.

sumMap(key, value)

Totals the 'value' array according to the keys specified in the 'key' array. The number of elements in 'key' and 'value' must be the same for each row that is totaled. Returns a tuple of two arrays: keys in sorted order, and values ​​summed for the corresponding keys.

Example:

CREATE TABLE sum_map(
    date Date,
    timeslot DateTime,
    statusMap Nested(
        status UInt16,
        requests UInt64
    )
) ENGINE = Log;
INSERT INTO sum_map VALUES
    ('2000-01-01', '2000-01-01 00:00:00', [1, 2, 3], [10, 10, 10]),
    ('2000-01-01', '2000-01-01 00:00:00', [3, 4, 5], [10, 10, 10]),
    ('2000-01-01', '2000-01-01 00:01:00', [4, 5, 6], [10, 10, 10]),
    ('2000-01-01', '2000-01-01 00:01:00', [6, 7, 8], [10, 10, 10]);
SELECT
    timeslot,
    sumMap(statusMap.status, statusMap.requests)
FROM sum_map
GROUP BY timeslot

┌────────────timeslot─┬─sumMap(statusMap.status, statusMap.requests)─┐
│ 2000-01-01 00:00:00 │ ([1,2,3,4,5],[10,10,20,10,10])               │
│ 2000-01-01 00:01:00 │ ([4,5,6,7,8],[10,10,20,10,10])               │
└─────────────────────┴──────────────────────────────────────────────┘

skewPop

Computes the skewness of a sequence.

skewPop(expr)

Parameters

expr — Expression returning a number.

Returned value

The skewness of the given distribution. Type — Float64

Example

SELECT skewPop(value) FROM series_with_value_column

skewSamp

Computes the sample skewness of a sequence.

It represents an unbiased estimate of the skewness of a random variable if passed values form its sample.

skewSamp(expr)

Parameters

expr — Expression returning a number.

Returned value

The skewness of the given distribution. Type — Float64. If n <= 1 (n is the size of the sample), then the function returns nan.

Example

SELECT skewSamp(value) FROM series_with_value_column

kurtPop

Computes the kurtosis of a sequence.

kurtPop(expr)

Parameters

expr — Expression returning a number.

Returned value

The kurtosis of the given distribution. Type — Float64

Example

SELECT kurtPop(value) FROM series_with_value_column

kurtSamp

Computes the sample kurtosis of a sequence.

It represents an unbiased estimate of the kurtosis of a random variable if passed values form its sample.

kurtSamp(expr)

Parameters

expr — Expression returning a number.

Returned value

The kurtosis of the given distribution. Type — Float64. If n <= 1 (n is a size of the sample), then the function returns nan.

Example

SELECT kurtSamp(value) FROM series_with_value_column

timeSeriesGroupSum(uid, timestamp, value)

timeSeriesGroupSum can aggregate different time series that sample timestamp not alignment. It will use linear interpolation between two sample timestamp and then sum time-series together.

• uid is the time series unique id, UInt64.
• timestamp is Int64 type in order to support millisecond or microsecond.
• value is the metric.

The function returns array of tuples with (timestamp, aggregated_value) pairs.

Before using this function make sure timestamp is in ascending order.

Example:

┌─uid─┬─timestamp─┬─value─┐
│ 1   │     2     │   0.2 │
│ 1   │     7     │   0.7 │
│ 1   │    12     │   1.2 │
│ 1   │    17     │   1.7 │
│ 1   │    25     │   2.5 │
│ 2   │     3     │   0.6 │
│ 2   │     8     │   1.6 │
│ 2   │    12     │   2.4 │
│ 2   │    18     │   3.6 │
│ 2   │    24     │   4.8 │
└─────┴───────────┴───────┘

CREATE TABLE time_series(
    uid       UInt64,
    timestamp Int64,
    value     Float64
) ENGINE = Memory;
INSERT INTO time_series VALUES
    (1,2,0.2),(1,7,0.7),(1,12,1.2),(1,17,1.7),(1,25,2.5),
    (2,3,0.6),(2,8,1.6),(2,12,2.4),(2,18,3.6),(2,24,4.8);

SELECT timeSeriesGroupSum(uid, timestamp, value)
FROM (
    SELECT * FROM time_series order by timestamp ASC
);

And the result will be:

[(2,0.2),(3,0.9),(7,2.1),(8,2.4),(12,3.6),(17,5.1),(18,5.4),(24,7.2),(25,2.5)]

timeSeriesGroupRateSum(uid, ts, val)

Similarly timeSeriesGroupRateSum, timeSeriesGroupRateSum will Calculate the rate of time-series and then sum rates together. Also, timestamp should be in ascend order before use this function.

Use this function, the result above case will be:

[(2,0),(3,0.1),(7,0.3),(8,0.3),(12,0.3),(17,0.3),(18,0.3),(24,0.3),(25,0.1)]

avg(x)

Calculates the average. Only works for numbers. The result is always Float64.

uniq

Calculates the approximate number of different values of the argument.

uniq(x[, ...])

Parameters

The function takes a variable number of parameters. Parameters can be Tuple, Array, Date, DateTime, String, or numeric types.

Returned value

• A UInt64-type number.

Implementation details

Function:

• Calculates a hash for all parameters in the aggregate, then uses it in calculations.

• Uses an adaptive sampling algorithm. For the calculation state, the function uses a sample of element hash values up to 65536.

  This algorithm is very accurate and very efficient on the CPU. When the query contains several of these functions, using uniq is almost as fast as using other aggregate functions.

• Provides the result deterministically (it doesn't depend on the query processing order).

We recommend using this function in almost all scenarios.

See Also

• uniqCombined
• uniqCombined64
• uniqHLL12
• uniqExact

uniqCombined

Calculates the approximate number of different argument values.

uniqCombined(HLL_precision)(x[, ...])

The uniqCombined function is a good choice for calculating the number of different values, but keep in mind that the estimation error for large sets (200 million elements and more) will be larger than the theoretical value due to the poor hash function choice.

Parameters

The function takes a variable number of parameters. Parameters can be Tuple, Array, Date, DateTime, String, or numeric types.

HLL_precision is the base-2 logarithm of the number of cells in HyperLogLog. Optional, you can use the function as uniqCombined(x[, ...]). The default value for HLL_precision is 17, which is effectively 96 KiB of space (2^17 cells, 6 bits each).

Returned value

• A number UInt64-type number.

Implementation details

Function:

• Calculates a hash (64-bit hash for String and 32-bit otherwise) for all parameters in the aggregate, then uses it in calculations.

• Uses a combination of three algorithms: array, hash table, and HyperLogLog with an error correction table.

  For a small number of distinct elements, an array is used. When the set size is larger, a hash table is used. For a larger number of elements, HyperLogLog is used, which will occupy a fixed amount of memory.

• Provides the result deterministically (it doesn't depend on the query processing order).

!! note "Note" Since it uses 32-bit hash for non-String type, the result will have very high error for cardinalities significantly larger than UINT_MAX (error will raise quickly after a few tens of billions of distinct values), hence in this case you should use uniqCombined64

Compared to the uniq function, the uniqCombined:

• Consumes several times less memory.
• Calculates with several times higher accuracy.
• Usually has slightly lower performance. In some scenarios, uniqCombined can perform better than uniq, for example, with distributed queries that transmit a large number of aggregation states over the network.

See Also

• uniq
• uniqCombined64
• uniqHLL12
• uniqExact

uniqCombined64

Same as uniqCombined, but uses 64-bit hash for all data types.

uniqHLL12

Calculates the approximate number of different argument values, using the HyperLogLog algorithm.

uniqHLL12(x[, ...])

Parameters

The function takes a variable number of parameters. Parameters can be Tuple, Array, Date, DateTime, String, or numeric types.

Returned value

• A UInt64-type number.

Implementation details

Function:

• Calculates a hash for all parameters in the aggregate, then uses it in calculations.

• Uses the HyperLogLog algorithm to approximate the number of different argument values.

  212 5-bit cells are used. The size of the state is slightly more than 2.5 KB. The result is not very accurate (up to ~10% error) for small data sets (<10K elements). However, the result is fairly accurate for high-cardinality data sets (10K-100M), with a maximum error of ~1.6%. Starting from 100M, the estimation error increases, and the function will return very inaccurate results for data sets with extremely high cardinality (1B+ elements).

• Provides the determinate result (it doesn't depend on the query processing order).

We don't recommend using this function. In most cases, use the uniq or uniqCombined function.

See Also

• uniq
• uniqCombined
• uniqExact

uniqExact

Calculates the exact number of different argument values.

uniqExact(x[, ...])

Use the uniqExact function if you absolutely need an exact result. Otherwise use the uniq function.

The uniqExact function uses more memory than uniq, because the size of the state has unbounded growth as the number of different values increases.

Parameters

The function takes a variable number of parameters. Parameters can be Tuple, Array, Date, DateTime, String, or numeric types.

See Also

• uniq
• uniqCombined
• uniqHLL12

groupArray(x), groupArray(max_size)(x)

Creates an array of argument values. Values can be added to the array in any (indeterminate) order.

The second version (with the max_size parameter) limits the size of the resulting array to max_size elements. For example, groupArray (1) (x) is equivalent to [any (x)].

In some cases, you can still rely on the order of execution. This applies to cases when SELECT comes from a subquery that uses ORDER BY.

groupArrayInsertAt(x)

Inserts a value into the array in the specified position.

Accepts the value and position as input. If several values ​​are inserted into the same position, any of them might end up in the resulting array (the first one will be used in the case of single-threaded execution). If no value is inserted into a position, the position is assigned the default value.

Optional parameters:

• The default value for substituting in empty positions.
• The length of the resulting array. This allows you to receive arrays of the same size for all the aggregate keys. When using this parameter, the default value must be specified.

groupArrayMovingSum

Calculates the moving sum of input values.

groupArrayMovingSum(numbers_for_summing)
groupArrayMovingSum(window_size)(numbers_for_summing)

The function can take the window size as a parameter. If left unspecified, the function takes the window size equal to the number of rows in the column.

Parameters

• numbers_for_summing — Expression resulting in a numeric data type value.
• window_size — Size of the calculation window.

Returned values

• Array of the same size and type as the input data.

Example

The sample table:

CREATE TABLE t
(
    `int` UInt8,
    `float` Float32,
    `dec` Decimal32(2)
)
ENGINE = TinyLog

┌─int─┬─float─┬──dec─┐
│   1 │   1.1 │ 1.10 │
│   2 │   2.2 │ 2.20 │
│   4 │   4.4 │ 4.40 │
│   7 │  7.77 │ 7.77 │
└─────┴───────┴──────┘

The queries:

SELECT
    groupArrayMovingSum(int) AS I,
    groupArrayMovingSum(float) AS F,
    groupArrayMovingSum(dec) AS D
FROM t

┌─I──────────┬─F───────────────────────────────┬─D──────────────────────┐
│ [1,3,7,14] │ [1.1,3.3000002,7.7000003,15.47] │ [1.10,3.30,7.70,15.47] │
└────────────┴─────────────────────────────────┴────────────────────────┘

SELECT
    groupArrayMovingSum(2)(int) AS I,
    groupArrayMovingSum(2)(float) AS F,
    groupArrayMovingSum(2)(dec) AS D
FROM t

┌─I──────────┬─F───────────────────────────────┬─D──────────────────────┐
│ [1,3,6,11] │ [1.1,3.3000002,6.6000004,12.17] │ [1.10,3.30,6.60,12.17] │
└────────────┴─────────────────────────────────┴────────────────────────┘

groupArrayMovingAvg

Calculates the moving average of input values.

groupArrayMovingAvg(numbers_for_summing)
groupArrayMovingAvg(window_size)(numbers_for_summing)

The function can take the window size as a parameter. If left unspecified, the function takes the window size equal to the number of rows in the column.

Parameters

• numbers_for_summing — Expression resulting in a numeric data type value.
• window_size — Size of the calculation window.

Returned values

• Array of the same size and type as the input data.

The function uses rounding towards zero. It truncates the decimal places insignificant for the resulting data type.

Example

The sample table b:

CREATE TABLE t
(
    `int` UInt8,
    `float` Float32,
    `dec` Decimal32(2)
)
ENGINE = TinyLog

┌─int─┬─float─┬──dec─┐
│   1 │   1.1 │ 1.10 │
│   2 │   2.2 │ 2.20 │
│   4 │   4.4 │ 4.40 │
│   7 │  7.77 │ 7.77 │
└─────┴───────┴──────┘

The queries:

SELECT
    groupArrayMovingAvg(int) AS I,
    groupArrayMovingAvg(float) AS F,
    groupArrayMovingAvg(dec) AS D
FROM t

┌─I─────────┬─F───────────────────────────────────┬─D─────────────────────┐
│ [0,0,1,3] │ [0.275,0.82500005,1.9250001,3.8675] │ [0.27,0.82,1.92,3.86] │
└───────────┴─────────────────────────────────────┴───────────────────────┘

SELECT
    groupArrayMovingAvg(2)(int) AS I,
    groupArrayMovingAvg(2)(float) AS F,
    groupArrayMovingAvg(2)(dec) AS D
FROM t

┌─I─────────┬─F────────────────────────────────┬─D─────────────────────┐
│ [0,1,3,5] │ [0.55,1.6500001,3.3000002,6.085] │ [0.55,1.65,3.30,6.08] │
└───────────┴──────────────────────────────────┴───────────────────────┘

groupUniqArray(x), groupUniqArray(max_size)(x)

Creates an array from different argument values. Memory consumption is the same as for the uniqExact function.

The second version (with the max_size parameter) limits the size of the resulting array to max_size elements. For example, groupUniqArray(1)(x) is equivalent to [any(x)].

quantile(level)(x)

Approximates the level quantile. level is a constant, a floating-point number from 0 to 1. We recommend using a level value in the range of [0.01, 0.99] Don't use a level value equal to 0 or 1 – use the min and max functions for these cases.

In this function, as well as in all functions for calculating quantiles, the level parameter can be omitted. In this case, it is assumed to be equal to 0.5 (in other words, the function will calculate the median).

Works for numbers, dates, and dates with times. Returns: for numbers – Float64; for dates – a date; for dates with times – a date with time.

Uses reservoir sampling with a reservoir size up to 8192. If necessary, the result is output with linear approximation from the two neighboring values. This algorithm provides very low accuracy. See also: quantileTiming, quantileTDigest, quantileExact.

The result depends on the order of running the query, and is nondeterministic.

When using multiple quantile (and similar) functions with different levels in a query, the internal states are not combined (that is, the query works less efficiently than it could). In this case, use the quantiles (and similar) functions.

quantileDeterministic(level)(x, determinator)

Works the same way as the quantile function, but the result is deterministic and does not depend on the order of query execution.

To achieve this, the function takes a second argument – the "determinator". This is a number whose hash is used instead of a random number generator in the reservoir sampling algorithm. For the function to work correctly, the same determinator value should not occur too often. For the determinator, you can use an event ID, user ID, and so on.

Don't use this function for calculating timings. There is a more suitable function for this purpose: quantileTiming.

quantileTiming

Computes the quantile of the specified level with determined precision. The function is intended for calculating page loading time quantiles in milliseconds.

quantileTiming(level)(expr)

Parameters

• level — Quantile level. Range: [0, 1].

• expr — Expression returning a Float*-type number. The function expects input values in unix timestamp format in milliseconds, but it doesn't validate format.

  • If negative values are passed to the function, the behavior is undefined.
  • If the value is greater than 30,000 (a page loading time of more than 30 seconds), it is assumed to be 30,000.

Accuracy

The calculation is accurate if:

• Total number of values doesn't exceed 5670.
• Total number of values exceeds 5670, but the page loading time is less than 1024ms.

Otherwise, the result of the calculation is rounded to the nearest multiple of 16 ms.

!! note "Note" For calculating page loading time quantiles, this function is more effective and accurate than quantile.

Returned value

• Quantile of the specified level.

Type: Float32.

!!! note "Note" If no values are passed to the function (when using quantileTimingIf), NaN is returned. The purpose of this is to differentiate these cases from cases that result in zero. See ORDER BY clause for notes on sorting NaN values.

The result is deterministic (it doesn't depend on the query processing order).

Example

SELECT quantileTiming(0.5)(number / 2) FROM numbers(10)

┌─quantileTiming(0.5)(divide(number, 2))─┐
│                                      2 │
└────────────────────────────────────────┘

quantileTimingWeighted(level)(x, weight)

Differs from the quantileTiming function in that it has a second argument, "weights". Weight is a non-negative integer. The result is calculated as if the x value were passed weight number of times to the quantileTiming function.

quantileExact(level)(x)

Computes the quantile of 'level' exactly. To do this, all the passed values ​​are combined into an array, which is then partially sorted. Therefore, the function consumes O(n) memory, where 'n' is the number of values that were passed. However, for a small number of values, the function is very effective.

quantileExactWeighted(level)(x, weight)

Computes the quantile of 'level' exactly. In addition, each value is counted with its weight, as if it is present 'weight' times. The arguments of the function can be considered as histograms, where the value 'x' corresponds to a histogram "column" of the height 'weight', and the function itself can be considered as a summation of histograms.

A hash table is used as the algorithm. Because of this, if the passed values ​​are frequently repeated, the function consumes less RAM than quantileExact. You can use this function instead of quantileExact and specify the weight as 1.

quantileTDigest(level)(x)

Approximates the quantile level using the t-digest algorithm. The maximum error is 1%. Memory consumption by State is proportional to the logarithm of the number of passed values.

The performance of the function is lower than for quantile or quantileTiming. In terms of the ratio of State size to precision, this function is much better than quantile.

The result depends on the order of running the query, and is nondeterministic.

median(x)

All the quantile functions have corresponding median functions: median, medianDeterministic, medianTiming, medianTimingWeighted, medianExact, medianExactWeighted, medianTDigest. They are synonyms and their behavior is identical.

quantiles(level1, level2, ...)(x)

All the quantile functions also have corresponding quantiles functions: quantiles, quantilesDeterministic, quantilesTiming, quantilesTimingWeighted, quantilesExact, quantilesExactWeighted, quantilesTDigest. These functions calculate all the quantiles of the listed levels in one pass, and return an array of the resulting values.

varSamp(x)

Calculates the amount Σ((x - x̅)^2) / (n - 1), where n is the sample size and x̅is the average value of x.

It represents an unbiased estimate of the variance of a random variable if passed values form its sample.

Returns Float64. When n <= 1, returns +∞.

varPop(x)

Calculates the amount Σ((x - x̅)^2) / n, where n is the sample size and x̅is the average value of x.

In other words, dispersion for a set of values. Returns Float64.

stddevSamp(x)

The result is equal to the square root of varSamp(x).

stddevPop(x)

The result is equal to the square root of varPop(x).

topK(N)(column)

Returns an array of the most frequent values in the specified column. The resulting array is sorted in descending order of frequency of values (not by the values themselves).

Implements the Filtered Space-Saving algorithm for analyzing TopK, based on the reduce-and-combine algorithm from Parallel Space Saving.

topK(N)(column)

This function doesn't provide a guaranteed result. In certain situations, errors might occur and it might return frequent values that aren't the most frequent values.

We recommend using the N < 10 value; performance is reduced with large N values. Maximum value of N = 65536.

Arguments

• 'N' is the number of values.
• ' x ' – The column.

Example

Take the OnTime data set and select the three most frequently occurring values in the AirlineID column.

SELECT topK(3)(AirlineID) AS res
FROM ontime

┌─res─────────────────┐
│ [19393,19790,19805] │
└─────────────────────┘

covarSamp(x, y)

Calculates the value of Σ((x - x̅)(y - y̅)) / (n - 1).

Returns Float64. When n <= 1, returns +∞.

covarPop(x, y)

Calculates the value of Σ((x - x̅)(y - y̅)) / n.

corr(x, y)

Calculates the Pearson correlation coefficient: Σ((x - x̅)(y - y̅)) / sqrt(Σ((x - x̅)^2) * Σ((y - y̅)^2)).

simpleLinearRegression

Performs simple (unidimensional) linear regression.

simpleLinearRegression(x, y)

Parameters:

• x — Column with dependent variable values.
• y — Column with explanatory variable values.

Returned values:

Constants (a, b) of the resulting line y = a*x + b.

Examples

SELECT arrayReduce('simpleLinearRegression', [0, 1, 2, 3], [0, 1, 2, 3])

┌─arrayReduce('simpleLinearRegression', [0, 1, 2, 3], [0, 1, 2, 3])─┐
│ (1,0)                                                             │
└───────────────────────────────────────────────────────────────────┘

SELECT arrayReduce('simpleLinearRegression', [0, 1, 2, 3], [3, 4, 5, 6])

┌─arrayReduce('simpleLinearRegression', [0, 1, 2, 3], [3, 4, 5, 6])─┐
│ (1,3)                                                             │
└───────────────────────────────────────────────────────────────────┘

stochasticLinearRegression

This function implements stochastic linear regression. It supports custom parameters for learning rate, L2 regularization coefficient, mini-batch size and has few methods for updating weights (Adam (used by default), simple SGD, Momentum, Nesterov).

Parameters

There are 4 customizable parameters. They are passed to the function sequentially, but there is no need to pass all four - default values will be used, however good model required some parameter tuning.

stochasticLinearRegression(1.0, 1.0, 10, 'SGD')

1. learning rate is the coefficient on step length, when gradient descent step is performed. Too big learning rate may cause infinite weights of the model. Default is 0.00001.
2. l2 regularization coefficient which may help to prevent overfitting. Default is 0.1.
3. mini-batch size sets the number of elements, which gradients will be computed and summed to perform one step of gradient descent. Pure stochastic descent uses one element, however having small batches(about 10 elements) make gradient steps more stable. Default is 15.
4. method for updating weights, they are: Adam (by default), SGD, Momentum, Nesterov. Momentum and Nesterov require little bit more computations and memory, however they happen to be useful in terms of speed of convergance and stability of stochastic gradient methods.

Usage

stochasticLinearRegression is used in two steps: fitting the model and predicting on new data. In order to fit the model and save its state for later usage we use -State combinator, which basically saves the state (model weights, etc). To predict we use function evalMLMethod, which takes a state as an argument as well as features to predict on.

1. Fitting

   Such query may be used.

   CREATE TABLE IF NOT EXISTS train_data
   (
       param1 Float64,
       param2 Float64,
       target Float64
   ) ENGINE = Memory;
   
   CREATE TABLE your_model ENGINE = Memory AS SELECT
   stochasticLinearRegressionState(0.1, 0.0, 5, 'SGD')(target, param1, param2)
   AS state FROM train_data;
   
   

   Here we also need to insert data into train_data table. The number of parameters is not fixed, it depends only on number of arguments, passed into linearRegressionState. They all must be numeric values. Note that the column with target value(which we would like to learn to predict) is inserted as the first argument.

2. Predicting

   After saving a state into the table, we may use it multiple times for prediction, or even merge with other states and create new even better models.

   WITH (SELECT state FROM your_model) AS model SELECT
   evalMLMethod(model, param1, param2) FROM test_data
   

   The query will return a column of predicted values. Note that first argument of evalMLMethod is AggregateFunctionState object, next are columns of features.

   test_data is a table like train_data but may not contain target value.

Notes

1. To merge two models user may create such query:

   SELECT state1 + state2 FROM your_models
   

   where your_models table contains both models. This query will return new AggregateFunctionState object.

2. User may fetch weights of the created model for its own purposes without saving the model if no -State combinator is used.

   SELECT stochasticLinearRegression(0.01)(target, param1, param2) FROM train_data
   

   Such query will fit the model and return its weights - first are weights, which correspond to the parameters of the model, the last one is bias. So in the example above the query will return a column with 3 values.

See Also

• stochasticLogisticRegression
• Difference between linear and logistic regressions

stochasticLogisticRegression

This function implements stochastic logistic regression. It can be used for binary classification problem, supports the same custom parameters as stochasticLinearRegression and works the same way.

Parameters

Parameters are exactly the same as in stochasticLinearRegression: learning rate, l2 regularization coefficient, mini-batch size, method for updating weights. For more information see parameters.

stochasticLogisticRegression(1.0, 1.0, 10, 'SGD')

1. Fitting

   See the Fitting section in the stochasticLinearRegression description.

   Predicted labels have to be in [-1, 1].

2. Predicting

   Using saved state we can predict probability of object having label 1.

   WITH (SELECT state FROM your_model) AS model SELECT
   evalMLMethod(model, param1, param2) FROM test_data
   

   The query will return a column of probabilities. Note that first argument of evalMLMethod is AggregateFunctionState object, next are columns of features.

   We can also set a bound of probability, which assigns elements to different labels.

   SELECT ans < 1.1 AND ans > 0.5 FROM
   (WITH (SELECT state FROM your_model) AS model SELECT
   evalMLMethod(model, param1, param2) AS ans FROM test_data)
   

   Then the result will be labels.

   test_data is a table like train_data but may not contain target value.

See Also

• stochasticLinearRegression
• Difference between linear and logistic regressions.

groupBitmapAnd

Calculations the AND of a bitmap column, return cardinality of type UInt64, if add suffix -State, then return bitmap object.

groupBitmapAnd(expr)

Parameters

expr – An expression that results in AggregateFunction(groupBitmap, UInt*) type.

Return value

Value of the UInt64 type.

Example

DROP TABLE IF EXISTS bitmap_column_expr_test2;
CREATE TABLE bitmap_column_expr_test2
(
    tag_id String,
    z AggregateFunction(groupBitmap, UInt32)
)
ENGINE = MergeTree
ORDER BY tag_id;

INSERT INTO bitmap_column_expr_test2 VALUES ('tag1', bitmapBuild(cast([1,2,3,4,5,6,7,8,9,10] as Array(UInt32))));
INSERT INTO bitmap_column_expr_test2 VALUES ('tag2', bitmapBuild(cast([6,7,8,9,10,11,12,13,14,15] as Array(UInt32))));
INSERT INTO bitmap_column_expr_test2 VALUES ('tag3', bitmapBuild(cast([2,4,6,8,10,12] as Array(UInt32))));

SELECT groupBitmapAnd(z) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─groupBitmapAnd(z)─┐
│               3   │
└───────────────────┘

SELECT groupBitmapAndMerge(z) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─groupBitmapAnd(z)─┐
│               3   │
└───────────────────┘

SELECT arraySort(bitmapToArray(groupBitmapAndState(z))) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─arraySort(bitmapToArray(groupBitmapAndState(z)))─┐
│ [6,8,10]                                         │
└──────────────────────────────────────────────────┘

groupBitmapOr

Calculations the OR of a bitmap column, return cardinality of type UInt64, if add suffix -State, then return bitmap object. This is equivalent to groupBitmapMerge.

groupBitmapOr(expr)

Parameters

expr – An expression that results in AggregateFunction(groupBitmap, UInt*) type.

Return value

Value of the UInt64 type.

Example

DROP TABLE IF EXISTS bitmap_column_expr_test2;
CREATE TABLE bitmap_column_expr_test2
(
    tag_id String,
    z AggregateFunction(groupBitmap, UInt32)
)
ENGINE = MergeTree
ORDER BY tag_id;

INSERT INTO bitmap_column_expr_test2 VALUES ('tag1', bitmapBuild(cast([1,2,3,4,5,6,7,8,9,10] as Array(UInt32))));
INSERT INTO bitmap_column_expr_test2 VALUES ('tag2', bitmapBuild(cast([6,7,8,9,10,11,12,13,14,15] as Array(UInt32))));
INSERT INTO bitmap_column_expr_test2 VALUES ('tag3', bitmapBuild(cast([2,4,6,8,10,12] as Array(UInt32))));

SELECT groupBitmapOr(z) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─groupBitmapOr(z)─┐
│             15   │
└──────────────────┘

SELECT groupBitmapOrMerge(z) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─groupBitmapOrMerge(z)─┐
│                  15   │
└───────────────────────┘

SELECT arraySort(bitmapToArray(groupBitmapOrState(z))) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─arraySort(bitmapToArray(groupBitmapOrState(z)))─┐
│ [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]           │
└─────────────────────────────────────────────────┘

groupBitmapXor

Calculations the XOR of a bitmap column, return cardinality of type UInt64, if add suffix -State, then return bitmap object.

groupBitmapOr(expr)

Parameters

expr – An expression that results in AggregateFunction(groupBitmap, UInt*) type.

Return value

Value of the UInt64 type.

Example

DROP TABLE IF EXISTS bitmap_column_expr_test2;
CREATE TABLE bitmap_column_expr_test2
(
    tag_id String,
    z AggregateFunction(groupBitmap, UInt32)
)
ENGINE = MergeTree
ORDER BY tag_id;

INSERT INTO bitmap_column_expr_test2 VALUES ('tag1', bitmapBuild(cast([1,2,3,4,5,6,7,8,9,10] as Array(UInt32))));
INSERT INTO bitmap_column_expr_test2 VALUES ('tag2', bitmapBuild(cast([6,7,8,9,10,11,12,13,14,15] as Array(UInt32))));
INSERT INTO bitmap_column_expr_test2 VALUES ('tag3', bitmapBuild(cast([2,4,6,8,10,12] as Array(UInt32))));

SELECT groupBitmapXor(z) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─groupBitmapXor(z)─┐
│              10   │
└───────────────────┘

SELECT groupBitmapXorMerge(z) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─groupBitmapXorMerge(z)─┐
│                   10   │
└────────────────────────┘

SELECT arraySort(bitmapToArray(groupBitmapXorState(z))) FROM bitmap_column_expr_test2 WHERE like(tag_id, 'tag%');
┌─arraySort(bitmapToArray(groupBitmapXorState(z)))─┐
│ [1,3,5,6,8,10,11,13,14,15]                       │
└──────────────────────────────────────────────────┘

Original article