Bootstrapping the Out-of-sample Predictions for Efficient and Accurate Cross-Validation (1708.07180v2)

Abstract: Cross-Validation (CV), and out-of-sample performance-estimation protocols in general, are often employed both for (a) selecting the optimal combination of algorithms and values of hyper-parameters (called a configuration) for producing the final predictive model, and (b) estimating the predictive performance of the final model. However, the cross-validated performance of the best configuration is optimistically biased. We present an efficient bootstrap method that corrects for the bias, called Bootstrap Bias Corrected CV (BBC-CV). BBC-CV's main idea is to bootstrap the whole process of selecting the best-performing configuration on the out-of-sample predictions of each configuration, without additional training of models. In comparison to the alternatives, namely the nested cross-validation and a method by Tibshirani and Tibshirani, BBC-CV is computationally more efficient, has smaller variance and bias, and is applicable to any metric of performance (accuracy, AUC, concordance index, mean squared error). Subsequently, we employ again the idea of bootstrapping the out-of-sample predictions to speed up the CV process. Specifically, using a bootstrap-based hypothesis test we stop training of models on new folds of statistically-significantly inferior configurations. We name the method Bootstrap Corrected with Early Dropping CV (BCED-CV) that is both efficient and provides accurate performance estimates.

• The paper introduces a bootstrap bias correction mechanism that improves cross-validation accuracy without requiring additional model training.
• It employs bootstrapping of out-of-sample predictions to accurately estimate and correct bias across multiple performance metrics.
• Early dropping of inferior configurations yields up to 5x speed-ups while maintaining reliable performance estimates in model selection.

Overview of Bootstrap Bias Corrected Cross-Validation Methods

The paper "Bootstrapping the Out-of-sample Predictions for Efficient and Accurate Cross-Validation" presents two methodologies aimed at improving both the computational efficiency and the accuracy of performance estimates in machine learning model selection: Bootstrap Bias Corrected CV (BBC-CV) and Bootstrap Corrected with Early Dropping CV (BCED-CV). Cross-Validation (CV) protocols, which are the cornerstone of model evaluation and hyper-parameter tuning, are prone to optimistic bias, especially when multiple configurations are tested. The authors propose an innovative bootstrap mechanism to address the limitations inherent in traditional CV methodologies.

Methodology

The core innovation in the paper is the reapplication of bootstrapping, not on the datasets as traditionally practiced, but on the out-of-sample predictions. This pivot in methodology allows estimating the bias with minimal computational overhead compared to Nested Cross-Validation (NCV), which is recognized for being computationally expensive. BBC-CV leverages the pooled predictions of all configurations, bootstrapping them to correct bias without the need to train new models. This approach is generalized for any performance metric, be it accuracy, AUC, or mean squared error, making it versatile across different types of learning tasks.

BCED-CV, on the other hand, extends the bootstrapped predictions' utility to hypothesis testing within the CV loops. It provides a mechanism to eliminate statistically inferior configurations early, based on statistical significance derived from bootstrapping. This "early dropping" is advantageous for computational efficiency, allowing significant reduction in resource allocation to unpromising configurations.

Results

Empirical results confirm that BBC-CV accurately estimates the performance with minimal bias, achieving results comparable to NCV but with a notable reduction in computational cost. BCED-CV demonstrates significant speed gains often achieving speed-ups of 2-5 times—and up to the fold count when early dropping is applied—without sacrificing model quality or performance estimation accuracy. Together, they outperform existing methods such as the TT algorithm in both computational efficiency and estimate accuracy.

Implications

These methodologies hold substantial potential for practical applications where resource constraints and accuracy are critical. The methods are particularly favorable for large-scale machine learning tasks, where the multiplicity of configurations magnifies the inefficiency of traditional methods. The ability to provide bootstrapped confidence intervals adds a robust statistic to the estimation arsenal, offering a conservative view of model performance that scales with dataset size and number of configurations.

Future Directions

The conceptual advancements of the paper invite further exploration into various domains of machine learning beyond binary classification. Investigating their applicability in regression analysis or survival analysis tasks could prove insightful. Future work may also refine early dropping criteria, possibly integrating more sophisticated statistical techniques or machine learning heuristics to optimize configuration selection dynamically.

In essence, this paper provides a significant leap in addressing the biases and computational burdens of cross-validation in model training pipelines. The methodologies established here contribute valuably to the theoretical underpinnings and practical applications in data-driven domains.