Quantile Estimator for Constrained ML Classification
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Solution Overview
Problem
Existing machine learning classification models face inefficiencies when adjusting thresholds to satisfy constraints such as precision or recall, leading to suboptimal performance and increased resource intensity in constrained optimization problems.
Innovation Solution
The method involves training classification models by optimizing an unconstrained objective function where the decision threshold is expressed as an estimator of a quantile function, transforming constrained optimization into an unconstrained problem, allowing for efficient gradient-based optimization and improved performance in specific regimes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If threshold adjustment is used to satisfy constraints on precision or recall, then the classification model can achieve desired operating points, but the model performance becomes suboptimal and resource-intensive
Solution Approach 1:
The patent applies preliminary action by incorporating the quantile function estimator directly into the training objective function before the model is deployed. Instead of adjusting thresholds after training, the method pre-computes the appropriate threshold through the quantile function during training, so the model is ready to satisfy constraints immediately upon deployment without requiring post-training threshold adjustment.
Solution Approach 2:
The patent extracts the threshold adjustment problem from the post-training phase and transforms it into part of the training objective itself. By expressing the decision threshold as an estimator of a quantile function in the objective function, the method separates the constraint satisfaction requirement from the standard classification objective, allowing both to be optimized simultaneously during training.
2Reliability
If constrained optimization is used to directly learn accurate conditional probabilities, then the model can satisfy constraints during training, but the optimization becomes more challenging and resource-intensive
Solution Approach 1:
The patent applies mechanics substitution by replacing the complex constrained optimization machinery with a simpler unconstrained optimization framework. Instead of using Lagrange multipliers or other constrained optimization techniques, the method substitutes the constraint handling mechanism with a quantile function estimator that naturally incorporates constraint satisfaction into the objective function, allowing standard gradient-based optimization to be used.
Solution Approach 2:
The patent changes the parameterization of the decision threshold from a fixed post-training adjustment parameter to a dynamic quantile function estimator during training. By expressing the threshold as q(F(x), 1-c) where F is the cumulative distribution function and c is the constraint parameter, the method transforms the constraint satisfaction problem into a parameter estimation problem that can be solved through standard optimization.
Data Source
AI summary
Example aspects of the present disclosure are directed to systems and methods for learning classification models which satisfy constraints such as, for example, constraints that can be expressed as a predicted positive rate or negative rate on a subset of the training dataset. In particular, through the use of quantile estimators, the systems and methods of the present disclosure can transform a constrained optimization problem into an unconstrained optimization problem that is solved more efficiently and generally than the constrained optimization problem. As one example, the unconstrained optimization problem can include optimizing an objective function where a decision threshold of the classification model is expressed as an estimator of a quantile function on the classification scores of the machine-learned classification model for a subset of the training dataset at a desired quantile.