ﻻ يوجد ملخص باللغة العربية
We propose an efficient statistical method (denoted as SSR-Tensor) to robustly and quickly detect hot-spots that are sparse and temporal-consistent in a spatial-temporal dataset through the tensor decomposition. Our main idea is first to build an SSR model to decompose the tensor data into a Smooth global trend mean, Sparse local hot-spots, and Residuals. Next, tensor decomposition is utilized as follows: bases are introduced to describe within-dimension correlation, and tensor products are used for between-dimension interaction. Then, a combination of LASSO and fused LASSO is used to estimate the model parameters, where an efficient recursive estimation procedure is developed based on the large-scale convex optimization, where we first transform the general LASSO optimization into regular LASSO optimization and apply FISTA to solve it with the fastest convergence rate. Finally, a CUSUM procedure is applied to detect when and where the hot-spot event occurs. We compare the performance of the proposed method in a numerical simulation study and a real-world case study, which contains a dataset including a collection of three types of crime rates for U.S. mainland states during the year 1965-2014. In both cases, the proposed SSR-Tensor is able to achieve the fast detection and accurate localization of the hot-spots.
In many bio-surveillance and healthcare applications, data sources are measured from many spatial locations repeatedly over time, say, daily/weekly/monthly. In these applications, we are typically interested in detecting hot-spots, which are defined
Hot-spot-based policing programs aim to deter crime through increased proactive patrols at high-crime locations. While most hot spot programs target easily identified chronic hot spots, we introduce models for predicting temporary hot spots to addres
We develop a distribution-free, unsupervised anomaly detection method called ECAD, which wraps around any regression algorithm and sequentially detects anomalies. Rooted in conformal prediction, ECAD does not require data exchangeability but approxim
Both Bayesian and varying coefficient models are very useful tools in practice as they can be used to model parameter heterogeneity in a generalizable way. Motivated by the need of enhancing Marketing Mix Modeling at Uber, we propose a Bayesian Time
Medical imaging studies have collected high dimensional imaging data to identify imaging biomarkers for diagnosis, screening, and prognosis, among many others. These imaging data are often represented in the form of a multi-dimensional array, called