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#pragma once
#include <AggregateFunctions/IAggregateFunction.h>
#include <Common/assert_cast.h>
#include <DataTypes/DataTypesNumber.h>
#include <Common/HashTable/HashMap.h>
#include <AggregateFunctions/UniqVariadicHash.h>
/** Aggregate function that calculates statistics on top of cross-tab:
* - histogram of every argument and every pair of elements.
* These statistics include:
* - Cramer's V;
* - Theil's U;
* - contingency coefficient;
* It can be interpreted as interdependency coefficient between arguments;
* or non-parametric correlation coefficient.
*/
namespace DB
{
struct CrossTabData
{
/// Total count.
UInt64 count = 0;
/// Count of every value of the first and second argument (values are pre-hashed).
/// Note: non-cryptographic 64bit hash is used, it means that the calculation is approximate.
HashMapWithStackMemory<UInt64, UInt64, TrivialHash, 4> count_a;
HashMapWithStackMemory<UInt64, UInt64, TrivialHash, 4> count_b;
/// Count of every pair of values. We pack two hashes into UInt128.
HashMapWithStackMemory<UInt128, UInt64, UInt128Hash, 4> count_ab;
void add(UInt64 hash1, UInt64 hash2)
{
++count;
++count_a[hash1];
++count_b[hash2];
UInt128 hash_pair{hash1, hash2};
++count_ab[hash_pair];
}
void merge(const CrossTabData & other)
{
count += other.count;
for (const auto & [key, value] : other.count_a)
count_a[key] += value;
for (const auto & [key, value] : other.count_b)
count_b[key] += value;
for (const auto & [key, value] : other.count_ab)
count_ab[key] += value;
}
void serialize(WriteBuffer & buf) const
{
writeBinary(count, buf);
count_a.write(buf);
count_b.write(buf);
count_ab.write(buf);
}
void deserialize(ReadBuffer & buf)
{
readBinary(count, buf);
count_a.read(buf);
count_b.read(buf);
count_ab.read(buf);
}
/** See https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_V
*
* φ² is χ² divided by the sample size (count).
* χ² is the sum of squares of the normalized differences between the "expected" and "observed" statistics.
* ("Expected" in the case when one of the hypotheses is true).
* Something resembling the L2 distance.
*
* Note: statisticians use the name χ² for every statistic that has χ² distribution in many various contexts.
*
* Let's suppose that there is no association between the values a and b.
* Then the frequency (e.g. probability) of (a, b) pair is equal to the multiplied frequencies of a and b:
* count_ab / count = (count_a / count) * (count_b / count)
* count_ab = count_a * count_b / count
*
* Let's calculate the difference between the values that are supposed to be equal if there is no association between a and b:
* count_ab - count_a * count_b / count
*
* Let's sum the squares of the differences across all (a, b) pairs.
* Then divide by the second term for normalization: (count_a * count_b / count)
*
* This will be the χ² statistics.
* This statistics is used as a base for many other statistics.
*/
Float64 getPhiSquared() const
{
Float64 chi_squared = 0;
for (const auto & [key, value_ab] : count_ab)
{
Float64 value_a = count_a.at(key.items[0]);
Float64 value_b = count_b.at(key.items[1]);
Float64 expected_value_ab = (value_a * value_b) / count;
Float64 chi_squared_elem = value_ab - expected_value_ab;
chi_squared_elem = chi_squared_elem * chi_squared_elem / expected_value_ab;
chi_squared += chi_squared_elem;
}
return chi_squared / count;
}
};
template <typename Data>
class AggregateFunctionCrossTab : public IAggregateFunctionDataHelper<Data, AggregateFunctionCrossTab<Data>>
{
public:
explicit AggregateFunctionCrossTab(const DataTypes & arguments)
: IAggregateFunctionDataHelper<Data, AggregateFunctionCrossTab<Data>>({arguments}, {}, createResultType())
{
}
String getName() const override
{
return Data::getName();
}
bool allocatesMemoryInArena() const override
{
return false;
}
static DataTypePtr createResultType()
{
return std::make_shared<DataTypeNumber<Float64>>();
}
void add(
AggregateDataPtr __restrict place,
const IColumn ** columns,
size_t row_num,
Arena *) const override
{
UInt64 hash1 = UniqVariadicHash<false, false>::apply(1, &columns[0], row_num);
UInt64 hash2 = UniqVariadicHash<false, false>::apply(1, &columns[1], row_num);
this->data(place).add(hash1, hash2);
}
void merge(AggregateDataPtr __restrict place, ConstAggregateDataPtr rhs, Arena *) const override
{
this->data(place).merge(this->data(rhs));
}
void serialize(ConstAggregateDataPtr __restrict place, WriteBuffer & buf, std::optional<size_t>) const override
{
this->data(place).serialize(buf);
}
void deserialize(AggregateDataPtr __restrict place, ReadBuffer & buf, std::optional<size_t>, Arena *) const override
{
this->data(place).deserialize(buf);
}
void insertResultInto(AggregateDataPtr __restrict place, IColumn & to, Arena *) const override
{
Float64 result = this->data(place).getResult();
auto & column = static_cast<ColumnVector<Float64> &>(to);
column.getData().push_back(result);
}
};
}
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