In this work we consider a new family of algorithms for sequential prediction, Hierarchical Partitioning Forecasters (HPFs). Our goal is to provide appealing theoretical - regret guarantees on a powerful model class - and practical - empirical performance comparable to deep networks - properties at the same time. We built upon three principles: hierarchically partitioning the feature space into sub-spaces, blending forecasters specialized to each sub-space and learning HPFs via local online learning applied to these individual forecasters. Following these principles allows us to obtain regret guarantees, where Constant Partitioning Forecasters (CPFs) serve as competitor. A CPF partitions the feature space into sub-spaces and predicts with a fixed forecaster per sub-space. Fixing a hierarchical partition $\mathcal H$ and considering any CPF with a partition that can be constructed using elements of $\mathcal H$ we provide two guarantees: first, a generic one that unveils how local online learning determines regret of learning the entire HPF online; second, a concrete instance that considers HPF with linear forecasters (LHPF) and exp-concave losses where we obtain $O(k \log T)$ regret for sequences of length $T$ where $k$ is a measure of complexity for the competing CPF. Finally, we provide experiments that compare LHPF to various baselines, including state of the art deep learning models, in precipitation nowcasting. Our results indicate that LHPF is competitive in various settings.

翻译：本文提出一种新的序列预测算法族——分层划分预测器（HPFs）。我们的目标是同时实现两类理想特性：在强大模型类上具有吸引力的理论保障（遗憾界），以及媲美深度网络的实际性能。该工作基于三项核心原则：将特征空间分层划分为子空间、针对各子空间融合专用预测器、通过局部在线学习对每个预测器进行独立学习来训练HPF。遵循这些原则使我们能够获得以恒定划分预测器（CPF）为竞争对象的遗憾界。CPF将特征空间划分为子空间，并在每个子空间中使用固定预测器进行预测。固定一个分层划分$\mathcal H$，考虑任意可通过$\mathcal H$元素构建其划分的CPF，我们提供两项保障：其一，通用理论揭示局部在线学习如何决定整个HPF在线学习的遗憾界；其二，针对线性预测器HPF（LHPF）及指数凹损失函数的具体实例，我们得到序列长度$T$下$O(k \log T)$的遗憾界，其中$k$表示竞争CPF的复杂度度量。最后，通过在降水临近预报任务中将LHPF与各类基线（包括最先进的深度学习模型）进行比较实验，结果表明LHPF在多种场景下均具有竞争力。