Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics

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Date 12/04/2020
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Document Table of Contents
Document Table of Contents x
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics x
Legal Information About This Document About Summary Statistics Algorithms and Interfaces in Summary Statistics Common Usage Model of Summary Statistics Algorithms Processing Data in Blocks Detecting Outliers in Datasets Dealing with Missing Observations Computing Quantiles for Streaming Data Bibliography
About This Document x
Conventions and Symbols
Algorithms and Interfaces in Summary Statistics x
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and Variance-Covariance/Correlation/Cross-Product Matrix Computing Median Absolute Deviation Computing Mean Absolute Deviation Computing Minimum/Maximum Values Calculating Order Statistics Estimating Quantiles Estimating a Pooled/Group Variance-Covariance Matrices/Means Estimating a Partial Variance-Covariance Matrix Performing Robust Estimation of a Variance-Covariance Matrix Detecting Multivariate Outliers Handling Missing Values in Matrices of Observations Parameterizing a Correlation Matrix Sorting an Observation Matrix
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and Variance-Covariance/Correlation/Cross-Product Matrix x
Computing Estimations for Large Datasets Calculating Multiple Estimates
Estimating Quantiles x
Computing Quantiles for Streaming Data with VSL_SS_METHOD_SQUANTS_ZW
Handling Missing Values in Matrices of Observations x
Basic Assumptions for the MI Method Basic Components of the MI Method
Detecting Outliers in Datasets x
Using the BACON Algorithm for Outlier Detection Using Robust Methods
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics

Parameterizing a Correlation Matrix

Use a Spectral Decomposition method to parameterize a correlation matrix [Rebonato1999]. The input of the algorithm is a matrix that resembles a correlation matrix but lacks the property of positive semi-definiteness. The output of the algorithm is a parameterized correlation matrix with non-negative eigenvalues.

Summary Statistics supports two usage models for parametrizing a correlation matrix:

  1. The dataset and its parameters are provided into the library through a constructor or editors of the Summary Statistics. The correlation matrix for this dataset is computed using the approaches described above. Parameterization of the correlation is performed with the method of Spectral Decomposition.

  2. The correlation matrix computed earlier using Summary Statistics algorithms or other tools is simply registered in the Summary Statistics task. The dimension of the task defines the order of the matrix. In this case, you do not need to provide the dataset and its attributes such as number of observations and its storage format to the library.

The example below illustrates the second parameterization model:

#include "mkl_vsl.h"
#define DIM 3     /* dimension of the task */
 
int main()
{
    VSLSSTaskPtr task;
    MKL_INT p;
    MKL_INT corstorage, pcorstorage;
    int status;
    float cor[DIM*DIM], pcor[DIM*DIM];
 
    p = DIM;
    corstorage  = VSL_SS_MATRIX_STORAGE_FULL;
    pcorstorage = VSL_SS_MATRIX_STORAGE_FULL;
 
    /* Create a task */
    status = vslsSSNewTask( &task, &p, 0, 0, 0, 0, 0 );
 
    /* Register arrays for parameterization of the correlation matrix */ 
    status = vslsSSEditCorParameterization( task, cor, &corstorage, 
                                            pcor, &pcorstorage );
    /* Compute a task */
    status = vslsSSCompute( task, VSL_SS_PARAMTR_COR, VSL_SS_METHOD_SD );
 
    /* Delete the task */
    status = vslSSDeleteTask( &task );
 
    return 0;
}

 

Parent topic: Algorithms and Interfaces in Summary Statistics
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