Joint-Probabilistic Ensemble Forecasting via Kernel Density Estimation
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Solution Overview
Problem
Conventional digital forecasting systems face limitations due to rigid assumptions about error distributions and dependencies between prediction models, leading to inaccurate forecasts when error distributions do not conform to assumed forms or when models have complex dependencies.
Innovation Solution
The system generates a joint-probability distribution function that accounts for the error values from multiple forecasters using kernel density estimation, allowing for flexible and accurate ensemble forecasting regardless of error distribution form or complexity of dependencies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional ensemble forecasting systems use regression-based algorithms or Bayesian Model Averaging with rigid assumptions about error distributions, then the systems can generate digital predictions, but the accuracy and applicability are limited when error distributions do not conform to assumed forms or when models have complex dependencies
Solution Approach 1:
The patent changes the fundamental parameters of the forecasting system by replacing rigid distributional assumptions with a flexible kernel density estimation approach. Instead of assuming Gaussian or other specific error distributions, the system estimates the actual error distribution from historical data and uses it to generate predictions, thereby adapting to various error distribution forms and improving both accuracy and applicability.
Solution Approach 2:
The system introduces dynamics by allowing the error distribution to be estimated and updated from historical data rather than being fixed by assumption. The kernel density estimation continuously adapts to the actual error patterns observed in the data, making the forecasting system flexible and responsive to different error distribution scenarios.
2Productivity
If conventional systems assume independence or simple correlation structures between forecasters, then the systems can process multiple forecasters, but they cannot accurately capture complicated dependencies between prediction models
Solution Approach 1:
The patent introduces an intermediary mechanism - the kernel density estimation of error distributions - that mediates between multiple forecasters with complex dependencies. This intermediary allows the system to capture complicated dependency structures by estimating the joint error distribution from historical data, rather than relying on simple independence or correlation assumptions.
3Ease of manufacture
If conventional digital forecasting systems make rigid assumptions about error distributions to simplify the forecasting process, then the systems can operate with simpler algorithms, but they generate inaccurate forecasts when prediction models do not conform to these assumptions
Solution Approach 1:
The patent changes the approach from assuming fixed distributional parameters to estimating parameters from data. By using kernel density estimation, the system maintains algorithmic simplicity while improving accuracy, as the method automatically adapts to the actual error distribution without requiring complex manual specification of distributional assumptions.
Data Source
AI summary
Methods, systems, and computer readable storage media are disclosed for generating joint-probabilistic ensemble forecasts for future events based on a plurality of different prediction models for the future events. For example, in one or more embodiments the disclosed system determines error values for various predictions from a plurality of different prediction models (i.e., “forecasters”) for previous events. Moreover, in one or more embodiments the system generates an error probability density function by mapping the error values to an error space and applying a kernel density estimation. Furthermore, the system can apply the error probability density function(s) to a plurality of predictions from the forecasters for a future event to generate a likelihood function and a new prediction for the future event.