前饋神經網路之信賴交叉驗證法

Abstract

交叉驗證(Cross-validation, CV)是機器學習中用於模型選擇和效能評估的基礎技術。然而，傳統的交叉驗證方法可能因折疊損失間的相關性而低估預測風險變異，且未能充分考慮測試數據中的近似誤差。信賴交叉驗證(Cross-Validation with Confidence, CVC)方法的提出解決了這些限制，為模型選擇結果提供統計信心，但其應用主要侷限於線性模型。

本研究探討將CVC方法應用於前饋式神經網路(Feed-Forward Neural Networks, FNNs)，主要關注模型選擇的問題。透過數值研究，我們觀察到這個方法相較於傳統交叉驗證方法，在模型選擇時可能提供額外的參考資訊。

研究結果顯示，將CVC應用於神經網路可能有助於降低神經網路訓練中常見的不穩定性。我們的方法嘗試為神經網路架構選擇提供額外的統計考量。本研究初步探討了CVC在神經網路上的可能應用，期待未來能有更多相關的理論發展與實務應用。

Cross-Validation (CV) is a fundamental technique in machine learning for model selection and performance evaluation. However, traditional CV methods may underestimate prediction risk variance due to correlations among fold losses and fail to account for approximation errors in test data. Cross-Validation with Confidence (CVC) has been proposed to address these limitations by providing statistical confidence in model selection results, but its application has primarily been limited to linear models.

This thesis investigates the application of CVC to Feed-Forward Neural Networks (FNNs), focusing on architecture selection. Through simulation studies, we explore how this approach might provide additional insights for model selection compared to conventional CV methods. The investigation suggests that our approach could offer complementary information to existing model selection techniques.

The results indicate that applying CVC to neural networks might help reduce the instability typically associated with neural network training. This study represents an initial exploration of CVC in neural network architecture selection, contributing to the ongoing discussion of confident model selection in neural networks.