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1. The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data

   https://doi.org/10.1109/ICCV48922.2021.01324  

   Gu, Cheng; Learned-Miller, Erik; Sheldon, Daniel; Gallego, Guillermo; Bideau, Pia (January 2021, Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV))

   Event cameras, inspired by biological vision systems, provide a natural and data efficient representation of visual information. Visual information is acquired in the form of events that are triggered by local brightness changes. However, because most brightness changes are triggered by relative motion of the camera and the scene, the events recorded at a single sensor location seldom correspond to the same world point. To extract meaningful information from event cameras, it is helpful to register events that were triggered by the same underlying world point. In this work we propose a new model of event data that captures its natural spatio-temporal structure. We start by developing a model for aligned event data. That is, we develop a model for the data as though it has been perfectly registered already. In particular, we model the aligned data as a spatio-temporal Poisson point process. Based on this model, we develop a maximum likelihood approach to registering events that are not yet aligned. That is, we find transformations of the observed events that make them as likely as possible under our model. In particular we extract the camera rotation that leads to the best event alignment. We show new state of the art accuracy for rotational velocity estimation on the DAVIS 240C dataset [??]. In addition, our method is also faster and has lower computational complexity than several competing methods. 

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2. The Information Bottleneck and Geometric Clustering

   https://doi.org/10.1162/neco_a_01136  

   Strouse, DJ; Schwab, David J. (March 2019, Neural Computation)

   The information bottleneck (IB) approach to clustering takes a joint distribution [Formula: see text] and maps the data [Formula: see text] to cluster labels [Formula: see text], which retain maximal information about [Formula: see text] (Tishby, Pereira, & Bialek, 1999 ). This objective results in an algorithm that clusters data points based on the similarity of their conditional distributions [Formula: see text]. This is in contrast to classic geometric clustering algorithms such as [Formula: see text]-means and gaussian mixture models (GMMs), which take a set of observed data points [Formula: see text] and cluster them based on their geometric (typically Euclidean) distance from one another. Here, we show how to use the deterministic information bottleneck (DIB) (Strouse & Schwab, 2017 ), a variant of IB, to perform geometric clustering by choosing cluster labels that preserve information about data point location on a smoothed data set. We also introduce a novel intuitive method to choose the number of clusters via kinks in the information curve. We apply this approach to a variety of simple clustering problems, showing that DIB with our model selection procedure recovers the generative cluster labels. We also show that, in particular limits of our model parameters, clustering with DIB and IB is equivalent to [Formula: see text]-means and EM fitting of a GMM with hard and soft assignments, respectively. Thus, clustering with (D)IB generalizes and provides an information-theoretic perspective on these classic algorithms. 

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3. Estimation and Inference for Spatio-Temporal Single-Index Models

   https://doi.org/10.3390/math11204289  

   Wang, Hongxia; Zhao, Zihan; Hao, Hongxia; Huang, Chao (October 2023, Mathematics)

   To better fit the actual data, this paper will consider both spatio-temporal correlation and heterogeneity to build the model. In order to overcome the “curse of dimensionality” problem in the nonparametric method, we improve the estimation method of the single-index model and combine it with the correlation and heterogeneity of the spatio-temporal model to obtain a good estimation method. In this paper, assuming that the spatio-temporal process obeys the α mixing condition, a nonparametric procedure is developed for estimating the variance function based on a fully nonparametric function or dimensional reduction structure, and the resulting estimator is consistent. Then, a reweighting estimation of the parametric component can be obtained via taking the estimated variance function into account. The rate of convergence and the asymptotic normality of the new estimators are established under mild conditions. Simulation studies are conducted to evaluate the efficacy of the proposed methodologies, and a case study about the estimation of the air quality evaluation index in Nanjing is provided for illustration. 

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4. Fast estimation of multivariate spatiotemporal Hawkes processes and network reconstruction

   https://doi.org/10.1007/s10463-020-00780-1  

   Yuan, Baichuan; Schoenberg, Frederic P.; Bertozzi, Andrea L. (January 2021, Annals of the Institute of Statistical Mathematics)

   null (Ed.)

   We present a fast, accurate estimation method for multivariate Hawkes self-exciting point processes widely used in seismology, criminology, finance and other areas. There are two major ingredients. The first is an analytic derivation of exact maximum likelihood estimates of the nonparametric triggering density. We develop this for the multivariate case and add regularization to improve stability and robustness. The second is a moment-based method for the background rate and triggering matrix estimation, which is extended here for the spatiotemporal case. Our method combines them together in an efficient way, and we prove the consistency of this new approach. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media. 

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5. Real-time detection of clustered events in video-imaging data with applications to additive manufacturing

   https://doi.org/10.1080/24725854.2021.1882013  

   Yan, Hao; Grasso, Marco; Paynabar, Kamran; Colosimo, Bianca Maria (January 2021, IISE Transactions)

   The use of video-imaging data for in-line process monitoring applications has become popular in industry. In this framework, spatio-temporal statistical process monitoring methods are needed to capture the relevant information content and signal possible out-of-control states. Video-imaging data are characterized by a spatio-temporal variability structure that depends on the underlying phenomenon, and typical out-of-control patterns are related to events that are localized both in time and space. In this article, we propose an integrated spatio-temporal decomposition and regression approach for anomaly detection in video-imaging data. Out-of-control events are typically sparse, spatially clustered and temporally consistent. The goal is not only to detect the anomaly as quickly as possible (“when”) but also to locate it in space (“where”). The proposed approach works by decomposing the original spatio-temporal data into random natural events, sparse spatially clustered and temporally consistent anomalous events, and random noise. Recursive estimation procedures for spatio-temporal regression are presented to enable the real-time implementation of the proposed methodology. Finally, a likelihood ratio test procedure is proposed to detect when and where the anomaly happens. The proposed approach was applied to the analysis of high-sped video-imaging data to detect and locate local hot-spots during a metal additive manufacturing process. 

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