Distributed Processing

Intel® oneAPI Data Analytics Library Developer Guide and Reference

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ID 772611

Date 7/13/2023

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Distributed Processing

This mode assumes that the data set is split into nblocks blocks across computation nodes.

Algorithm Parameters

The low order moments algorithm in the distributed processing mode has the following parameters:

Algorithm Parameters for Low Order Moments (Distributed Processing)
Parameter	Default Valude	Description
`computeStep`	Not applicable	The parameter required to initialize the algorithm. Can be: `step1Local` - the first step, performed on local nodes `step2Master` - the second step, performed on a master node
`algorithmFPType`	`float`	The floating-point type that the algorithm uses for intermediate computations. Can be `float` or `double`.
`method`	`defaultDense`	Available methods for computation of low order moments: defaultDense default performance-oriented method singlePassDense implementation of the single-pass algorithm proposed by D.H.D. West sumDense implementation of the algorithm in the cases where the basic statistics associated with the numeric table are pre-computed sums; returns an error if pre-computed sums are not defined fastCSR performance-oriented method for CSR numeric tables singlePassCSR implementation of the single-pass algorithm proposed by D.H.D. West; optimized for CSR numeric tables sumCSR implementation of the algorithm in the cases where the basic statistics associated with the numeric table are pre-computed sums; optimized for CSR numeric tables; returns an error if pre-computed sums are not defined
`estimatesToCompute`	`estimatesAll`	Estimates to be computed by the algorithm: `estimatesAll` - all supported moments `estimatesMinMax` - minimum and maximum `estimatesMeanVariance` - mean and variance

Computation of low order moments follows the general schema described in Algorithms:

Step 1 - on Local Nodes

In this step, the low order moments algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Algorithm Input for Low Order Moments (Distributed Processing, Step 1)
Input ID	Input
`data`	Pointer to the numeric table of size $n_{i} \times p$ that represents the i-th data block on the local node. While the input for `defaultDense`, `singlePassDense`, or `sumDense` method can be an object of any class derived from `NumericTable`, the input for `fastCSR`, `singlePassCSR`, or `sumCSR` method can only be an object of the `CSRNumericTable` class.

In this step, the low order moments algorithm calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Algorithm Output for Low Order Moments (Distributed Processing, Step 1)
Result ID	Result
`nObservations`	Pointer to the $1 i m e s 1$ numeric table that contains the number of observations processed so far on the local node. By default, this result is an object of the `HomogenNumericTable` class, but you can define the result as an object of any class derived from `NumericTable` except `CSRNumericTable`.

Partial characteristics computed so far on the local node, each in a $1 i m e s p$ numeric table. By default, each table is an object of the HomogenNumericTable class, but you can define the tables as objects of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

Partial Characteristics for Low Order Moments (Distributed Processing, Step 1)
Result ID	Result
`partialMinimum`	Partial minimums
`partialMaximum`	Partial maximums
`partialSum`	Partial sums
`partialSumSquares`	Partial sums of squares
`partialSumSquaresCentered`	Partial sums of squared differences from the means

Step 2 - on Master Node

Algorithm Input for Low Order Moments (Distributed Processing, Step 2)
Input ID	Input
`partialResults`	A collection that contains numeric tables with partial results computed in Step 1 on local nodes (six numeric tables from each local node). These numeric tables can be objects of any class derived from the `NumericTable` class except `PackedSymmetricMatrix` and `PackedTriangularMatrix`.

In this step, the low order moments algorithm calculates the results described in the following table. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

NOTE:

Each result is a pointer to the $1 i m e s p$ numeric table that contains characteristics for each feature in the data set. By default, the tables are objects of the HomogenNumericTable class, but you can define each table as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

Algorithm Output for Low Order Moments (Distributed Processing, Step 2)
Result ID	Characteristic
`minimum`	Minimums
`maximum`	Maximums
`sum`	Sums
`sumSquares`	Sums of squares
`sumSquaresCentered`	Sums of squared differences from the means
`mean`	Estimates for the means
`secondOrderRawMoment`	Estimates for the second order raw moments
`variance`	Estimates for the variances
`standardDeviation`	Estimates for the standard deviations
`variation`	Estimates for the variations

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

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Intel® oneAPI Data Analytics Library Developer Guide and Reference

Distributed Processing

Algorithm Parameters

Step 1 - on Local Nodes

Step 2 - on Master Node