Sample Size Planning for Classification Models

Abstract: In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classifiers. However, building a good model is actually not enough: the performance must also be proven. We discuss learning curves for typical small sample size situations with 5 - 25 independent samples per class. Although the classification models achieve acceptable performance, the learning curve can be completely masked by the random testing uncertainty due to the equally limited test sample size. In consequence, we determine test sample sizes necessary to achieve reasonable precision in the validation and find that 75 - 100 samples will usually be needed to test a good but not perfect classifier. Such a data set will then allow refined sample size planning on the basis of the achieved performance. We also demonstrate how to calculate necessary sample sizes in order to show the superiority of one classifier over another: this often requires hundreds of statistically independent test samples or is even theoretically impossible. We demonstrate our findings with a data set of ca. 2550 Raman spectra of single cells (five classes: erythrocytes, leukocytes and three tumour cell lines BT-20, MCF-7 and OCI-AML3) as well as by an extensive simulation that allows precise determination of the actual performance of the models in question.

• The paper introduces a learning curve approach to determine effective training sample sizes for classification models, especially in scarce data scenarios.
• It combines real biospectroscopy data with Monte Carlo simulations to establish that 75-100 test samples are typically needed for reliable validation.
• The study highlights challenges in statistically proving model superiority, often requiring hundreds of independent test samples for rigorous comparisons.

Sample Size Planning for Classification Models: A Formal Analysis

The paper "Sample Size Planning for Classification Models" by Beleites et al. addresses a critical aspect of experimental design in biospectroscopy classification: determining the appropriate sample size necessary to build and validate effective classification models. In biospectroscopy, obtaining suitably annotated, statistically independent samples for classifier training and testing is challenging due to their scarcity and cost. This study explores methods to systematically plan and assess the sample size needed to ensure classifier accuracy and reliability, utilizing both real and simulated data.

Main Contributions

The authors propose leveraging learning curves as a tool to understand model performance relative to the training sample size. By analyzing learning curves in situations with very small sample sizes (e.g., 5-25 samples per class), the paper highlights a key finding: while obtaining a well-performing model may be feasible, the process of proving its performance through adequate testing is often hindered by the limited test sample size. As a result, it is estimated that 75-100 test samples are typically required to achieve reasonable precision in validation.

The paper further provides methodologies to compute the necessary sample sizes for demonstrating the superiority of one classifier over another, stressing that such comparisons often necessitate hundreds of statistically independent test samples and, in some scenarios, may even be theoretically impossible.

Methodological Insights

The study employs a robust methodological framework that includes both empirical data from Raman spectroscopy and Monte Carlo simulations. This dual approach facilitates an in-depth analysis of model performance across different constraints, specifically considering:

• Classifier Performance Metrics: Sensitivity, specificity, and predictive values are central to understanding classifier efficacy, with particular attention given to the estimation of these metrics under conditions of small sample sizes.
• Bernoulli Process Approximation: The classification task is modeled as a Bernoulli process, allowing the authors to quantify the variance around observed performance metrics.
• Iterated Cross Validation: To assess classifier performance, particularly in limited data contexts, the authors rely on iterated k-fold cross-validation—a method shown to generate unbiased estimates when set aside test data does not affect model accuracy.

Results and Implications

The authors successfully demonstrate the feasibility of training robust classification models with minimal datasets but emphasize the challenges associated with validating these models given testing constraints. Notably, the research indicates that while small samples can be sufficient to develop models that achieve near-optimal sensitivity, testing these models to confirm such performance is considerably more demanding in terms of sample requirements.

For practitioners and researchers in machine learning and biospectroscopy, these findings illuminate the critical balance between training and test sample sizes in experimental design. The paper implies that insufficient test sample size can significantly hinder the ability to confidently validate model performance, potentially leading to inaccurate conclusions about model capabilities.

Future Directions and Concluding Remarks

The paper opens several avenues for future research. Firstly, developing improved methodologies for precise estimation of sample size requirements remains essential. Additionally, adopting techniques that can exploit hierarchical data structures frequently found in biospectroscopy (e.g., multiple measurements from the same specimen) may provide enhanced strategies for classifier training and validation.

This research offers a rigorous foundation for understanding the complexities of sample size determination in classification models. By revealing the intricacies and potential pitfalls inherent in small sample size scenarios, it lays the groundwork for advancing methodologies in experimental design, ultimately contributing to the broader field of AI where classification problems under constrained data conditions persist.