Probability Distribution Convolution for Future Value Prediction
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Solution Overview
Problem
Current methods for predicting future value, such as Monte Carlo methods and neural nets, are costly in terms of time and resources, and struggle to incorporate both explicit and tacit knowledge effectively, often relying on explicit rules and assumptions that do not capture the complexity of real-world decision-making processes.
Innovation Solution
A system that allows users to define value probability models at specific points in time, incorporating both explicit and tacit knowledge, using transformed and scaled beta distributions to represent likelihoods, and employing interpolation and convolution methods to calculate probability distributions across multiple tasks and parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Monte Carlo methods are used to predict future value, then the system can handle complex non-linear systems with coupled interactions, but hundreds of thousands of trials are needed resulting in high computational cost and time consumption
Solution Approach 1:
The patent applies preliminary action by pre-defining probability distributions for input variables and using analytical methods to calculate output distributions directly, rather than performing repeated random sampling. This allows the system to prepare the computational framework in advance and obtain results through direct calculation, significantly reducing the number of trials needed while maintaining accuracy in handling complex non-linear systems.
Solution Approach 2:
The patent substitutes the mechanical Monte Carlo simulation process (repeated random sampling and statistical aggregation) with an analytical mathematical approach using probability distribution transformations, convolutions, and analytical solutions. This replacement eliminates the need for hundreds of thousands of computational trials while preserving the ability to model complex non-linear relationships.
2Ease of manufacture
If neural nets are used to replace programmed rules, then learning sets can train the nets to predict outcomes, but histogram approximations are produced rather than exact probability distributions
Solution Approach 1:
The patent applies parameter changes by transforming probability distribution parameters (mean, variance, skewness, kurtosis) through analytical methods to directly obtain output distribution parameters. This approach maintains precise mathematical representation of probability distributions rather than relying on histogram approximations, while still allowing flexible modeling of complex relationships through parameter transformations.
3Productivity
If optimization techniques are used to reduce the number of trials, then local and global optima can be found, but understanding of interactions and solution space distribution is lost
Solution Approach 1:
The patent applies feedback by using probability distribution characteristics (mean, variance, skewness, kurtosis) of input variables and their relationships to iteratively refine and validate the analytical solution. This feedback mechanism ensures that the reduced computational approach still captures the essential interactions and provides accurate information about the solution space distribution, maintaining both efficiency and understanding.
Data Source
AI summary
A system and method for determining a composite bounded probability distribution of values of a first parameter at one or more values of a second parameter. A bounded probability distribution of values of a common first parameter is defined for each of one or more values of a common second parameter. A composite bounded probability distribution is determined for the portfolio at a selected value of the second parameter by performing a frequency domain convolution using the bounded probability distribution of each object at the selected value of the second parameter.