Hernando Ombao’s contribution to the Discussion of ‘the Discussion Meeting on Probabilistic and statistical aspects of machine learning’
Hernando Ombao 对机器学习概率与统计讨论会论文的评论AI 解读 ↓
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Hernando Ombao 对机器学习概率与统计讨论会论文的评论
- 研究问题
- 这篇评论关注神经网络变点方法能否改善局部时频表示中的二进分割约束，使非平稳时间序列的变点定位更精细。
- 方法与思路
- 评论回顾小波包与局部复指数基，通过惩罚 Kullback–Leibler 准则选择表示，并建议以二进变点初始化神经网络细化。
- 材料陈述的贡献
- 评论指出最佳基算法的计算便利伴随二进定位限制，并提出结合神经网络的潜在改进方向；所给文本未报告实施验证。
- 阅读关注点
- 应核对被评论主论文的神经网络结果、最佳基选择与分割的联系，以及初始化后细化变点是否有算法和误差保证。
- 阅读边界
- 这是讨论评论，索引版本未注明；神经网络细化属于建议，不能据此声称作者已建立新方法或验证其性能。
原文摘要
I congratulate the authors for their fundamental contribution that demonstrates how the existing tests for change-points can be represented by a neural network. The major consequence is that with sufficient data, the performance of these neural networks should be at par with these existing tests. This formulation is very insightful and inspired me to revisit the previous work on models for non-stationary time series that use time-localized representations such as wavelets, wavelet packets (WP), and the smooth localized complex exponentials (SLEXs). Orthonormal representations are mathematically elegant and they generalize the Cramer representation for stationary time series which use the Fourier basis functions. One advantage of the WP and SLEX is that they form a library of many bases and thus provide a collection of candidate representations. The best representation is selected data-adaptively to be the one that minimizes the penalized Kullback–Leibler criterion. Due to the localized nature of the basis functions, the best model gives a specific segmentation of the time series data (in the case of SLEX, this is the segmentation of time). Thus, selecting the best model implicitly provides the estimated change-points in the tine series data. The current implementation limits the choice of the model to have a dyadic segmentation of time (in the case of SLEX) or frequency (in the case of WPs). This dyadic constraint is necessary to take advantage of the best basis algorithm of Coifman and Wickerhauser which requires the magnitude of O(T) operations (where T is the number of time points). The dyadic nature is a primary limitation of these methods because the change-points are constrained to lie on dyadic time points. This is where the current work of Li et al. can provide a major improvement. The dyadic change-points could serve as the initial values of these change-points but could be refined and made more precise by taking advantage of the neural networks.