Iterative simple linear regression coefficient calculation for big data using components
AssigneeCloud & Stream Gears LLC
InventorJizhu Lu
Life of this patent
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Abstract
Methods, systems, and computing system program products for iteratively calculating Simple Linear Regression (SLR) coefficients for Big Data, including iteratively calculating one or more components of SLR coefficients for a modified computation set based on one or more components of SLR coefficients calculated for a pre-modified computation set and then calculating the SLR coefficients for the modified computation set based on the iteratively calculated components. Iteratively calculating SLR coefficients avoids visiting all data elements in the modified computation set and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.
Claims20
At a computing-device-based computing system, the computing-device-based computing system comprising one or more computing devices, each of the one or more computing devices comprising one or more processors, the computing-device-based computing system comprising one or more storage media, the one or more storage media having stored one or two data sets, a computing-system-implemented method for calculating simple linear regression coefficients for a modified computation set of a specified number of pairs of data elements of the one or two data sets, each of said pairs of data elements containing an observation of an independent variable and an observation of a dependent variable, the method comprising:
- initializing, by the computing-device-based computing system, a sum or a mean or both for each variable, and one or more components of simple linear regression coefficients other than a sum and a mean for a pre-modified computation set with a specified size n (n≥6) of one or two data sets on the one or more storage media;
- accessing, by the computing-device-based computing system, a pair of data elements to be removed from the pre-modified computation set and a pair of data elements to be added to the pre-modified computation set;
- modifying, by the computing-device-based computing system, the pre-modified computation set by removing the to be removed pair of data elements from the pre-modified computation set and adding the to-be-added pair of data elements to the pre-modified computation set;
- iteratively deriving, by the computing-device-based computing system, a sum or a mean or both for each variable in the modified computation set;
- directly iteratively deriving, by the computing-device-based computing system and based at least in part on the one or more components of simple linear regression coefficients other than a sum and a mean for the pre-modified computation set, one or more components of simple linear regression coefficients other than a sum and a mean for the modified computation set, wherein directly iteratively deriving includes:
- accessing the one or more components other than a sum and a mean without accessing all data elements in the modified computation set to reduce data accessing latency thereby saving computing resources and reducing the computing system's power consumption;
- and
- removing any contribution of the removed pair of data elements from each of the one or more accessed components mathematically and adding any contribution of the added pair of data elements to each of the one or more accessed components mathematically wherein not all data elements in the modified computation set are used during the directly iteratively deriving the one or more components to reduce number of operations performed by the computing system thereby increasing calculation efficiency;
- and
- generating, by the computing-device-based computing system and based on one or more of the derived components, simple linear regression coefficients for the modified computation set.
A computing system, the computing system comprising:
- one or more computing devices;
- each computing device comprising one or more processors;
- one or more storage media comprising one or two data sets;
- and
- one or more calculation modules that, when executed by at least one of the one or more computing devices, determine simple linear regression coefficients for a specified number of pairs of data elements in a modified computation set of the one or two data sets, each of said pairs of data elements containing an observation of an independent variable and an observation of a dependent variable, wherein determination of the simple linear regression coefficients includes to:
- a. initialize a sum or a mean or both for each variable, and one or more components of simple linear regression coefficients other than a sum and a mean for a pre-modified computation set of a specified size n (n≥6), wherein the pre-modified computation set contains n pairs of data elements of the one or two data sets;
- b. access a pair of data elements to be removed from the pre-modified computation set and a pair of data elements to be added to the pre-modified computation set;
- c. modify the pre-modified computation set, wherein modification of the pre-modified computation set includes to remove the to-be-removed pair of data elements from the pre-modified computation set and to add the to-be-added pair of data elements to the pre-modified computation set;
- d. iteratively calculate a sum or a mean or both for each variable in the modified computation set;
- e. directly iteratively calculate one or more components of simple linear regression coefficients other than a sum and a mean for the modified computation set based at least in part on the one or more components other than a sum and a mean for the pre-modified computation set, wherein direct iterative calculation of the one or more components includes to remove any contribution of the removed pair of data elements from each of the one or more components mathematically and to add any contribution of the added pair of data elements to each of the one or more components mathematically without accessing and using all data elements in the modified computation set in order to reduce data access latency and number of operations performed by the computing system, thereby increasing calculation efficiency, saving computing resources and reducing the computing system's power consumption;
- and
- f. generate, based on one or more of the calculated components for the modified computation set, simple linear regression coefficients for the modified computation set.
A computing system program product for use at a configured computing system that comprises one or more computing devices, each of the computing devices comprising one or more processors, the computing system comprising one or more storage media, the one or more storage media comprising one or two data sets, the computing system program product for implementing a method for generating simple linear regression coefficients for a specified number of pairs of data elements in a modified computation set of the one or two data sets, each of said pairs of data elements containing an observation of an independent variable and an observation of a dependent variable, the computing system program product comprising one or more non-transitory computing-device-readable storage media having stored thereon computing-device-executable instructions that, when executed by at least one of the one or more computing devices, cause the configured computing system to perform the method, the method including to:
- initialize, by the configured computing system, a sum or a mean or both for each variable, and one or more components of simple linear regression coefficients other than a sum and a mean for a pre-modified computation set of a specified size n (n≥6) of one or two data sets on the one or more storage media;
- access, by the configured computing system, a pair of data elements to be removed from the pre-modified computation set and a pair of data elements to be added to the pre-modified computation set;
- modify, by the configured computing system, the pre-modified computation set by removing the to-be-removed pair of data elements from the pre-modified computation set and adding the to-be-added pair of data elements to the pre-modified computation set;
- iteratively calculate, by the configured computing system, a sum or a mean or both for the modified computation set;
- directly iteratively calculate, by the configured computing system, one or more components of simple linear regression coefficients other than a sum and a mean for the modified computation set based at least in part on the one or more components of simple linear regression coefficients other than a sum and a mean for the pre-modified computation set, wherein not all data elements in the modified computation set are accessed and used in order to reduce data access latency and number of operations performed by the computing system, thereby saving computing resources and increasing calculation efficiency, including to:
- access the one or more components other than a sum and a mean without accessing all data elements in the modified computation set to reduce data accessing latency thereby saving computing resources and reducing the configured computing system's power consumption;
- and
- remove any contribution of the removed pair of data elements from each of the one or more accessed components mathematically and add any contribution of the added pair of data elements to each of the one or more accessed components mathematically without using all data elements in the modified computation set in order to reduce the number of operations performed by the configured computing system thereby increasing calculation efficiency;
- and
- generate, by the configured computing system, simple linear regression coefficients for the modified computation set based on one or more of the calculated components.
Dependencies are inferred from the claim text.