Spherical Geo-Probability Grid Estimation With Fixed-Memory Lookup
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Solution Overview
Problem
Existing methods for probability density estimation are inefficient when scaling to billions of samples, leading to impractical memory and time requirements for training and storing kernel density estimators.
Innovation Solution
A system and method for efficient grid-estimation of spherical geo-probability function using a von Mises-Fisher distribution to generate and combine grid points, forming a geo-grid for efficient storage and retrieval of probability values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If kernel density estimator is used to estimate probability density function for billions of samples, then estimation accuracy is improved, but memory requirement and training time grow to exceed practical limits
Solution Approach 1:
The patent segments the continuous probability density estimation problem into a discrete grid-based representation. Instead of storing kernel density artifacts for all billions of samples, the system divides the spatial domain into discrete grid cells and stores only the aggregated probability values for each cell, dramatically reducing memory requirements while maintaining practical estimation accuracy.
Solution Approach 2:
The patent creates a simplified copy of the probability density function in the form of a grid-based approximation. Rather than storing the full kernel density estimator artifacts, the system creates a discrete grid representation that captures the essential probability distribution characteristics, enabling efficient storage and retrieval while preserving the core functionality.
2Measurement precision
If kernel density estimator is used to estimate probability density function for billions of samples, then estimation accuracy is improved, but training time grows to exceed practical limits
Solution Approach 1:
The patent segments the continuous probability density estimation problem into a discrete grid-based representation. Instead of storing kernel density artifacts for all billions of samples, the system divides the spatial domain into discrete grid cells and stores only the aggregated probability values for each cell, dramatically reducing memory requirements while maintaining practical estimation accuracy.
Solution Approach 2:
The patent changes the parameter representation from continuous kernel density artifacts to discrete grid-based probability values. By transforming the probability density function into a grid representation with fixed resolution, the system enables efficient storage and constant-time queries, trading some continuous precision for computational efficiency and scalability.
3Quantity of substance
If grid points are combined into geo-grid by adding probability values, then storage efficiency is improved, but precision of individual probability values may be lost
Solution Approach 1:
The patent merges multiple grid points with identical coordinates into a single aggregated probability value in the geo-grid. By combining probability values from overlapping grid cells, the system achieves efficient storage while maintaining the ability to retrieve meaningful probability estimates through the aggregation of contributing grid points.
Data Source
AI summary
A system of one embodiment provides for efficient grid-estimation of spherical geo-probability function. The system includes a memory and a processor. The system accesses data, wherein the data includes training points and each training point includes a latitude value and a longitude value. The system also generates one or more grid points around each training point in the data. The system calculates a probability value for each grid point in the plurality of grid points using a probability density function. The system also combines each grid point into a geo-grid. The systems stores the geo-grid. In some embodiments, the system combines each grid point into a geo-grid by adding a probability value of a first grid point to a probability value of second grid point.