SLP-ProbHard：通过结构潜在参数化的概率硬约束学习
SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterization
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中文总结 AI 辅助
SLP-ProbHard提出结构可行潜在参数化框架，通过潜在分布与可行映射直接生成满足硬约束的预测分布，在仿射和非线性约束下减少随机坐标并提升MSE/MAE，表明精确可行性不唯一决定预测分布。
中文摘要 AI 辅助
许多概率预测器必须在每个随机实现中满足精确的结构，但常见的硬约束方法是在环境坐标中形成预测，然后进行校正或投影。我们引入了SLP-ProbHard，这是一个跨家族、以表示为中心的概率硬约束学习框架，适用于存在显式结构参数化的情况。其核心对象——结构可行潜在参数化（SFLP），将结构潜在分布 $Z \sim P^Z_\theta(\cdot\mid x)$ 与满足每个潜在实现约束的可行映射 $Y=h_\phi(x,Z)$ 相结合。这些组件共同定义了预测分布本身，包括其支撑集和边界概率，而非作为最终的可行性包装器。我们研究了可行坐标和映射如何影响随机维度、依赖性、校准、表达能力和计算。实验使用高斯潜在分布和固定几何推导的映射，涵盖仿射等式、排序和单纯形约束、非线性流形，以及七流域水文流量历时曲线（FDC）数据的三种结构表示。在与ProbHardE2E/DPPL的官方来源仿射比较中，两种方法均实现了零实际约束违规。SLP-ProbHard使用8个而非11个随机坐标，并改善了MSE/MAE，而DPPL提供了更好的边际CRPS和更接近标称的覆盖率；配对检验在十个种子下未检测到能量分数差异。真实世界的仿射和非线性FDC表示分别将环境坐标从13降至7和从14降至8个计算坐标。因此，仅精确可行性并不能决定预测分布，这促使在存在有意义的可行坐标时直接进行结构生成。
英文摘要
Many probabilistic predictors must satisfy exact structure in every stochastic realization, yet common hard-constraint approaches form predictions in ambient coordinates and then correct or project them. We introduce SLP-ProbHard, a cross-family, representation-centered framework for probabilistic hard-constrained learning when explicit structural parameterizations are available. Its core object, a Structural Feasible Latent Parameterization (SFLP), combines a structural latent law $Z \sim P^Z_θ(\cdot\mid x)$ with a feasible map $Y=h_ϕ(x,Z)$ that satisfies the constraint for every latent realization. Together these components define the predictive law itself, including its support and boundary probabilities, rather than serving as a final feasibility wrapper. We study how feasible coordinates and maps affect stochastic dimension, dependence, calibration, expressiveness, and computation. Experiments use Gaussian latent laws and fixed geometry-derived maps across affine equalities, ordering and simplex constraints, nonlinear manifolds, and three structural representations of seven-basin hydrological flow-duration-curve (FDC) data. In an official-source affine comparison with ProbHardE2E/DPPL, both methods achieve zero practical constraint violations. SLP-ProbHard uses 8 instead of 11 stochastic coordinates and improves MSE/MAE, while DPPL yields better marginal CRPS and closer-to-nominal coverage; a paired test detects no Energy Score difference across ten seeds. Real-world affine and nonlinear FDC representations reduce 13 to 7 and 14 to 8 ambient versus computational coordinates, respectively. Exact feasibility alone thus does not determine a predictive law, motivating direct structural generation when meaningful feasible coordinates are available.
发表机构
- University of Parma（帕尔马大学）
- University School for Advanced Studies IUSS Pavia（帕维亚高等研究院）
机构由 AI 辅助整理，请以论文原文为准。
