We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these dependencies through a structured latent dynamical component, while a decoder predicts the observations from the latent representations. We consider several variants of this model, corresponding to different prior hypothesis about the spatial relations between the series. The model is evaluated and compared to state-of-the-art baselines, on a variety of forecasting problems representative of different application areas: epidemiology, geo-spatial statistics and car-traffic prediction. Besides these evaluations, we also describe experiments showing the ability of this approach to extract relevant spatial relations.
In the machine learning domain, spatio-temporal modeling has been seldom considered, even though some spatio-temporal models have been proposed @cite_10 . @cite_7 introduce a tensor model for kriging and forecasting. @cite_15 use conditional random fields for detecting activity in video, where time is discretized at the frame level and one of the tasks is the prediction of future activity. Brain Computer Interface (BCI) is another domain for spatio-temporal data analysis with some work focused on learning spatio-temporal filters @cite_22 @cite_17 , but this is a very specific and different topic.
@cite_22 @cite_7 @cite_15 @cite_10 @cite_17
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Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by recent variational methods for learning deep generative models, we introduce a unified algorithm to efficiently learn a broad spectrum of Kalman filters. Of particular interest is the use of temporal generative models for counterfactual inference. We investigate the efficacy of such models for counterfactual inference, and to that end we introduce the "Healing MNIST" dataset where long-term structure, noise and actions are applied to sequences of digits. We show the efficacy of our method for modeling this dataset. We further show how our model can be used for counterfactual inference for patients, based on electronic health record data of 8,000 patients over 4.5 years. Accurate and efficient analysis of multivariate spatio-temporal data is critical in climatology, geology, and sociology applications. Existing models usually assume simple inter-dependence among variables, space, and time, and are computationally expensive. We propose a unified low rank tensor learning framework for multivariate spatio-temporal analysis, which can conveniently incorporate different properties in spatio-temporal data, such as spatial clustering and shared structure among variables. We demonstrate how the general framework can be applied to cokriging and forecasting tasks, and develop an efficient greedy algorithm to solve the resulting optimization problem with convergence guarantee. We conduct experiments on both synthetic datasets and real application datasets to demonstrate that our method is not only significantly faster than existing methods but also achieves lower estimation error. We consider the problem of detecting past activities as well as anticipating which activity will happen in the future and how. We start by modeling the rich spatio-temporal relations between human poses and objects (called affordances) using a conditional random field (CRF). However, because of the ambiguity in the temporal segmentation of the sub-activities that constitute an activity, in the past as well as in the future, multiple graph structures are possible. In this paper, we reason about these alternate possibilities by reasoning over multiple possible graph structures. We obtain them by approximating the graph with only additive features, which lends to efficient dynamic programming. Starting with this proposal graph structure, we then design moves to obtain several other likely graph structures. We then show that our approach improves the state-of-the-art significantly for detecting past activities as well as for anticipating future activities, on a dataset of 120 activity videos collected from four subjects. In this paper, we tackle the problem of power prediction of several photovoltaic (PV) plants spread over an extended geographic area and connected to a power grid. The paper is intended to be a comprehensive study of one-day ahead forecast of PV energy production along several dimensions of analysis: 1) The consideration of the spatio-temporal autocorrelation, which characterizes geophysical phenomena, to obtain more accurate predictions. 2) The learning setting to be considered, i.e., using simple output prediction for each hour or structured output prediction for each day. 3) The learning algorithms: We compare artificial neural networks, most often used for PV prediction forecast, and regression trees for learning adaptive models. The results obtained on two PV power plant datasets show that: taking into account spatio temporal autocorrelation is beneficial; the structured output prediction setting significantly outperforms the nonstructured output prediction setting; and regression trees provide better models than artificial neural networks. In recent years, deep learning approaches have been successfully used to learn hierarchical representations of image data, audio data etc. However, to our knowledge, these deep learning approaches have not been extensively studied for electroencephalographic (EEG) data. Considering the properties of EEG data, high-dimensional and multichannel, we applied convolutional deep belief networks to the feature learning of EEG data and evaluated it on the datasets from previous BCI competitions. Compared with other state-of-the-art feature extraction methods, the learned features using convolutional deep belief network have better performance.