Regression with Deferral to Multiple Experts: A Principled Approach with Strong Consistency Guarantees

Core Concepts

This work introduces a novel framework for regression with deferral, where the learner can choose to defer predictions to multiple experts. The authors present a comprehensive analysis for both single-stage and two-stage scenarios, deriving new surrogate loss functions with strong (H,R)-consistency bounds. Their versatile framework accommodates multiple experts, arbitrary bounded regression losses, and both instance-dependent and label-dependent costs.

Abstract

The key highlights and insights from the content are: The authors introduce a novel framework for regression with deferral, where the learner can choose to defer predictions to multiple experts. This is an extension of the well-studied problem of learning to defer in classification contexts. They present a comprehensive analysis for both the single-stage scenario (simultaneous learning of predictor and deferral functions) and the two-stage scenario (pre-trained predictor with learned deferral function). The authors introduce new surrogate loss functions for both scenarios and prove that they are supported by strong H-consistency bounds. These bounds provide consistency guarantees that are stronger than Bayes consistency, as they are non-asymptotic and hypothesis set-specific. The proposed framework is versatile, applying to multiple experts, accommodating any bounded regression losses, addressing both instance-dependent and label-dependent costs, and supporting both single-stage and two-stage methods. The authors show that their single-stage formulation includes the recent regression with abstention framework as a special case, where only a single expert, the squared loss and a label-independent cost are considered. Minimizing the proposed loss functions directly leads to novel algorithms for regression with deferral. The authors report the results of extensive experiments showing the effectiveness of their proposed algorithms.

Stats

The mean squared error (MSE) of the base model used in the two-stage algorithm ranges from 14.85 to 120.20 across the three datasets. With a single expert, the system MSE ranges from 13.16 to 104.38. With two experts, the system MSE ranges from 13.33 to 44.46. With three experts, the system MSE ranges from 8.53 to 37.83.

Quotes

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Key Insights Distilled From

Regression with Multi-Expert Deferral

by Anqi Mao,Meh... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19494.pdf

Deeper Inquiries

How can the proposed framework be extended to handle non-bounded regression losses or unbounded label spaces

The proposed framework can be extended to handle non-bounded regression losses or unbounded label spaces by modifying the surrogate loss functions to accommodate such scenarios. For non-bounded regression losses, the framework can incorporate loss functions that do not have a predefined upper limit, allowing for a more flexible modeling of the regression problem. This can involve adapting the surrogate loss functions to handle unbounded errors and adjusting the optimization process accordingly. Similarly, for unbounded label spaces, the framework can be adjusted to work with continuous or infinite label values by ensuring that the deferral and prediction functions can handle such variability in the label space. This may involve redefining the cost functions and adjusting the deferral mechanism to account for the unbounded nature of the labels.

What are the potential applications of regression with multi-expert deferral beyond the examples mentioned in the paper

The potential applications of regression with multi-expert deferral extend beyond the examples mentioned in the paper to various domains where accurate predictions with the option of deferral to multiple experts are valuable. Some potential applications include: Financial Forecasting: Utilizing multiple financial models or experts to predict stock prices, market trends, or economic indicators. Healthcare: Deferring medical diagnosis predictions to different specialists or AI models for more accurate and reliable diagnoses. Climate Modeling: Using a combination of climate models and expert opinions to predict weather patterns, natural disasters, or climate change impacts. Supply Chain Management: Deferring demand forecasting to different experts to optimize inventory management and supply chain operations. Energy Forecasting: Leveraging multiple models to predict energy consumption, production, or pricing for efficient resource allocation and decision-making.

How can the trade-off between prediction accuracy and deferral cost be further optimized in practical settings

To optimize the trade-off between prediction accuracy and deferral cost in practical settings, several strategies can be employed: Dynamic Cost Adjustment: Implementing a dynamic cost adjustment mechanism that considers the current prediction accuracy and adjusts the deferral cost accordingly. Cost-Benefit Analysis: Conducting a cost-benefit analysis to determine the optimal balance between accuracy improvement from deferral and the associated costs. Machine Learning Algorithms: Utilizing advanced machine learning algorithms to learn and adapt the deferral decisions based on historical data and feedback loops. Real-Time Decision Making: Implementing real-time decision-making processes that consider the evolving accuracy and cost factors to make optimal deferral choices. Continuous Monitoring: Continuously monitoring the performance metrics and cost implications to make informed decisions on when to defer predictions to experts.