arXiv subjects

Yujie Zhao

Publications and source records attributed to Yujie Zhao.

42 records · Page 3Linked to original sources

arXiv2023

A Survey of Numerical Algorithms that can Solve the Lasso Problems

In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including the iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage-thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.

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arXiv2022

Hot-spots Detection in Count Data by Poisson Assisted Smooth Sparse Tensor Decomposition

Count data occur widely in many bio-surveillance and healthcare applications, e.g., the numbers of new patients of different types of infectious diseases from different cities/counties/states repeatedly over time, say, daily/weekly/monthly. For this type of count data, one important task is the quick detection and localization of hot-spots in terms of unusual infectious rates so that we can respond appropriately. In this paper, we develop a method called Poisson assisted Smooth Sparse Tensor Decomposition (PoSSTenD), which not only detects when hot-spots occur but also localizes where hot-spots occur. The main idea of our proposed PoSSTenD method is articulated as follows. First, we represent the observed count data as a three-dimensional tensor including (1) a spatial dimension for location patterns, e.g., different cities/countries/states; (2) a temporal domain for time patterns, e.g., daily/weekly/monthly; (3) a categorical dimension for different types of data sources, e.g., different types of diseases. Second, we fit this tensor into a Poisson regression model, and then we further decompose the infectious rate into two components: smooth global trend and local hot-spots. Third, we detect when hot-spots occur by building a cumulative sum (CUSUM) control chart and localize where hot-spots occur by their LASSO-type sparse estimation. The usefulness of our proposed methodology is validated through numerical simulation studies and a real-world dataset, which records the annual number of 10 different infectious diseases from 1993 to 2018 for 49 mainland states in the United States.

stat.AP↗

arXiv2022

Three-dimensional instantaneous orbit map for rotor-bearing system based on a novel multivariate complex variational mode decomposition algorithm

Full spectrum and holospectrum are homogenous information fusion technology developed for the fault diagnosis of rotating machinery, which is extensively exploited in the analysis of the orbits of rotor-bearing systems. However, they are not adapted for non-stationary signals, nor can they be used for fusion analysis of vibrations of multiple bearing sections. By drawing inspiration from the multivariate variational mode decomposition (MVMD) and the complex-valued signal decomposition, we propose a method called multivariate complex variational mode decomposition (MCVMD). It can simultaneously extract the forward and backward components of multiple bearing sections and realize non-stationary complex signal decomposition of multiple bearing sections of the rotor. To achieve the visualization goal of condition monitoring, we propose the three-dimensional instantaneous orbit map (3D-IOM). It enables more features of shaft vibration of a rotor system to be displayed and offers a new way for the fusion analysis of vibration signals of multiple bearing sections of rotating machinery. Furthermore, making the most of the joint information, we also provide a high-resolution time-full spectrum (Time-FS) to display the forward and backward frequency components of multiple bearing sections. The effectiveness of the proposed method through both the simulated experiment and the real-life complex-valued signals is demonstrated in this paper.

eess.SP↗

arXiv2021

BOP2-DC: Bayesian optimal phase II designs with dual-criterion decision making

The conventional phase II trial design paradigm is to make the go/no-go decision based on the hypothesis testing framework. Statistical significance itself alone, however, may not be sufficient to establish that the drug is clinically effective enough to warrant confirmatory phase III trials. We propose the Bayesian optimal phase II trial design with dual-criterion decision making (BOP2-DC), which incorporates both statistical significance and clinical relevance into decision making. Based on the posterior probability that the treatment effect reaches the lower reference value (statistical significance) and the clinically meaningful value (clinical significance), BOP2-DC allows for go/consider/no-go decisions, rather than a binary go/no-go decision, and it is optimized to maximize the probability of a go decision when the treatment is effective or minimize the sample size when the treatment is futile. BOP2-DC is highly flexible and accommodates various types of endpoints, including binary, continuous, time-to-event, multiple, and co-primary endpoints, in single-arm and randomized trials. Simulation studies show that the BOP2-DC design yields desirable operating characteristics. The software to implement BOP2-DC is freely available at \url{www.trialdesign.org}.

stat.ME↗

arXiv2020

Rapid Detection of Hot-spots via Tensor Decomposition with applications to Crime Rate Data

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.

stat.AP↗

arXiv2020

Rapid Detection of Hot-spot by Tensor Decomposition with Application to Weekly Gonorrhea Data

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 as some structured outliers that are sparse over the spatial domain but persistent over time. In this paper, we propose a tensor decomposition method to detect when and where the hot-spots occur. Our proposed methods represent the observed raw data as a three-dimensional tensor including a circular time dimension for daily/weekly/monthly patterns, and then decompose the tensor into three components: smooth global trend, local hot-spots, and residuals. A combination of LASSO and fused LASSO is used to estimate the model parameters, and a CUSUM procedure is applied to detect when and where the hot-spots might occur. The usefulness of our proposed methodology is validated through numerical simulation and a real-world dataset in the weekly number of gonorrhea cases from $2006$ to $2018$ for $50$ states in the United States.

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