Aggregate functions operate on a set of values to compute a single result.
Except for :func:`!count`, :func:`!count_if`, :func:`!max_by`, :func:`!min_by` and
:func:`!approx_distinct`, all of these aggregate functions ignore null values
and return null for no input rows or when all values are null. For example,
:func:`!sum` returns null rather than zero and :func:`!avg` does not include null
values in the count. The coalesce function can be used to convert null into
zero.
Some aggregate functions such as :func:`!array_agg` produce different results depending on the order of input values. This ordering can be specified by writing an :ref:`order-by-clause` within the aggregate function:
array_agg(x ORDER BY y DESC) array_agg(x ORDER BY x, y, z)
.. function:: any_value(x) -> [same as input]
This is an alias for :func:`!arbitrary`.
.. function:: arbitrary(x) -> [same as input]
Returns an arbitrary non-null value of ``x``, if one exists.
.. function:: array_agg(x) -> array<[same as input]>
Returns an array created from the input ``x`` elements.
.. function:: avg(x) -> double
Returns the average (arithmetic mean) of all input values.
.. function:: avg(time interval type) -> time interval type
Returns the average interval length of all input values.
.. function:: bool_and(boolean) -> boolean
Returns ``TRUE`` if every input value is ``TRUE``, otherwise ``FALSE``.
.. function:: bool_or(boolean) -> boolean
Returns ``TRUE`` if any input value is ``TRUE``, otherwise ``FALSE``.
.. function:: checksum(x) -> varbinary
Returns an order-insensitive checksum of the given values.
.. function:: count(*) -> bigint
Returns the number of input rows.
.. function:: count(x) -> bigint
Returns the number of non-null input values.
.. function:: count_if(x) -> bigint
Returns the number of ``TRUE`` input values.
This function is equivalent to ``count(CASE WHEN x THEN 1 END)``.
.. function:: every(boolean) -> boolean
This is an alias for :func:`!bool_and`.
.. function:: geometric_mean(bigint) -> double
geometric_mean(double) -> double
geometric_mean(real) -> real
Returns the `geometric mean <https://en.wikipedia.org/wiki/Geometric_mean>`_ of all input values.
.. function:: max_by(x, y) -> [same as x]
Returns the value of ``x`` associated with the maximum value of ``y`` over all input values.
.. function:: max_by(x, y, n) -> array<[same as x]>
Returns ``n`` values of ``x`` associated with the ``n`` largest of all input values of ``y``
in descending order of ``y``.
.. function:: min_by(x, y) -> [same as x]
Returns the value of ``x`` associated with the minimum value of ``y`` over all input values.
.. function:: min_by(x, y, n) -> array<[same as x]>
Returns ``n`` values of ``x`` associated with the ``n`` smallest of all input values of ``y``
in ascending order of ``y``.
.. function:: max(x) -> [same as input]
Returns the maximum value of all input values.
.. function:: max(x, n) -> array<[same as x]>
Returns ``n`` largest values of all input values of ``x``.
.. function:: min(x) -> [same as input]
Returns the minimum value of all input values.
.. function:: min(x, n) -> array<[same as x]>
Returns ``n`` smallest values of all input values of ``x``.
.. function:: reduce_agg(inputValue T, initialState S, inputFunction(S,T,S), combineFunction(S,S,S)) -> S
Reduces all input values into a single value. ``inputFunction`` will be invoked
for each input value. In addition to taking the input value, ``inputFunction``
takes the current state, initially ``initialState``, and returns the new state.
``combineFunction`` will be invoked to combine two states into a new state.
The final state is returned. Throws an error if ``initialState`` is NULL.
The behavior is undefined if ``inputFunction`` or ``combineFunction`` return a NULL.
Take care when designing ``initialState``, ``inputFunction`` and ``combineFunction``.
These must support evaluating aggregation in a distributed manner using partial
aggregation on many nodes, followed by shuffle over group-by keys, followed by
final aggregation. Consider all possible values of state to ensure that
``combineFunction`` is `commutative <https://en.wikipedia.org/wiki/Commutative_property>`_
and `associative <https://en.wikipedia.org/wiki/Associative_property>`_
operation with ``initialState`` as the
`identity <https://en.wikipedia.org/wiki/Identity_element>`_ value.
combineFunction(s, initialState) = s for any s
combineFunction(s1, s2) = combineFunction(s2, s1) for any s1 and s2
combineFunction(s1, combineFunction(s2, s3)) = combineFunction(combineFunction(s1, s2), s3) for any s1, s2, s3
In addition, make sure that the following holds for the inputFunction:
inputFunction(inputFunction(initialState, x), y) = combineFunction(inputFunction(initialState, x), inputFunction(initialState, y)) for any x and y
::
SELECT id, reduce_agg(value, 0, (a, b) -> a + b, (a, b) -> a + b)
FROM (
VALUES
(1, 2),
(1, 3),
(1, 4),
(2, 20),
(2, 30),
(2, 40)
) AS t(id, value)
GROUP BY id;
-- (1, 9)
-- (2, 90)
SELECT id, reduce_agg(value, 1, (a, b) -> a * b, (a, b) -> a * b)
FROM (
VALUES
(1, 2),
(1, 3),
(1, 4),
(2, 20),
(2, 30),
(2, 40)
) AS t(id, value)
GROUP BY id;
-- (1, 24)
-- (2, 24000)
The state type must be a boolean, integer, floating-point, or date/time/interval.
.. function:: set_agg(x) -> array<[same as input]>
Returns an array created from the distinct input ``x`` elements.
If the input includes ``NULL``, ``NULL`` will be included in the returned array.
If the input includes arrays with ``NULL`` elements or rows with ``NULL`` fields, they will
be included in the returned array. This function uses ``IS DISTINCT FROM`` to determine
distinctness. ::
SELECT set_agg(x) FROM (VALUES(1), (2), (null), (2), (null)) t(x) -- ARRAY[1, 2, null]
SELECT set_agg(x) FROM (VALUES(ROW(ROW(1, null))), ROW((ROW(2, 'a'))), ROW((ROW(1, null))), (null)) t(x) -- ARRAY[ROW(1, null), ROW(2, 'a'), null]
.. function:: set_union(array(T)) -> array(T)
Returns an array of all the distinct values contained in each array of the input.
When all inputs are ``NULL``, this function returns an empty array. If ``NULL`` is
an element of one of the input arrays, ``NULL`` will be included in the returned array.
If the input includes arrays with ``NULL`` elements or rows with ``NULL`` fields, they will
be included in the returned array. This function uses ``IS DISTINCT FROM`` to determine
distinctness.
Example::
SELECT set_union(elements)
FROM (
VALUES
ARRAY[1, 2, 3],
ARRAY[2, 3, 4]
) AS t(elements);
Returns ARRAY[1, 2, 3, 4]
.. function:: sum(x) -> [same as input]
Returns the sum of all input values.
.. function:: bitwise_and_agg(x) -> bigint
Returns the bitwise AND of all input values in 2's complement representation.
.. function:: bitwise_or_agg(x) -> bigint
Returns the bitwise OR of all input values in 2's complement representation.
.. function:: bitwise_xor_agg(x) -> bigint
Returns the bitwise XOR of all input values in 2's complement representation.
.. function:: histogram(x) -> map(K,bigint)
Returns a map containing the count of the number of times each input value occurs.
.. function:: map_agg(key, value) -> map(K,V)
Returns a map created from the input ``key`` / ``value`` pairs.
.. function:: map_union(x(K,V)) -> map(K,V) Returns the union of all the input maps. If a key is found in multiple input maps, that key's value in the resulting map comes from an arbitrary input map.
.. function:: map_union_sum(x(K,V)) -> map(K,V)
Returns the union of all the input maps summing the values of matching keys in all
the maps. All null values in the original maps are coalesced to 0.
.. function:: multimap_agg(key, value) -> map(K,array(V))
Returns a multimap created from the input ``key`` / ``value`` pairs.
Each key can be associated with multiple values.
.. function:: approx_distinct(x) -> bigint
Returns the approximate number of distinct input values.
This function provides an approximation of ``count(DISTINCT x)``.
Zero is returned if all input values are null.
This function should produce a standard error of 2.3%, which is the
standard deviation of the (approximately normal) error distribution over
all possible sets. It does not guarantee an upper bound on the error for
any specific input set.
.. function:: approx_distinct(x, e) -> bigint
Returns the approximate number of distinct input values.
This function provides an approximation of ``count(DISTINCT x)``.
Zero is returned if all input values are null.
This function should produce a standard error of no more than ``e``, which
is the standard deviation of the (approximately normal) error distribution
over all possible sets. It does not guarantee an upper bound on the error
for any specific input set. The current implementation of this function
requires that ``e`` be in the range of ``[0.0040625, 0.26000]``.
.. function:: approx_percentile(x, percentage) -> [same as x]
Returns the approximate percentile for all input values of ``x`` at the
given ``percentage``. The value of ``percentage`` must be between zero and
one and must be constant for all input rows.
.. function:: approx_percentile(x, percentage, accuracy) -> [same as x]
As ``approx_percentile(x, percentage)``, but with a maximum rank error of
``accuracy``. The value of ``accuracy`` must be between zero and one
(exclusive) and must be constant for all input rows. Note that a lower
"accuracy" is really a lower error threshold, and thus more accurate. The
default accuracy is ``0.01``.
.. function:: approx_percentile(x, percentages) -> array<[same as x]>
Returns the approximate percentile for all input values of ``x`` at each of
the specified percentages. Each element of the ``percentages`` array must be
between zero and one, and the array must be constant for all input rows.
.. function:: approx_percentile(x, percentages, accuracy) -> array<[same as x]>
As ``approx_percentile(x, percentages)``, but with a maximum rank error of
``accuracy``.
.. function:: approx_percentile(x, w, percentage) -> [same as x]
Returns the approximate weighed percentile for all input values of ``x``
using the per-item weight ``w`` at the percentage ``p``. The weight must be
an integer value of at least one. It is effectively a replication count for
the value ``x`` in the percentile set. The value of ``p`` must be between
zero and one and must be constant for all input rows.
.. function:: approx_percentile(x, w, percentage, accuracy) -> [same as x]
As ``approx_percentile(x, w, percentage)``, but with a maximum rank error of
``accuracy``.
.. function:: approx_percentile(x, w, percentages) -> array<[same as x]>
Returns the approximate weighed percentile for all input values of ``x``
using the per-item weight ``w`` at each of the given percentages specified
in the array. The weight must be an integer value of at least one. It is
effectively a replication count for the value ``x`` in the percentile set.
Each element of the array must be between zero and one, and the array must
be constant for all input rows.
.. function:: approx_percentile(x, w, percentages, accuracy) -> array<[same as x]>
As ``approx_percentile(x, w, percentages)``, but with a maximum rank error of
``accuracy``.
.. function:: approx_set(x) -> HyperLogLog
:noindex:
See :doc:`hyperloglog`.
.. function:: merge(x) -> HyperLogLog
:noindex:
See :doc:`hyperloglog`.
.. function:: khyperloglog_agg(x) -> KHyperLogLog
:noindex:
See :doc:`khyperloglog`.
.. function:: merge(qdigest(T)) -> qdigest(T)
:noindex:
See :doc:`qdigest`.
.. function:: qdigest_agg(x) -> qdigest<[same as x]>
:noindex:
See :doc:`qdigest`.
.. function:: qdigest_agg(x, w) -> qdigest<[same as x]>
:noindex:
See :doc:`qdigest`.
.. function:: qdigest_agg(x, w, accuracy) -> qdigest<[same as x]>
:noindex:
See :doc:`qdigest`.
.. function:: numeric_histogram(buckets, value, weight) -> map<double, double>
Computes an approximate histogram with up to ``buckets`` number of buckets
for all ``value``\ s with a per-item weight of ``weight``. The keys of the
returned map are roughly the center of the bin, and the entry is the total
weight of the bin. The algorithm is based loosely on [BenHaimTomTov2010]_.
``buckets`` must be a ``bigint``. ``value`` and ``weight`` must be numeric.
.. function:: numeric_histogram(buckets, value) -> map<double, double>
Computes an approximate histogram with up to ``buckets`` number of buckets
for all ``value``\ s. This function is equivalent to the variant of
:func:`!numeric_histogram` that takes a ``weight``, with a per-item weight of ``1``.
In this case, the total weight in the returned map is the count of items in the bin.
.. function:: corr(y, x) -> double
Returns correlation coefficient of input values.
.. function:: covar_pop(y, x) -> double
Returns the population covariance of input values.
.. function:: covar_samp(y, x) -> double
Returns the sample covariance of input values.
.. function:: entropy(c) -> double
Returns the log-2 entropy of count input-values.
.. math::
\mathrm{entropy}(c) = \sum_i \left[ {c_i \over \sum_j [c_j]} \log_2\left({\sum_j [c_j] \over c_i}\right) \right].
``c`` must be a ``bigint`` column of non-negative values.
The function ignores any ``NULL`` count. If the sum of non-``NULL`` counts is 0,
it returns 0.
.. function:: kurtosis(x) -> double
Returns the excess kurtosis of all input values. Unbiased estimate using
the following expression:
.. math::
\mathrm{kurtosis}(x) = {n(n+1) \over (n-1)(n-2)(n-3)} { \sum[(x_i-\mu)^4] \over \sigma^4} -3{ (n-1)^2 \over (n-2)(n-3) }
where :math:`\mu` is the mean, and :math:`\sigma` is the standard deviation.
.. function:: regr_intercept(y, x) -> double
Returns linear regression intercept of input values. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_slope(y, x) -> double
Returns linear regression slope of input values. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_avgx(y, x) -> double
Returns the average of the independent value in a group. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_avgy(y, x) -> double
Returns the average of the dependent value in a group. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_count(y, x) -> double
Returns the number of non-null pairs of input values. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_r2(y, x) -> double
Returns the coefficient of determination of the linear regression. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_sxy(y, x) -> double
Returns the sum of the product of the dependent and independent values in a group. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_syy(y, x) -> double
Returns the sum of the squares of the dependent values in a group. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: regr_sxx(y, x) -> double
Returns the sum of the squares of the independent values in a group. ``y`` is the dependent
value. ``x`` is the independent value.
.. function:: skewness(x) -> double
Returns the skewness of all input values.
.. function:: stddev(x) -> double
This is an alias for :func:`!stddev_samp`.
.. function:: stddev_pop(x) -> double
Returns the population standard deviation of all input values.
.. function:: stddev_samp(x) -> double
Returns the sample standard deviation of all input values.
.. function:: variance(x) -> double
This is an alias for :func:`!var_samp`.
.. function:: var_pop(x) -> double
Returns the population variance of all input values.
.. function:: var_samp(x) -> double
Returns the sample variance of all input values.
The following functions each measure how some metric of a binary confusion matrix changes as a function of classification thresholds. They are meant to be used in conjunction.
For example, to find the precision-recall curve, use
WITH
recall_precision AS (
SELECT
CLASSIFICATION_RECALL(10000, correct, pred) AS recalls,
CLASSIFICATION_PRECISION(10000, correct, pred) AS precisions
FROM
classification_dataset
)
SELECT
recall,
precision
FROM
recall_precision
CROSS JOIN UNNEST(recalls, precisions) AS t(recall, precision)
To get the corresponding thresholds for these values, use
WITH
recall_precision AS (
SELECT
CLASSIFICATION_THRESHOLDS(10000, correct, pred) AS thresholds,
CLASSIFICATION_RECALL(10000, correct, pred) AS recalls,
CLASSIFICATION_PRECISION(10000, correct, pred) AS precisions
FROM
classification_dataset
)
SELECT
threshold,
recall,
precision
FROM
recall_precision
CROSS JOIN UNNEST(thresholds, recalls, precisions) AS t(threshold, recall, precision)
To find the ROC curve, use
WITH
fallout_recall AS (
SELECT
CLASSIFICATION_FALLOUT(10000, correct, pred) AS fallouts,
CLASSIFICATION_RECALL(10000, correct, pred) AS recalls
FROM
classification_dataset
)
SELECT
fallout
recall,
FROM
recall_fallout
CROSS JOIN UNNEST(fallouts, recalls) AS t(fallout, recall)
.. function:: classification_miss_rate(buckets, y, x, weight) -> array<double>
Computes the miss-rate with up to ``buckets`` number of buckets. Returns
an array of miss-rate values.
``y`` should be a boolean outcome value; ``x`` should be predictions, each
between 0 and 1; ``weight`` should be non-negative values, indicating the weight of the instance.
The
`miss-rate <https://en.wikipedia.org/wiki/Type_I_and_type_II_errors#False_positive_and_false_negative_rates>`_
is defined as a sequence whose :math:`j`-th entry is
.. math ::
{
\sum_{i \;|\; x_i \leq t_j \bigwedge y_i = 1} \left[ w_i \right]
\over
\sum_{i \;|\; x_i \leq t_j \bigwedge y_i = 1} \left[ w_i \right]
+
\sum_{i \;|\; x_i > t_j \bigwedge y_i = 1} \left[ w_i \right]
},
where :math:`t_j` is the :math:`j`-th smallest threshold,
and :math:`y_i`, :math:`x_i`, and :math:`w_i` are the :math:`i`-th
entries of ``y``, ``x``, and ``weight``, respectively.
.. function:: classification_miss_rate(buckets, y, x) -> array<double>
This function is equivalent to the variant of
:func:`!classification_miss_rate` that takes a ``weight``, with a per-item weight of ``1``.
.. function:: classification_fall_out(buckets, y, x, weight) -> array<double>
Computes the fall-out with up to ``buckets`` number of buckets. Returns
an array of fall-out values.
``y`` should be a boolean outcome value; ``x`` should be predictions, each
between 0 and 1; ``weight`` should be non-negative values, indicating the weight of the instance.
The
`fall-out <https://en.wikipedia.org/wiki/Information_retrieval#Fall-out>`_
is defined as a sequence whose :math:`j`-th entry is
.. math ::
{
\sum_{i \;|\; x_i > t_j \bigwedge y_i = 0} \left[ w_i \right]
\over
\sum_{i \;|\; y_i = 0} \left[ w_i \right]
},
where :math:`t_j` is the :math:`j`-th smallest threshold,
and :math:`y_i`, :math:`x_i`, and :math:`w_i` are the :math:`i`-th
entries of ``y``, ``x``, and ``weight``, respectively.
.. function:: classification_fall_out(buckets, y, x) -> array<double>
This function is equivalent to the variant of
:func:`!classification_fall_out` that takes a ``weight``, with a per-item weight of ``1``.
.. function:: classification_precision(buckets, y, x, weight) -> array<double>
Computes the precision with up to ``buckets`` number of buckets. Returns
an array of precision values.
``y`` should be a boolean outcome value; ``x`` should be predictions, each
between 0 and 1; ``weight`` should be non-negative values, indicating the weight of the instance.
The
`precision <https://en.wikipedia.org/wiki/Positive_and_negative_predictive_values>`_
is defined as a sequence whose :math:`j`-th entry is
.. math ::
{
\sum_{i \;|\; x_i > t_j \bigwedge y_i = 1} \left[ w_i \right]
\over
\sum_{i \;|\; x_i > t_j} \left[ w_i \right]
},
where :math:`t_j` is the :math:`j`-th smallest threshold,
and :math:`y_i`, :math:`x_i`, and :math:`w_i` are the :math:`i`-th
entries of ``y``, ``x``, and ``weight``, respectively.
.. function:: classification_precision(buckets, y, x) -> array<double>
This function is equivalent to the variant of
:func:`!classification_precision` that takes a ``weight``, with a per-item weight of ``1``.
.. function:: classification_recall(buckets, y, x, weight) -> array<double>
Computes the recall with up to ``buckets`` number of buckets. Returns
an array of recall values.
``y`` should be a boolean outcome value; ``x`` should be predictions, each
between 0 and 1; ``weight`` should be non-negative values, indicating the weight of the instance.
The
`recall <https://en.wikipedia.org/wiki/Precision_and_recall#Recall>`_
is defined as a sequence whose :math:`j`-th entry is
.. math ::
{
\sum_{i \;|\; x_i > t_j \bigwedge y_i = 1} \left[ w_i \right]
\over
\sum_{i \;|\; y_i = 1} \left[ w_i \right]
},
where :math:`t_j` is the :math:`j`-th smallest threshold,
and :math:`y_i`, :math:`x_i`, and :math:`w_i` are the :math:`i`-th
entries of ``y``, ``x``, and ``weight``, respectively.
.. function:: classification_recall(buckets, y, x) -> array<double>
This function is equivalent to the variant of
:func:`!classification_recall` that takes a ``weight``, with a per-item weight of ``1``.
.. function:: classification_thresholds(buckets, y, x) -> array<double>
Computes the thresholds with up to ``buckets`` number of buckets. Returns
an array of threshold values.
``y`` should be a boolean outcome value; ``x`` should be predictions, each
between 0 and 1.
The thresholds are defined as a sequence whose :math:`j`-th entry is the :math:`j`-th smallest threshold.
The following functions approximate the binary differential entropy. That is, for a random variable x, they approximate
h(x) = - \int x \log_2\left(f(x)\right) dx,
where f(x) is the partial density function of x.
.. function:: differential_entropy(sample_size, x)
Returns the approximate log-2 differential entropy from a random variable's sample outcomes. The function internally
creates a reservoir (see [Black2015]_), then calculates the
entropy from the sample results by approximating the derivative of the cumulative distribution
(see [Alizadeh2010]_).
``sample_size`` (``long``) is the maximal number of reservoir samples.
``x`` (``double``) is the samples.
For example, to find the differential entropy of ``x`` of ``data`` using 1000000 reservoir samples, use
.. code-block:: none
SELECT
differential_entropy(1000000, x)
FROM
data
.. note::
If :math:`x` has a known lower and upper bound,
prefer the versions taking ``(bucket_count, x, 1.0, "fixed_histogram_mle", min, max)``,
or ``(bucket_count, x, 1.0, "fixed_histogram_jacknife", min, max)``,
as they have better convergence.
.. function:: differential_entropy(sample_size, x, weight)
Returns the approximate log-2 differential entropy from a random variable's sample outcomes. The function
internally creates a weighted reservoir (see [Efraimidis2006]_), then calculates the
entropy from the sample results by approximating the derivative of the cumulative distribution
(see [Alizadeh2010]_).
``sample_size`` is the maximal number of reservoir samples.
``x`` (``double``) is the samples.
``weight`` (``double``) is a non-negative double value indicating the weight of the sample.
For example, to find the differential entropy of ``x`` with weights ``weight`` of ``data``
using 1000000 reservoir samples, use
.. code-block:: none
SELECT
differential_entropy(1000000, x, weight)
FROM
data
.. note::
If :math:`x` has a known lower and upper bound,
prefer the versions taking ``(bucket_count, x, weight, "fixed_histogram_mle", min, max)``,
or ``(bucket_count, x, weight, "fixed_histogram_jacknife", min, max)``,
as they have better convergence.
.. function:: differential_entropy(bucket_count, x, weight, method, min, max) -> double
Returns the approximate log-2 differential entropy from a random variable's sample outcomes. The function
internally creates a conceptual histogram of the sample values, calculates the counts, and
then approximates the entropy using maximum likelihood with or without Jacknife
correction, based on the ``method`` parameter. If Jacknife correction (see [Beirlant2001]_) is used, the
estimate is
.. math ::
n H(x) - (n - 1) \sum_{i = 1}^n H\left(x_{(i)}\right)
where :math:`n` is the length of the sequence, and :math:`x_{(i)}` is the sequence with the :math:`i`-th element
removed.
``bucket_count`` (``long``) determines the number of histogram buckets.
``x`` (``double``) is the samples.
``method`` (``varchar``) is either ``'fixed_histogram_mle'`` (for the maximum likelihood estimate)
or ``'fixed_histogram_jacknife'`` (for the jacknife-corrected maximum likelihood estimate).
``min`` and ``max`` (both ``double``) are the minimal and maximal values, respectively;
the function will throw if there is an input outside this range.
``weight`` (``double``) is the weight of the sample, and must be non-negative.
For example, to find the differential entropy of ``x``, each between ``0.0`` and ``1.0``,
with weights 1.0 of ``data`` using 1000000 bins and jacknife estimates, use
.. code-block:: none
SELECT
differential_entropy(1000000, x, 1.0, 'fixed_histogram_jacknife', 0.0, 1.0)
FROM
data
To find the differential entropy of ``x``, each between ``-2.0`` and ``2.0``,
with weights ``weight`` of ``data`` using 1000000 buckets and maximum-likelihood estimates, use
.. code-block:: none
SELECT
differential_entropy(1000000, x, weight, 'fixed_histogram_mle', -2.0, 2.0)
FROM
data
.. note::
If :math:`x` doesn't have known lower and upper bounds, prefer the versions taking ``(sample_size, x)``
(unweighted case) or ``(sample_size, x, weight)`` (weighted case), as they use reservoir
sampling which doesn't require a known range for samples.
Otherwise, if the number of distinct weights is low,
especially if the number of samples is low, consider using the version taking
``(bucket_count, x, weight, "fixed_histogram_jacknife", min, max)``, as jacknife bias correction,
is better than maximum likelihood estimation. However, if the number of distinct weights is high,
consider using the version taking ``(bucket_count, x, weight, "fixed_histogram_mle", min, max)``,
as this will reduce memory and running time.
.. function:: approx_most_frequent(buckets, value, capacity) -> map<[same as value], bigint>
Computes the top frequent values up to ``buckets`` elements approximately.
Approximate estimation of the function enables us to pick up the frequent
values with less memory. Larger ``capacity`` improves the accuracy of
underlying algorithm with sacrificing the memory capacity. The returned
value is a map containing the top elements with corresponding estimated
frequency.
The error of the function depends on the permutation of the values and its
cardinality. We can set the capacity same as the cardinality of the
underlying data to achieve the least error.
``buckets`` and ``capacity`` must be ``bigint``. ``value`` can be numeric
or string type.
The function uses the stream summary data structure proposed in the paper
`Efficient computation of frequent and top-k elements in data streams <https://www.cse.ust.hk/~raywong/comp5331/References/EfficientComputationOfFrequentAndTop-kElementsInDataStreams.pdf>`_ by A.Metwally, D.Agrawal and A.Abbadi.
Reservoir sample functions use a fixed sample size, as opposed to :ref:`TABLESAMPLE <sql-tablesample>`. Fixed sample sizes always result in a fixed total size while still guaranteeing that each record in dataset has an equal probability of being chosen. See [Vitter1985].
.. function:: reservoir_sample(initial_sample: array(T), initial_processed_count: bigint, values_to_sample: T, desired_sample_size: int) -> row(processed_count: bigint, sample: array(T))
Computes a new reservoir sample given:
- ``initial_sample``: an initial sample array, or ``NULL`` if creating a new
sample.
- ``initial_processed_count``: the number of records processed to generate
the initial sample array. This should be 0 or ``NULL`` if
``initital_sample`` is ``NULL``.
- ``values_to_sample``: the column to sample from.
- ``desired_sample_size``: the size of reservoir sample.
The function outputs a single row type with two columns:
#. Processed count: The total number of rows the function sampled
from. It includes the total from the ``initial_processed_count``,
if provided.
#. Reservoir sample: An array with length equivalent to the minimum of
``desired_sample_size`` and the number of values in the
``values_to_sample`` argument.
.. code-block:: sql
WITH result as (
SELECT
reservoir_sample(NULL, 0, col, 5) as reservoir
FROM (
VALUES
1, 2, 3, 4, 5, 6, 7, 8, 9, 0
) as t(col)
)
SELECT
reservoir.processed_count, reservoir.sample
FROM result;
.. code-block:: none
processed_count | sample
-----------------+-----------------
10 | [1, 2, 8, 4, 5]
To merge older samples with new data, supply valid arguments to the
``initial_sample`` argument and ``initial_processed_count`` arguments.
.. code-block:: sql
WITH initial_sample as (
SELECT
reservoir_sample(NULL, 0, col, 3) as reservoir
FROM (
VALUES
0, 1, 2, 3, 4
) as t(col)
),
new_sample as (
SELECT
reservoir_sample(
(SELECT reservoir.sample FROM initial_sample),
(SELECT reservoir.processed_count FROM initial_sample),
col,
3
) as result
FROM (
VALUES
5, 6, 7, 8, 9
) as t(col)
)
SELECT
result.processed_count, result.sample
FROM new_sample;
.. code-block:: none
processed_count | sample
-----------------+-----------
10 | [8, 3, 2]
To sample an entire row of a table, use a ``ROW`` type input with
each subfield corresponding to the columns of the source table.
.. code-block:: sql
WITH result as (
SELECT
reservoir_sample(NULL, 0, CAST(row(idx, val) AS row(idx int, val varchar)), 2) as reservoir
FROM (
VALUES
(1, 'a'), (2, 'b'), (3, 'c'), (4, 'd'), (5, 'e')
) as t(idx, val)
)
SELECT
reservoir.processed_count, reservoir.sample
FROM result;
.. code-block:: none
processed_count | sample
-----------------+----------------------------------
5 | [{idx=1, val=a}, {idx=5, val=e}]
See :doc:`noisy`.
| [Alizadeh2010] | Alizadeh Noughabi, Hadi & Arghami, N. (2010). "A New Estimator of Entropy". |
| [Beirlant2001] | Beirlant, Dudewicz, Gyorfi, and van der Meulen, "Nonparametric entropy estimation: an overview", (2001) |
| [BenHaimTomTov2010] | Yael Ben-Haim and Elad Tom-Tov, "A streaming parallel decision tree algorithm", J. Machine Learning Research 11 (2010), pp. 849--872. |
| [Black2015] | Black, Paul E. (26 January 2015). "Reservoir sampling". Dictionary of Algorithms and Data Structures. |
| [Efraimidis2006] | Efraimidis, Pavlos S.; Spirakis, Paul G. (2006-03-16). "Weighted random sampling with a reservoir". Information Processing Letters. 97 (5): 181–185. |
| [Vitter1985] | Vitter, Jeffrey S. "Random sampling with a reservoir." ACM Transactions on Mathematical Software (TOMS) 11.1 (1985): 37-57. |