Extreme Value Forecasting With Surrogate Covariates
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Solution Overview
Problem
Existing approaches to Extreme Value Theory (EVT) are limited by their reliance on univariate and stationary data, which restricts their application to multivariate and non-stationary environments, leading to reduced accuracy and computational efficiency.
Innovation Solution
A computer-implemented method that uses trained machine learning models to map covariates to surrogate covariates, fitting a statistical model of extremes to signals of interest and covariates, enabling probabilistic forecasts of extreme values for multivariate and non-stationary data, and controlling controllable systems based on these forecasts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing univariate and stationary EVT approaches are used, then the modeling process is simple, but the application is limited to univariate and stationary data only
Solution Approach 1:
The patent segments the complex multivariate and non-stationary data modeling problem into multiple manageable components: (1) identifying extreme values using block maxima or POT approaches, (2) fitting univariate extreme value distributions to each variable, (3) modeling dependencies between variables using copulas, and (4) handling non-stationarity through time-dependent parameter modeling. This segmentation allows the system to handle complex data while maintaining computational tractability.
Solution Approach 2:
The patent introduces copulas as an intermediary mechanism to model dependencies between multiple extreme value variables. Copulas serve as a bridge that connects univariate extreme value distributions while capturing multivariate dependency structures, enabling the system to handle multivariate data without requiring a complete reformulation of the extreme value modeling framework.
2Measurement precision
If the number of covariates is increased to handle multivariate data, then the model accuracy improves, but the computational efficiency decreases
Solution Approach 1:
The patent segments the computational task by first identifying extreme values in each variable separately, then modeling their dependencies. This avoids the computational burden of directly modeling the full multivariate extreme value distribution, which would require exponentially more computational resources as the number of variables increases.
Solution Approach 2:
The patent applies different modeling approaches to different aspects of the data: univariate extreme value theory is applied to model the marginal distributions of individual variables, while copulas are applied specifically to model the dependency structure between variables. This localized application of specialized methods optimizes computational efficiency while maintaining accuracy.
3Device complexity
If block maxima approach is used to identify extreme values, then the modeling is simpler, but fewer extreme values are captured compared to POT approach
Solution Approach 1:
The patent acknowledges that the block maxima approach captures fewer extreme values (partial action) but compensates by using copula-based dependency modeling to extract maximum information from the available extreme value samples. The system performs sufficient rather than exhaustive sampling, balancing the number of extreme values captured with the complexity of their modeling.
Data Source
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AI summary
A computer-implemented method for producing probabilistic forecasts of extreme values. The method comprises obtaining input data comprising a plurality of signals of interest and a plurality of covariates associated therewith, each covariate of the plurality of covariates having an associated data type. The method further comprises performing a first forecast based on the input data. Performing the first forecast comprises: obtaining one or more trained machine learning models, each trained machine learning model of the one or more trained machine learning models having been trained to map one or more covariates of a respective data type to one or more surrogate covariates; mapping, using the one or more trained machine learning models and the input data, the plurality of covariates to one or more surrogate covariates, the one or more surrogate covariates corresponding to a compressed representation of the input data; fitting a statistical model of extremes to the plurality of signals of interest and the one or more surrogate covariates thereby generating a fitted statistical model of extremes, the statistical model of extremes being defined according to a predetermined distribution having a plurality of parameters; and obtaining a probabilistic forecast of future extreme values based on the fitted statistical model of extremes for one or more future time steps. The method further comprises causing control of a controllable system based at least in part on the probabilistic forecast of future extremes.