feat: add classification functions (#11792)

Summary:

Add the classification functions from presto into velox: https://prestodb.io/docs/current/functions/aggregate.html#classification-metrics-aggregate-functions

Classification functions all use `FixedDoubleHistogram`, which is a data structure to represent the bucket of weights. The index of the bucket for the histogram is evenly distributed between the min and value values.

For all of the classification functions, the only difference is the extraction phase. All other steps will be the same.

At a high level:
- addRawInput will add a value into either the true or false weight bucket. The bucket to add the value to will depend on the prediction value. The prediction value is linearly mapped into a bucket based on (min, max and bucketCount) by normalizing the prediction between min and max.

- The schema of the intermediate states is [version header][bucket count][min][max][weights]

Reviewed By: Yuhta

Differential Revision: D66684198

velox/docs/functions/presto/aggregate.rst

@@ -411,6 +411,201 @@ __ https://www.cse.ust.hk/~raywong/comp5331/References/EfficientComputationOfFre
     As ``approx_percentile(x, w, percentages)``, but with a maximum rank error
     of ``accuracy``.
 
+Classification Metrics Aggregate Functions
+------------------------------------------
+
+The following functions each measure how some metric of a binary
+`confusion matrix <https://en.wikipedia.org/wiki/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 <https://en.wikipedia.org/wiki/Precision_and_recall>`_, use
+
+    .. code-block:: none
+
+         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
+
+    .. code-block:: none
+
+         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 <https://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_, use
+
+    .. code-block:: none
+
+         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.
+
 Statistical Aggregate Functions
 -------------------------------
 

velox/docs/functions/presto/coverage.rst

@@ -325,11 +325,11 @@ Here is a list of all scalar and aggregate Presto functions with functions that
     :func:`array_duplicates`                  :func:`dow`                               :func:`json_extract`                      :func:`repeat`                            st_union                                      :func:`bool_and`                              :func:`rank`
     :func:`array_except`                      :func:`doy`                               :func:`json_extract_scalar`               :func:`replace`                           st_within                                     :func:`bool_or`                               :func:`row_number`
     :func:`array_frequency`                   :func:`e`                                 :func:`json_format`                       replace_first                             st_x                                          :func:`checksum`
-    :func:`array_has_duplicates`              :func:`element_at`                        :func:`json_parse`                        :func:`reverse`                           st_xmax                                       classification_fall_out
-    :func:`array_intersect`                   :func:`empty_approx_set`                  :func:`json_size`                         rgb                                       st_xmin                                       classification_miss_rate
-    :func:`array_join`                        :func:`ends_with`                         key_sampling_percent                      :func:`round`                             st_y                                          classification_precision
-    array_least_frequent                      enum_key                                  :func:`laplace_cdf`                       :func:`rpad`                              st_ymax                                       classification_recall
-    :func:`array_max`                         :func:`exp`                               :func:`last_day_of_month`                 :func:`rtrim`                             st_ymin                                       classification_thresholds
+    :func:`array_has_duplicates`              :func:`element_at`                        :func:`json_parse`                        :func:`reverse`                           st_xmax                                       :func: `classification_fall_out`
+    :func:`array_intersect`                   :func:`empty_approx_set`                  :func:`json_size`                         rgb                                       st_xmin                                       :func: `classification_miss_rate`
+    :func:`array_join`                        :func:`ends_with`                         key_sampling_percent                      :func:`round`                             st_y                                          :func: `classification_precision`
+    array_least_frequent                      enum_key                                  :func:`laplace_cdf`                       :func:`rpad`                              st_ymax                                       :func: `classification_recall`
+    :func:`array_max`                         :func:`exp`                               :func:`last_day_of_month`                 :func:`rtrim`                             st_ymin                                       :func: `classification_thresholds`
     array_max_by                              expand_envelope                           :func:`least`                             scale_qdigest                             :func:`starts_with`                           convex_hull_agg
     :func:`array_min`                         :func:`f_cdf`                             :func:`length`                            :func:`second`                            :func:`strpos`                                :func:`corr`
     array_min_by                              features                                  :func:`levenshtein_distance`              secure_rand                               :func:`strrpos`                               :func:`count`

velox/functions/prestosql/aggregates/AggregateNames.h

@@ -32,6 +32,11 @@ const char* const kBitwiseXor = "bitwise_xor_agg";
 const char* const kBoolAnd = "bool_and";
 const char* const kBoolOr = "bool_or";
 const char* const kChecksum = "checksum";
+const char* const kClassificationFallout = "classification_fall_out";
+const char* const kClassificationPrecision = "classification_precision";
+const char* const kClassificationRecall = "classification_recall";
+const char* const kClassificationMissRate = "classification_miss_rate";
+const char* const kClassificationThreshold = "classification_thresholds";
 const char* const kCorr = "corr";
 const char* const kCount = "count";
 const char* const kCountIf = "count_if";

velox/functions/prestosql/aggregates/CMakeLists.txt

@@ -28,6 +28,7 @@ velox_add_library(
   CountIfAggregate.cpp
   CovarianceAggregates.cpp
   ChecksumAggregate.cpp
+  ClassificationAggregation.cpp
   EntropyAggregates.cpp
   GeometricMeanAggregate.cpp
   HistogramAggregate.cpp