Density Model for Non-Uniform Data Approximation
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Solution Overview
Problem
Existing data processing systems face inefficiencies in storing, retrieving, and analyzing large datasets due to the limitations of general statistics like mean, median, and mode, which are not effective for non-uniform data sets, leading to resource misallocation and increased processing time.
Innovation Solution
The development of a density modeling technique that iteratively varies and optimizes functional components of a density model to better approximate value densities in data, using expectation and maximization steps to determine adjusted components and evaluate model quality, allowing for more accurate data representation and prediction without scanning every data value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If general statistics (mean, median, mode) are used to represent data, then storage space is reduced, but accuracy in predicting specific values deteriorates for non-uniform data sets
Solution Approach 1:
The patent transforms the data representation from simple statistical parameters (mean, median, mode) to density model parameters that capture the distribution characteristics of non-uniform data. By changing the parameters from general statistics to density function parameters, the system maintains both storage efficiency and prediction accuracy for non-uniform data sets.
Solution Approach 2:
The patent creates a composite representation by combining multiple functional components (density functions) to model complex non-uniform data distributions. This composite density model integrates multiple parameters and functions to accurately represent the underlying data structure while maintaining compact storage.
2Measurement precision
If density modeling with iterative optimization is implemented, then accuracy in representing data distribution improves, but processing time and computational resources increase
Solution Approach 1:
The patent performs preliminary density modeling during data ingestion or batch processing, creating the density model in advance before queries are executed. This preliminary action allows the model to be ready for rapid querying, shifting computational burden from query time to data preparation time.
Solution Approach 2:
The patent creates a simplified copy or approximation of the data distribution through the density model, which captures essential characteristics without requiring access to the full data set. This copy enables fast predictions and analysis by working with the compact model rather than the original large data set.
3Measurement precision
If comprehensive metadata is stored for large data sets, then data analysis accuracy improves, but storage overhead and processing complexity increase
Solution Approach 1:
The patent extracts essential distribution characteristics from the data and stores them as density model parameters, separating the critical analytical information from the complete data set. This extraction provides sufficient accuracy for analysis while avoiding the complexity of managing comprehensive metadata for entire large data sets.
Data Source
AI summary
Processes, machines, and stored machine instructions are provided for approximating value densities in data. While generating a resulting density model to approximate value densities in a set of data, density modeling logic selects a functional component of a first model to vary based at least in part on how much the functional component contributes to how well the first model approximates the value densities. The density modeling logic then uses at least the functional component and a variation of the functional component as seed components to determine adjusted functional components of a second model by iteratively determining, in an expectation step, how much the seed components contribute to how well the second model explains the values, and, in a maximization step, new seed components, optionally to be used in further iterations, based at least in part on how much of the values are attributable to the seed components.