Quantile Estimation in Distributed Data Systems via Sampling
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Solution Overview
Problem
Estimating quantiles in large data sets stored in distributed systems is challenging due to the complexity of handling varying data across different nodes, and existing methods are inefficient in converging on precise quantile values.
Innovation Solution
The system identifies minimum and maximum data values, defines data bins, and determines the total number of data values within each bin to estimate quantiles by iteratively refining the bins until convergence, using sampling techniques to minimize iterations and adapt the number of bins based on available data points.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional quantile estimation methods are used on distributed data, then all data values must be processed to ensure accuracy, but the computational complexity and time required increase significantly
Solution Approach 1:
The patent divides the distributed data into multiple data bins across different nodes, allowing each node to process only its local portion. The quantile estimation is performed by aggregating bin statistics rather than processing individual data points, thus maintaining accuracy while improving computational efficiency.
Solution Approach 2:
The patent uses sampling techniques to select a subset of data bins for detailed analysis rather than processing all bins. By strategically selecting bins that are most likely to contain the quantile value, the system achieves accurate estimation with reduced computational effort.
2Measurement precision
If the number of data bins is increased to improve quantile precision, then the estimation accuracy improves, but the number of iterations required for convergence increases
Solution Approach 1:
The patent dynamically adjusts the number of data bins based on the available data and convergence requirements. The system starts with a reasonable number of bins and refines the partitioning iteratively, increasing precision when necessary while avoiding unnecessary iterations that would waste time.
Solution Approach 2:
The system uses feedback from previous iterations to guide subsequent binning decisions. By analyzing the distribution of data across bins and the convergence progress, the system adjusts bin boundaries and selection strategies to achieve precise quantile estimation with minimal iterations.
3Productivity
If sampling techniques are used to reduce computational load, then processing time decreases, but the complexity of selecting representative samples increases
Solution Approach 1:
The patent performs preliminary processing to organize data into bins and compute basic statistics before the actual quantile estimation. This preliminary structuring simplifies the subsequent sampling process, as the algorithm only needs to work with aggregated bin data rather than individual data points, reducing both time and complexity.
Data Source
AI summary
In accordance with the teachings described herein, systems and methods are provided for estimating or determining quantiles for data stored in a distributed system. In one embodiment, an instruction is received to estimate or determine a specified quantile for a variate in a set of data stored at a plurality of nodes in the distributed system. A plurality of data bins for the variate are defined that are each associated with a different range of data values in the set of data. Lower and upper quantile bounds for each of the plurality of data bins are determined based on the total number of data values that fall within each of the plurality of data bins. The specified quantile is estimated or determined based on an identified one of the plurality of data bins that includes the specified quantile based on the lower and upper quantile bounds.