HyperLogLog Cardinality Estimation with Poisson Maximum Likelihood
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Solution Overview
Problem
Current HyperLogLog (HLL) algorithms face biased estimation errors in extreme cardinality ranges and lack direct support for calculating set operations like intersections or relative complements, leading to inaccurate results and increased CPU and memory requirements.
Innovation Solution
The creation of histogram data from HLL structures to calculate correction terms for low and high cardinality ranges, combined with a maximum likelihood approach using a Poisson approximation model, enables accurate cardinality estimation for set operations by generating differential histogram data for set operations like intersections or relative complements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If HyperLogLog algorithm is used for cardinality estimation, then memory consumption is reduced, but estimation accuracy deteriorates in extreme cardinality ranges
Solution Approach 1:
The patent applies parameter changes by modifying the HyperLogLog estimation parameters (α, β, γ) based on the observed cardinality range. When the estimated cardinality falls into extreme ranges (very small or very large), the algorithm dynamically adjusts these parameters to correct the biased error behavior, thereby maintaining measurement precision without increasing memory consumption.
Solution Approach 2:
The patent introduces dynamic adaptation by making the correction factors and estimation parameters variable rather than fixed. The algorithm dynamically selects different correction strategies based on the current cardinality estimate, transitioning between different error correction models depending on whether the cardinality is in extreme or moderate ranges.
2Measurement precision
If combined estimator approach is used to correct extreme range errors, then estimation accuracy in extreme ranges is improved, but CPU requirements increase
Solution Approach 1:
The patent applies partial action by not always using the full combined estimator approach. Instead, it selectively applies correction factors only when the cardinality estimate falls into extreme ranges, avoiding the computational overhead of complex combined estimation when simple HLL estimation is sufficient.
Solution Approach 2:
The patent segments the cardinality estimation process into different ranges (extreme low, extreme high, and moderate). Each segment uses an optimized estimation strategy appropriate for that range, avoiding the application of complex correction methods when they are not needed.
3Measurement precision
If heuristic correction factors are applied, then estimation error in extreme ranges is reduced, but reliability of correction factors deteriorates
Solution Approach 1:
The patent incorporates feedback mechanisms where the algorithm monitors the performance of correction factors and adapts them based on observed estimation errors. This feedback loop allows the system to verify and adjust correction factors, improving their reliability over time rather than relying on static heuristic values.
Data Source
AI summary
A system and method for the estimation of the cardinality of large sets of transaction trace data is disclosed. The estimation is based on HyperLogLog data sketches that are capable to store cardinality relevant data of large sets with low and fixed memory requirements. The disclosure contains improvements to the known analysis methods for HyperLogLog data sketches that provide improved relative error behavior by eliminating a cardinality range dependent bias of the relative error. A new analysis method for HyperLogLog data structures is shown that uses maximum likelihood analysis methods on a Poisson based approximated probability model. In addition, a variant of the new analysis model is disclosed that uses multiple HyperLogLog data structured to directly provide estimation results for set operations like intersections or relative complement directly from the HyperLogLog input data.