贝叶斯分位数深度回声状态网络用于非线性时间序列
Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series
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中文总结 AI 辅助
针对高维非线性时间序列的贝叶斯分位数回归难题，提出基于深度回声状态网络固定特征的Q-DESN模型，采用多种似然与先验，并通过MCMC或变分推断实现，实验证明其能提升有限网格分位数评分。
中文摘要 AI 辅助
条件分位数对于非对称决策损失、尾部风险评估和区间预测至关重要，但当时间特征向量为高维时，非线性时间序列的贝叶斯分位数回归可能变得困难。我们开发了分位数深度回声状态网络（Q-DESN），这是一种以深度回声状态网络生成的固定特征为条件的贝叶斯分位数回归模型。在给定的储层构造和特征映射条件下，后验不确定性被分配给回归系数、似然函数和收缩参数。单层拟合使用非对称拉普拉斯或分位数固定的广义非对称拉普拉斯工作似然，并采用岭或正则化马蹄先验。后验计算在计算上可行时使用马尔可夫链蒙特卡洛，对于需要重复拟合的分析则使用模型特定的变分贝叶斯近似。对于分位数网格，我们比较了独立的逐层回归后进行单调重排与联合分位数向量回归（该回归收缩相邻分位数特定系数差异）两种方法。合成研究、单一来源的回顾性全球洪水感知系统（GloFAS）径流案例以及回顾性PriceFM比较，确定了这种固定特征贝叶斯回归能够改善有限网格分位数评分的场景。
英文摘要
Conditional quantiles are central to asymmetric decision losses, tail-risk assessment, and interval forecasts, but Bayesian quantile regression for nonlinear time series can be difficult when the temporal feature vector is high-dimensional. We develop the quantile deep echo state network (Q-DESN), a Bayesian quantile regression model conditional on fixed features generated by a deep echo state network. Conditional on a specified reservoir construction and feature map, posterior uncertainty is assigned to the regression coefficients, likelihood, and shrinkage parameters. Single-level fits use asymmetric Laplace or quantile-fixed generalized asymmetric Laplace working likelihoods with ridge or regularized-horseshoe priors. Posterior computation uses Markov chain Monte Carlo when computationally practical and a model-specific variational Bayes approximation for analyses requiring repeated fitting. For quantile grids, we compare independent level-wise regressions followed by monotone rearrangement with a joint quantile-vector regression that shrinks adjacent quantile-specific coefficient differences. Synthetic studies, a single-origin retrospective Global Flood Awareness System (GloFAS) streamflow case, and a retrospective PriceFM comparison identify settings where this fixed-feature Bayesian regression improves finite-grid quantile scores.
发表机构
- University of California, Santa Cruz（加州大学圣克鲁兹分校）
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