Variance Estimation via Regularized Maximum Likelihood
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Solution Overview
Problem
Existing methods for assessing uncertainty in predictive models, such as the delta method and bootstrap sampling, are computationally complex and infeasible for large machine learning models with many parameters, making variance computation prohibitive.
Innovation Solution
A computer-implemented method that performs fitting operations using regularized maximum likelihood estimates to determine variance, enabling computationally efficient variance computation in deep learning and other machine learning domains.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the delta method or bootstrap sampling method is used to assess uncertainty in predictive models, then measurement precision of variance is improved, but device complexity and computational requirements become prohibitive for large machine learning models
Solution Approach 1:
The patent extracts and isolates the essential computational operations needed for variance estimation, separating them from the full machine learning model evaluation process. By focusing only on the critical path operations and using targeted perturbations rather than full bootstrap sampling, the method extracts the necessary uncertainty information with minimal computational overhead.
Solution Approach 2:
The patent changes the parameter of computational effort from extensive bootstrap sampling to a small number of targeted fitting operations with perturbed inputs. By modifying the approach from repeated full-model training to parameter perturbation around a single fitted model, it achieves variance estimation with dramatically reduced computational requirements while maintaining measurement precision.
2Measurement precision
If bootstrap sampling is performed repeatedly to estimate variance, then measurement precision is improved, but productivity and computational feasibility deteriorate
Solution Approach 1:
The patent performs preliminary fitting of the machine learning model to the training data once, before any variance estimation operations. This preliminary fit establishes a baseline model that can then be used for rapid perturbation-based variance estimation, avoiding the need to perform full model fitting repeatedly during bootstrap sampling.
Solution Approach 2:
Instead of creating multiple bootstrap samples and refitting the model to each, the patent creates virtual copies through parameter perturbations around a single fitted model. This copying approach uses the existing fitted model as a template and generates variance information through controlled modifications, dramatically reducing the need for repeated expensive model fitting operations.
3Measurement precision
If the delta method is applied to complex machine learning models with many parameters, then variance estimation is achieved, but device complexity and computational requirements become prohibitive
Solution Approach 1:
The patent introduces perturbation parameters as intermediaries between the model inputs and the variance estimation process. These small perturbations act as mediators that allow the system to probe the model's sensitivity and estimate variance without directly confronting the full complexity of the high-dimensional parameter space through repeated fitting.
Data Source
AI summary
One or more embodiments include a computer-implemented method that includes receiving a data set generated by a machine learning model, wherein the data set comprises a plurality of data samples that are independent of each other, performing two or more fitting operations to fit the data set to a regularized maximum likelihood estimators (MLEs), determining a variance associated with the data set based on a derivative associated with the regularized MLEs, and performing one or more operations associated with the machine learning model based on the variance.