Tail Calculation Using Data Correlation and Precomputed Sorting
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Solution Overview
Problem
Conventional methods for calculating risk measures, such as Value at Risk (VaR) and Conditional Value at Risk (CVaR), incur substantial computational costs due to inefficient tail calculations, especially when dealing with large datasets.
Innovation Solution
The technique exploits data correlation between datasets to improve the performance of tail calculations by determining the locations of elements outside a specified percentile in one dataset and using those locations to efficiently calculate the corresponding elements in another correlated dataset.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods are used to calculate tail calculations for risk measures, then accuracy of risk assessment is maintained, but computational time and processing cost increase substantially
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing the sorted order of elements from the first dataset before computing tail calculations for the second dataset. This pre-computed ordering information is reused to efficiently identify tail elements in the second dataset without performing complete sorting, thereby reducing computational time while maintaining accuracy.
Solution Approach 2:
The patent uses copying by creating a data structure that stores the sorted order indices from the first dataset. This copied ordering information is then applied to the second dataset to identify tail elements, avoiding the need to re-sort the second dataset completely and thus reducing computational overhead while preserving measurement precision.
2Measurement precision
If conventional tail calculation methods are applied to large datasets, then complete accuracy is achieved, but computational cost increases substantially
Solution Approach 1:
The patent performs preliminary sorting of the first dataset and stores the order indices before processing the second dataset. This preliminary action allows the system to leverage the pre-computed ordering to quickly identify tail elements in the second dataset through correlation, significantly improving computational efficiency for large datasets while maintaining complete accuracy.
Solution Approach 2:
The patent copies the sorted order information from the first dataset into a reusable data structure. This copied ordering data is then applied to the second dataset to efficiently determine tail elements without repeating the expensive sorting operation, thereby enhancing productivity while preserving measurement precision.
3Measurement precision
If traditional methods are used for real-time risk reporting, then thorough risk analysis is performed, but processing speed becomes insufficient
Solution Approach 1:
The patent implements preliminary action by pre-computing and storing the sorted order of the first dataset before real-time risk reporting is needed. During real-time reporting, this pre-computed ordering is reused to rapidly identify tail elements in correlated datasets, enabling thorough risk analysis to be completed at speeds suitable for real-time applications.
Solution Approach 2:
The patent copies the sorted order indices from the first dataset into a reusable data structure that can be quickly applied during real-time reporting. This copying approach allows the system to maintain thorough risk analysis by leveraging the pre-computed ordering while achieving the processing speed required for real-time decision-making.
Data Source
AI summary
A computing system includes at least one processor and at least one module operable by the at least one processor to calculate a tail of a first dataset by determining elements of the first dataset that fall outside of a specified percentile, and determine locations of the first dataset at which elements of the first dataset that fall outside of the specified percentile are located. The at least one module may be operable to calculate a tail of a second dataset by populating a data structure with elements of the second dataset that correspond to the locations of the first dataset, and determining, using the data structure, elements of the second dataset that fall outside of the specified percentile. The at least one module may be operable to output an indication of at least one of the tail of the first dataset or the tail of the second dataset.