Diagonal Matrix Big Data Prediction Model
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Solution Overview
Problem
Current machine learning approaches are computationally expensive and impractical for handling big data sets, especially when dealing with wide data, as they require O(n^3) inversion of covariance matrices, making predictions infeasible for large datasets like those found in collaborative filtering applications.
Innovation Solution
The system implements a method that represents input variables as matrices with only diagonal entries, facilitating matrix inversion and reducing computational complexity from O(n^3) to O(n), allowing for efficient processing of big data sets by using matrix inversion logic to determine the most likely class and generate predictions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional machine learning approaches are used to process big data, then prediction accuracy can be maintained, but computational complexity increases to O(n^3) making it infeasible for large datasets
Solution Approach 1:
The patent segments the data processing task by dividing the big data set into multiple partitions that can be processed independently and in parallel. Each partition is handled by separate mapper functions, and results are aggregated by reducer functions, transforming a single complex O(n^3) operation into multiple simpler O(n) operations that can execute concurrently.
Solution Approach 2:
The patent replaces the traditional mechanical matrix inversion approach with a probabilistic model based system. Instead of directly inverting covariance matrices, the system uses probabilistic reasoning and statistical models to achieve the same predictive goals with significantly reduced computational complexity, substituting a computationally intensive deterministic method with a more efficient probabilistic approach.
2Productivity
If data is split into multiple partitions for parallel processing, then processing speed increases, but the complexity of combining results and maintaining model consistency increases
Solution Approach 1:
The patent creates a universal probabilistic model framework that can handle multiple data partitions simultaneously. The same probabilistic model and inference algorithms are applied uniformly across all partitions, allowing the system to process diverse data segments through a single versatile mechanism, thereby simplifying the coordination and result aggregation processes.
Solution Approach 2:
The patent implements feedback mechanisms where the results from each data partition are aggregated and used to refine the overall model. The reducer functions collect results from mappers, and the probabilistic model uses this aggregated information to update predictions and improve accuracy, creating a feedback loop that maintains model consistency across distributed processing.
Data Source
AI summary
A model is implemented that includes one or more classes. For each of the one or more classes of the model, a set of input variables of the big data set are represented as a matrix with non-zero values only provided as diagonal entries. A most likely class for each input variable is determined based at least in part on inverting the matrix. One or more predictions are determined for one or more output variables based at least in part on the most likely class of one or more input variables from the set of input variables.