Quantile Computation Using Binning and Frequency Counters
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Solution Overview
Problem
Computing exact quantiles for distributed data systems and big data environments is challenging due to the large amount of unsorted data, which prevents efficient sorting and can lead to non-convergence issues with iterative algorithms and high computational costs with sorting-based methods.
Innovation Solution
A method that computes quantile values in at most three passes through the dataset by determining maximum and minimum values, binning, and calculating frequency counters, allowing for exact quantile computation without the need for expensive sorting or iterative convergence criteria, thereby efficiently handling large datasets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If sorting-based methods are used to compute quantiles, then measurement precision is improved, but computational cost increases significantly
Solution Approach 1:
The data range is segmented into multiple bins based on maximum and minimum values. Frequency counters are computed for each bin independently, allowing parallel processing and reducing overall computational complexity while maintaining quantile accuracy.
Solution Approach 2:
The approach transforms the problem from exact sorting to frequency-based estimation by changing the parameter representation. Instead of sorting all values, the method uses bin boundaries and frequency counts to determine quantiles, significantly reducing computational power requirements.
2Power
If iterative algorithms are used for quantile computation, then computational cost is reduced, but non-convergence issues occur
Solution Approach 1:
The method performs preliminary actions by computing maximum and minimum values first, then establishing bin boundaries before computing frequency counters. This preliminary structuring ensures that the quantile computation converges reliably without requiring iterative algorithms.
Solution Approach 2:
Bin boundaries and frequency counters serve as intermediaries between the raw data and the final quantile values. This intermediary structure provides a reliable computational path that avoids the non-convergence issues of direct iterative methods.
3Measurement precision
If multiple passes through the dataset are performed, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The method extracts only the essential information needed for quantile computation by computing frequency counters for bins rather than processing individual values multiple times. This extraction approach maintains precision while reducing the time cost of multiple passes.
Solution Approach 2:
Maximum and minimum values are computed in a preliminary pass to establish bin boundaries before the main frequency counting passes. This preliminary action structures the data efficiently, reducing the time required for subsequent precision-computing passes.
Data Source
AI summary
A computing device computes a quantile value. A maximum value and a minimum value are computed for unsorted variable values. An upper bin value and a lower bin value are computed for each bin of a plurality of bins using the maximum and minimum values. A frequency counter is computed for each bin by reading the unsorted variable values a second time. Each frequency counter is a count of the variable values within a respective bin. A bin number and a cumulative rank value are computed for a quantile. The bin number identifies a specific within which a quantile value associated with the quantile is located. The cumulative rank value identifies a cumulative rank for the quantile value associated with the quantile. Frequency data is computed using the frequency counters. The quantile value is computed using the frequency data and the cumulative rank value for the quantile and output.