Unexpected properties of bandwidth choice when smoothing discrete data for constructing a functional data classifier
构造函数型数据分类器时离散数据平滑带宽的意外性质AI 解读 ↓
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构造函数型数据分类器时离散数据平滑带宽的意外性质
- 研究问题
- 从离散观测构造函数型分类器时，最适合重建曲线的平滑程度是否也适合分类，训练数据与待分类数据的带宽作用有何差异？
- 方法与思路
- 作者分析分类错误率随平滑参数变化的展开，考察训练数据和新数据的平滑作用，以及展开项的符号和大小对最优带宽的影响。
- 材料陈述的贡献
- 摘要称分类中常适合欠平滑，但并非总如此；训练数据平滑可能影响更大，且某些情形下较大带宽更有效。
- 阅读关注点
- 应核对具体分类器、观测与噪声结构、错误率展开的条件，以及何种配置导致欠平滑或较大带宽成为合适选择。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；结论随分类器与数据情形变化，未提供可直接套用的统一带宽规则。
原文摘要
The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed. Existing literature shows that this approach is effective, and even optimal, when using functional data methods for prediction or hypothesis testing. However, in the present paper we show that this approach is not effective in classification problems. There a useful rule of thumb is that undersmoothing is often desirable, but there are several surprising qualifications to that approach. First, the effect of smoothing the training data can be more significant than that of smoothing the new data set to be classified; second, undersmoothing is not always the right approach, and in fact in some cases using a relatively large bandwidth can be more effective; and third, these perverse results are the consequence of very unusual properties of error rates, expressed as functions of smoothing parameters. For example, the orders of magnitude of optimal smoothing parameter choices depend on the signs and sizes of terms in an expansion of error rate, and those signs and sizes can vary dramatically from one setting to another, even for the same classifier.