Spatiotemporal data aggregated over regions or time windows at various resolutions demonstrate heterogeneous patterns and dynamics in each resolution. Meanwhile, the multi-resolution characteristic provides rich contextual information, which is critical for effective long-sequence forecasting. The importance of such inter-resolution information is more significant in practical cases, where fine-grained data is usually collected via approaches with lower costs but also lower qualities compared to those for coarse-grained data. However, existing works focus on uni-resolution data and cannot be directly applied to fully utilize the aforementioned extra information in multi-resolution data. In this work, we propose Spatiotemporal Koopman Multi-Resolution Network (ST-KMRN), a physics-informed learning framework for long-sequence forecasting from multi-resolution spatiotemporal data. Our method jointly models data aggregated in multiple resolutions and captures the inter-resolution dynamics with the self-attention mechanism. We also propose downsampling and upsampling modules among resolutions to further strengthen the connections among data of multiple resolutions. Moreover, we enhance the modeling of intra-resolution dynamics with physics-informed modules based on Koopman theory. Experimental results demonstrate that our proposed approach achieves the best performance on the long-sequence forecasting tasks compared to baselines without a specific design for multi-resolution data.

We study offline recommender learning from explicit rating feedback in the presence of selection bias. A current promising solution for dealing with the bias is the inverse propensity score (IPS) estimation. However, the existing propensity-based methods can suffer significantly from the propensity estimation bias. In fact, most of the previous IPS-based methods require some amount of missing-completely-at-random (MCAR) data to accurately estimate the propensity. This leads to a critical self-contradiction; IPS is ineffective without MCAR data, even though it originally aims to learn recommenders from only missing-not-at-random feedback. To resolve this propensity contradiction, we derive a propensity-independent generalization error bound and propose a novel algorithm to minimize the theoretical bound via adversarial learning. Our theory and algorithm do not require a propensity estimation procedure, thereby leading to a well-performing rating predictor without the true propensity information. Extensive experiments demonstrate that the proposed algorithm is superior to a range of existing methods both in rating prediction and ranking metrics in practical settings without MCAR data. Full version of the paper (including the appendix) is available at: https://arxiv.org/abs/1910.07295.

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