区间值时间序列的自适应分类
Adaptive Classification of Interval-Valued Time Series
AI总结：
本文提出一种基于区间上下界凸组合和图像转换的自适应方法，用于单变量及多变量区间值时间序列分类，通过ADMM优化系数并建立了基于间隔的多分类泛化界。
摘要：
近年来，区间值时间序列的建模和分析在计量经济学和统计学领域引起了广泛关注。然而，现有文献主要关注回归任务，而忽略了分类方面。在本文中，我们提出了一种用于区间值时间序列分类的自适应方法。具体而言，我们利用区间上下界的凸组合来表示区间值时间序列，并基于点值时间序列成像方法将这些表示转换为图像。我们利用细粒度图像分类神经网络对这些图像进行分类，以实现对原始区间值时间序列进行分类的目标。该方法适用于单变量和多变量区间值时间序列。在优化方面，我们将凸组合系数视为与神经网络参数类似的可学习参数，并提供了一种基于交替方向乘子法（ADMM）的高效估计方法。在理论方面，在特定条件下，我们为由卷积、池化和全连接层等基本模块组成的通用CNN建立了一个基于间隔的多分类泛化界。通过模拟研究和实际数据应用，我们验证了所提方法的有效性，并将其性能与多种点值时间序列分类方法进行了比较。
英文摘要：
In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while neglecting classification aspects. In this paper, we propose an adaptive approach for interval-valued time series classification. Specifically, we represent interval-valued time series using convex combinations of upper and lower bounds of intervals and transform these representations into images based on point-valued time series imaging methods. We utilize a fine-grained image classification neural network to classify these images, to achieve the goal of classifying the original interval-valued time series. This proposed method is applicable to both univariate and multivariate interval-valued time series. On the optimization front, we treat the convex combination coefficients as learnable parameters similar to the parameters of the neural network and provide an efficient estimation method based on the alternating direction method of multipliers (ADMM). On the theoretical front, under specific conditions, we establish a margin-based multiclass generalization bound for generic CNNs composed of basic blocks involving convolution, pooling, and fully connected layers. Through simulation studies and real data applications, we validate the effectiveness of the proposed method and compare its performance against a wide range of point-valued time series classification methods.
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