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Register a new userPrediction with Spatio-temporal Point Processes with Self Organizing Decision Trees
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We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the Hawkes process, which is a non-stationary and self-exciting point process. We extend the formulations of a standard point process model that can represent time-series data to represent a spatio-temporal data. We model the data as nonstationary in time and space. Furthermore, we partition the spatial region we are working on into subregions via an adaptive decision tree and model the source statistics in each subregion with individual but mutually interacting point processes. We also provide a gradient based joint optimization algorithm for the point process and decision tree parameters. Thus, we introduce a model that can jointly infer the source statistics and an adaptive partitioning of the spatial region. Finally, we provide experimental results on real-life data, which provides significant improvement due to space adaptation and joint optimization compared to standard well-known methods in the literature.
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We study the spatio-temporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatio-temporal prediction is extensively studied in Machine Learning literature due to its critical real-life applications such as crime, earthquake, and social event prediction. Despite these thorough studies, specific problems inherent to the application domain are not yet fully explored. Here, we address the non-stationary spatio-temporal prediction problem on both densely and sparsely distributed sequences. We introduce a probabilistic approach that partitions the spatial domain into subregions and models the event arrivals in each region with interacting point-processes. Our algorithm can jointly learn the spatial partitioning and the interaction between these regions through a gradient-based optimization procedure. Finally, we demonstrate the performance of our algorithm on both simulated data and two real-life datasets. We compare our approach with baseline and state-of-the-art deep learning-based approaches, where we achieve significant performance improvements. Moreover, we also show the effect of using different parameters on the overall performance through empirical results and explain the procedure for choosing the parameters.
Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting the global field into many lower-dimensional light cones. We review light cone decompositions for predictive state reconstruction, introducing three simple light cone algorithms. These methods allow for tractable inference of spatio-temporal data, such as full-frame video. The algorithms make few assumptions on the underlying process yet have good predictive performance and can provide distributions over spatio-temporal data, enabling sophisticated probabilistic inference.
Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over conventional uni-dimensional approaches by harnessing the information from both the temporal and spatial domains. Herein, we propose an spatio-temporal extension of RBF neural networks for the prediction of chaotic time series. The proposed algorithm utilizes the concept of time-space orthogonality and separately deals with the temporal dynamics and spatial non-linearity(complexity) of the chaotic series. The proposed RBF architecture is explored for the prediction of Mackey-Glass time series and results are compared with the standard RBF. The spatio-temporal RBF is shown to out perform the standard RBFNN by achieving significantly reduced estimation error.
Determinantal Point Processes (DPPs) provide an elegant and versatile way to sample sets of items that balance the point-wise quality with the set-wise diversity of selected items. For this reason, they have gained prominence in many machine learning applications that rely on subset selection. However, sampling from a DPP over a ground set of size $N$ is a costly operation, requiring in general an $O(N^3)$ preprocessing cost and an $O(Nk^3)$ sampling cost for subsets of size $k$. We approach this problem by introducing DPPNets: generative deep models that produce DPP-like samples for arbitrary ground sets. We develop an inhibitive attention mechanism based on transformer networks that captures a notion of dissimilarity between feature vectors. We show theoretically that such an approximation is sensible as it maintains the guarantees of inhibition or dissimilarity that makes DPPs so powerful and unique. Empirically, we demonstrate that samples from our model receive high likelihood under the more expensive DPP alternative.
Herein, we propose a spatio-temporal extension of RBFNN for nonlinear system identification problem. The proposed algorithm employs the concept of time-space orthogonality and separately models the dynamics and nonlinear complexities of the system. The proposed RBF architecture is explored for the estimation of a highly nonlinear system and results are compared with the standard architecture for both the conventional and fractional gradient decent-based learning rules. The spatio-temporal RBF is shown to perform better than the standard and fractional RBFNNs by achieving fast convergence and significantly reduced estimation error.
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