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1. Semi-parametric Learning of Structured Temporal Point Processes

   Xu, Ganggang; Wang, Ming; Bian, Jiangze; Huang, Hui; Burch, Timothy; Andrade, Sandro; Zhang, Jingfei; Guan, Yongtao (January 2020, Journal of machine learning research)

   null (Ed.)

   We propose a general framework of using a multi-level log-Gaussian Cox process to model repeatedly observed point processes with complex structures; such type of data has become increasingly available in various areas including medical research, social sciences, economics, and finance due to technological advances. A novel nonparametric approach is developed to efficiently and consistently estimate the covariance functions of the latent Gaussian processes at all levels. To predict the functional principal component scores, we propose a consistent estimation procedure by maximizing the conditional likelihood of super-positions of point processes. We further extend our procedure to the bivariate point process case in which potential correlations between the processes can be assessed. Asymptotic properties of the proposed estimators are investigated, and the effectiveness of our procedures is illustrated through a simulation study and an application to a stock trading dataset. 

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2. Localizing and Amortizing: Efficient Inference for Gaussian Processes

   Liu, Linfeng; Liu, Li-Ping (November 2020, Proceedings of The 12th Asian Conference on Machine Learning)

   null (Ed.)

   The inference of Gaussian Processes concerns the distribution of the underlying function given observed data points. GP inference based on local ranges of data points is able to capture fine-scale correlations and allow fine-grained decomposition of the computation. Following this direction, we propose a new inference model that considers the correlations and observations of the K nearest neighbors for the inference at a data point. Compared with previous works, we also eliminate the data ordering prerequisite to simplify the inference process. Additionally, the inference task is decomposed to small subtasks with several technique innovations, making our model well suits the stochastic optimization. Since the decomposed small subtasks have the same structure, we further speed up the inference procedure with amortized inference. Our model runs efficiently and achieves good performances on several benchmark tasks. 

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3. Row-clustering of a Point Process-valued Matrix

   Yin, Lihao; Xu, Ganggang; Sang, Huiyan; Guan, Yongtao (December 2021, Advances in neural information processing systems)

   Structured point process data harvested from various platforms poses new challenges to the machine learning community. To cluster repeatedly observed marked point processes, we propose a novel mixture model of multi-level marked point processes for identifying potential heterogeneity in the observed data. Specifically, we study a matrix whose entries are marked log-Gaussian Cox processes and cluster rows of such a matrix. An efficient semi-parametric Expectation-Solution (ES) algorithm combined with functional principal component analysis (FPCA) of point processes is proposed for model estimation. The effectiveness of the proposed framework is demonstrated through simulation studies and real data analyses. 

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4. Graphical Gaussian process models for highly multivariate spatial data

   https://doi.org/10.1093/biomet/asab061  

   Dey, Debangan; Datta, Abhirup; Banerjee, Sudipto (December 2021, Biometrika)

   Summary For multivariate spatial Gaussian process models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence between the variables. This is undesirable, especially in highly multivariate settings, where popular cross-covariance functions, such as multivariate Matérn functions, suffer from a curse of dimensionality as the numbers of parameters and floating-point operations scale up in quadratic and cubic order, respectively, with the number of variables. We propose a class of multivariate graphical Gaussian processes using a general construction called stitching that crafts cross-covariance functions from graphs and ensures process-level conditional independence between variables. For the Matérn family of functions, stitching yields a multivariate Gaussian process whose univariate components are Matérn Gaussian processes, and which conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matérn Gaussian process to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling. 

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5. Adaptive Activity Monitoring with Uncertainty Quantification in Switching Gaussian Process Models

   Randy Ardywibowo, Guang Zhao (April 2019, Proceedings of Machine Learning Research)

   Emerging wearable sensors have enabled the unprecedented ability to continuously monitor human activities for healthcare purposes. However, with so many ambient sensors collecting different measurements, it becomes important not only to maintain good monitoring accuracy, but also low power consumption to ensure sustainable monitoring. This power-efficient sensing scheme can be achieved by deciding which group of sensors to use at a given time, requiring an accurate characterization of the trade-off between sensor energy usage and the uncertainty in ignoring certain sensor signals while monitoring. To address this challenge in the context of activity monitoring, we have designed an adaptive activity monitoring framework. We first propose a switching Gaussian process to model the observed sensor signals emitting from the underlying activity states. To efficiently compute the Gaussian process model likelihood and quantify the context prediction uncertainty, we propose a block circulant embedding technique and use Fast Fourier Transforms (FFT) for inference. By computing the Bayesian loss function tailored to switching Gaussian processes, an adaptive monitoring procedure is developed to select features from available sensors that optimize the trade-off between sensor power consumption and the prediction performance quantified by state prediction entropy. We demonstrate the effectiveness of our framework on the popular benchmark of UCI Human Activity Recognition using Smartphones. 

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