[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123061-en":3,"doc-seo-123061-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123061,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling","Given synchronous multivariate sensor readings located in space, spatiotemporal forecasting predicts future observations for each sensor point while accounting for inter-series relationships. Existing spatiotemporal graph neural networks often assume complete inputs and miss latent spatiotemporal dynamics when measurements are unavailable. This work addresses missing data via hierarchical spatiotemporal downsampling that produces multi-scale representations, then uses interpretable attention conditioned on observed values and missing patterns to generate forecasts. Experiments show superior results on synthetic and real benchmarks, especially with contiguous missing blocks.","Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling  \nIvan Marisca 1 Cesare Alippi 1 2 Filippo Maria Bianchi 3 4  \nAbstract  \nGiven a set of synchronous time series, each associated with a sensor-point in space and characterized by inter-series relationships, the problem ofspatiotemporal forecasting consists of predicting future observations for each point. Spatiotemporal graph neural networks achieve striking results by representing the relationships across time series as a graph. Nonetheless, most existing methods rely on the often unrealistic assumption that inputs are always available and fail to capture hidden spatiotemporal dynamics when part of the data is missing. In this work, we tackle this problem through hierarchical spatiotemporal downsampling. The input time series are progressively coarsened over time and space, obtaining a pool of representations that capture heterogeneous temporal and spatial dynamics. Conditioned on observations and missing data patterns, such representations are combined by an interpretable attention mechanism to generate the forecasts. Our approach outperforms state-of-the-art methods on synthetic and real-world benchmarks under different missing data distributions, particularly in the presence of contiguous blocks of missing values.  \n1. Introduction  \nTime-series analysis and forecasting often deal with highdimensional data acquired by sensor networks (SNs), abroad term for systems that collect (multivariate) measurements over time at different spatial locations. Examples include systems monitoring air quality, where each sensor records air pollutants’ concentrations, or traffic, where  \n1IDSIA USI-SUPSI, Universit della Svizzera italiana 2Politecnico di Milano 3Dept. of Mathematics and Statistics, UiT the Arctic University of Norway 4NORCE, Norwegian Research Centre AS. Correspondence to: Ivan Marisca \u003C[ivan.marisca@usi.ch](ivan.marisca@usi.ch) >, Filippo Maria Bianchi \u003Cfil[ippo.m.bianchi@uit.no](ippo.m.bianchi@uit.no) >.  \nProceedings of the 41 st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024 . Copyright 2024 by the author(s) .  \nFigure 1 . Overview of the proposed framework. The hierarchical design allows us to learn a pool of multi-scale spatiotemporal representations. Conditioned on the data and the missing value pattern, the attention mechanism dynamically combines representation from different scales to compute the predictions.  \nsensors track vehicles’ flow or speed. Usually, data are sampled regularly over time and synchronously across the sensors, which are often characterized by strong correlationsand dependencies between each other, i.e., across the spatial dimension. For this reason, a prominent deep learning approach is to consider the time series and their relationships as graphs and to process them with architectures that combine graph neural networks (GNNs) (Battaglia et al., 2018 ; Bronstein et al., 2021) with sequence-processing operators (Hochreiter & Schmidhuber, 1997 ; Borovykh et al., 2017) . These architectures are known as spatiotemporal graph neural networks (STGNNs) (Jin et al., 2023) .  \nA notable limit of most existing STGNNs is the assumption that inputs are complete and regular sequences. However, real-world SNs are prone to failures and faults, resulting eventually in missing values in the collected time series. When missing data occurs randomly and sporadically, the localized processing imposed by the inductive biases in STGNNs acts as an effective regularization, exploiting observations close in time and space to the missing one (Ciniet al., 2022) . Challenges arise when data are missing in larger and contiguous blocks, with gaps that occur in consecutive time steps and are spatially proximate. In SNs, this might be due to a sensor failure lasting for multiple time lags or problems affecting a whole portion of the network. In such scenarios, reaching valid observations that may be significantly dis","cbCaio1cN2kvayJp","https://ap.wps.com/l/cbCaio1cN2kvayJp","pdf",3050629,1,20,"English","en",105,"# Introduction\n## Sensor networks and spatiotemporal graphs\n## Limitations of existing STGNNs with missing values\n## Proposed hierarchical spatiotemporal downsampling framework\n## Hierarchical multi-scale attention and interpretability\n## Experimental comparison on benchmarks","[{\"question\":\"What problem does the work address?\",\"answer\":\"It addresses spatiotemporal forecasting for sensor networks when some time series values are missing, aiming to predict future observations using relationships across spatial points and time.\"},{\"question\":\"How does the proposed method handle missing data?\",\"answer\":\"It progressively coarsens inputs across both time and space to build multi-scale representations, then combines them using an interpretable attention mechanism conditioned on the observation and missing-data pattern.\"},{\"question\":\"Why is hierarchical downsampling important in this context?\",\"answer\":\"Hierarchical coarsening expands the effective receptive field to reach temporally and spatially distant information when data gaps are contiguous, while limiting parameters and computation through a structured time-then-space design.\"}]","Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling | 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problem does the work address?","Question",{"text":75,"@type":76},"It addresses spatiotemporal forecasting for sensor networks when some time series values are missing, aiming to predict future observations using relationships across spatial points and time.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method handle missing data?",{"text":80,"@type":76},"It progressively coarsens inputs across both time and space to build multi-scale representations, then combines them using an interpretable attention mechanism conditioned on the observation and missing-data pattern.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is hierarchical downsampling important in this context?",{"text":84,"@type":76},"Hierarchical coarsening expands the effective receptive field to reach temporally and spatially distant information when data gaps are contiguous, while limiting parameters and computation through a structured time-then-space 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