Covariate Intensity Estimation via Gaussian-Process Equivalent Kernels
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Solution Overview
Problem
Existing technologies for estimating the intensity function for a covariate primarily rely on kernel density estimation methods, which may not achieve the same level of accuracy as Bayesian estimation methods using Gaussian processes as a prior distribution.
Innovation Solution
An information processing apparatus and method that utilizes a Bayesian estimation approach with a Gaussian process as a prior distribution to estimate the intensity function for a covariate, incorporating a processor and storage units to handle event occurrence and covariate data, and perform calculations for equivalent kernel functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If kernel density estimation method is used to estimate intensity function, then the estimation can be performed with simple computational procedures, but the accuracy of estimation is limited compared to Bayesian estimation methods
Solution Approach 1:
The patent transforms the Bayesian estimation problem into a computational problem by changing parameters and representations. Specifically, it converts the posterior distribution calculation into an equivalent kernel function computation, where the kernel function parameters are adjusted to reflect the Bayesian prior distribution (Gaussian process) while maintaining computational feasibility. This parameter transformation enables high-accuracy Bayesian estimation without requiring complex probabilistic programming.
Solution Approach 2:
The patent introduces an intermediary representation called the 'equivalent kernel function' that mediates between the Bayesian prior distribution and the observed data. This equivalent kernel function serves as a bridge, allowing the complex Bayesian inference to be computed through standard kernel density estimation techniques while incorporating the Gaussian process prior. The intermediary representation enables the system to achieve Bayesian accuracy using conventional computational tools.
2Measurement precision
If Bayesian estimation method with Gaussian process is used, then higher accuracy can be achieved, but the computational complexity and difficulty of implementation increase
Solution Approach 1:
The patent creates a copy of the kernel density estimation framework that is adapted for Bayesian inference. Instead of implementing full Bayesian inference from scratch, the patent copies the successful kernel density estimation algorithm and modifies it to incorporate the Gaussian process prior through the equivalent kernel function. This copying approach preserves the ease of implementation of kernel density estimation while achieving the higher accuracy of Bayesian methods.
Solution Approach 2:
The patent segments the Bayesian estimation process into distinct computational steps: (1) defining the Gaussian process prior, (2) computing the equivalent kernel function from the prior and observed data, and (3) performing kernel density estimation with the equivalent kernel. This segmentation breaks down the complex Bayesian inference into manageable, implementable steps that can be coded systematically, improving ease of implementation.
Data Source
AI summary
An information processing apparatus according to an aspect of the present invention includes a processor and a storage. The storage includes a first storage area and a second storage area. The first storage area stores event occurrence data related to the occurrence position of the event to be analyzed. The second storage area stores covariate data observed in the observation region of the event. The processor includes a kernel function designation unit, a calculation method designation unit, and an intensity function estimation unit. The kernel function designation unit receives designation of a kernel function in the Gaussian process. The calculation method designation unit receives designation of a calculation method of an equivalent kernel function. The intensity function estimation unit calculates an equivalent kernel function on the basis of the designated kernel function and calculation method, and estimates the intensity function for the covariate using the calculated equivalent kernel function.