发表机构
Indian Institute of Technology Guwahati; Sorbonne University Abu Dhabi; Leiden University; Sorbonne University（印度理工学院古瓦哈蒂分校; 阿布扎赫大学索邦大学; 莱顿大学; 索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对登革热预测中数据稀缺、序列复杂的问题，提出长记忆回声状态网络计算框架，包含fESN和wESN两个变体，能有效编码长期依赖性，优于统计和深度学习基线，结合共形预测可提供不确定性区间。
AI 中文摘要
准确的登革热预测对公共卫生规划至关重要，但具有挑战性，因为发病率序列往往短、有噪声、非平稳、非线性且受长期时间依赖性影响。自回归分数整合移动平均（ARFIMA）中的分数差分有助于平衡非平稳性和持续性，但其线性结构限制了捕捉非线性动态的能力。深度神经网络可建模非线性模式，但通常需要大量训练样本且未明确编码统计长记忆。回声状态网络（ESN）在这种情况下很有吸引力，因为它在仅训练简单读出时保留非线性递归动态，适用于数据稀缺场景。然而，标准ESN缺乏时间序列视角的长期记忆。本研究提出了一个长记忆回声状态网络计算框架，集成了专用长记忆和短记忆ESN储层与岭回归读出。引入了两个变体：分数ESN（fESN），将分数差分动态纳入储层以直接编码长期依赖性；小波ESN（wESN），通过小波平滑提取稳定低频成分，然后用记忆感知储层建模。建立了闭环储层动态的理论保证，表明标准ESN在温和条件下诱导短记忆过程，而所提出的长记忆储层产生与统计长记忆一致的多项式衰减依赖性。在多个登革热数据集和预测范围内，fESN和wESN优于统计和深度学习基线。将共形预测与fESN和wESN相结合可提供无分布校准的不确定性区间。
英文摘要
Accurate dengue forecasting is crucial for public health planning, but remains challenging because incidence series are often short, noisy, non-stationary, nonlinear, and often affected by long-range temporal dependence. Fractional differencing in Autoregressive Fractionally Integrated Moving Average (ARFIMA) helps balance non-stationarity and persistence, but its linear structure limits its ability to capture nonlinear dynamics. Deep neural networks can model nonlinear patterns, but usually require large training samples and do not explicitly encode statistical long memory. Echo State Networks (ESNs), a widely used reservoir computing framework, are attractive in this setting because they retain nonlinear recurrent dynamics while training only a simple readout, making them suitable for data-scarce scenarios. However, standard ESNs lack long-term memory from a time-series perspective. This study proposes a long-memory reservoir computing framework that integrates dedicated long-memory and short-memory ESN reservoirs with a ridge-regression readout. We introduce two variants: Fractional ESN (fESN), which incorporates fractional-differencing dynamics into the reservoir to encode long-range dependence directly, and Wavelet ESN (wESN), which extracts stable low-frequency components through wavelet smoothing before modeling them with a memory-aware reservoir. We establish theoretical guarantees for closed-loop reservoir dynamics, showing that standard ESNs induce short-memory processes under mild conditions, whereas the proposed long-memory reservoirs generate polynomially decaying dependence consistent with statistical long memory. Across multiple dengue datasets and forecasting horizons, fESN and wESN outperform statistical and deep learning baselines. Combining conformal prediction with fESN and wESN provides distribution-free calibrated uncertainty intervals.
