Subsampling Bias and The Best-Discrepancy Systematic Cross Validation
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Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which usually causes subsampling bias, inflates generalization errors and jeopardizes the reliability and effectiveness of cross-validation. Based on ordered systematic sampling theory in statistics and low-discrepancy sequence theory in number theory, we propose a new k-fold cross-validation procedure by replacing a pseudo-random sequence with a best-discrepancy sequence, which ensures low subsampling bias and leads to more precise Expected-Prediction-Error estimates. Experiments with 156 benchmark datasets and three classifiers (logistic regression, decision tree and naive bayes) show that in general, our cross-validation procedure can extrude subsampling bias in the MCCV by lowering the EPE around 7.18 comparison, the stratified MCCV can reduce the EPE and variances of the MCCV around 1.58 around 2.50 The computational time of our cross-validation procedure is just 8.64 MCCV, 8.67 that our approach is more beneficial for datasets characterized by relatively small size and large aspect ratio. This makes our approach particularly pertinent when solving bioscience classification problems. Our proposed systematic subsampling technique could be generalized to other machine learning algorithms that involve random subsampling mechanism.
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