Gaussian Processes for Time Series with Lead-Lag Effects with applications to biology data
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具有领先—滞后效应的时间序列高斯过程及其生物数据应用
- 研究问题
- 在观测时间不规则、领先—滞后效应短暂且受外部因素影响时，如何估计序列间时滞，并衡量成对序列的关系强弱？
- 方法与思路
- 作者建立高斯过程模型以处理不规则时间序列，估计领先—滞后关系并输出差异度分数，供多组序列的成对排序或聚类使用。
- 材料陈述的贡献
- 摘要称提供了所用核有效性及核参数可识别性的证明，并在模拟和动态染色质相互作用等真实应用中报告相对其他方法的改进。
- 阅读关注点
- 应核对时滞与外部因素的建模方式、核参数可识别条件，以及稀疏时间点下的估计不确定性和差异度分数的解释。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未给出证明条件或改进幅度，领先—滞后关系本身也不等同于因果识别。
原文摘要
Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several challenges. Firstly, due to technical reasons, the time points at which observations are made are not at uniform inintervals. Secondly, some lead-lag effects are transient, necessitating time-lag estimation based on a limited number of time points. Thirdly, external factors also impact these time series, requiring a similarity metric to assess the lead-lag relationship. To counter these issues, we introduce a model grounded in the Gaussian process, affording the flexibility to estimate lead-lag effects for irregular time series. In addition, our method outputs dissimilarity scores, thereby broadening its applications to include tasks such as ranking or clustering multiple pair-wise time series when considering their strength of lead-lag effects with external factors. Crucially, we offer a series of theoretical proofs to substantiate the validity of our proposed kernels and the identifiability of kernel parameters. Our model demonstrates advances in various simulations and real-world applications, particularly in the study of dynamic chromatin interactions, compared to other leading methods.