Online Hypothesis Testing and Non-Parametric Model Estimation Based on Correlated Observations

Online hypothesis testing and non-parametric model estimation is studied for a heterogeneous network of sensors collecting correlated observations. It is assumed that the statistical model for sensor data is not available and nonparametric estimation is used to estimate the model. Copula densities are used to model the correlation in sensor data. The batch-mode expectation maximization (EM) algorithm is first developed for Gaussian copulas and then extended to an online EM-based algorithm which performs the hypothesis detection and model estimation on a sample-by-sample basis. Results are presented for three real-world datasets and compared with those from widely-used supervised and unsupervised methods. It is shown that the proposed method achieves significant improvements in hypothesis testing compared to other unsupervised and even some supervised learning methods.

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