arXiv subjects

Qingyang Liu

Publications and source records attributed to Qingyang Liu.

40 records · Page 3Linked to original sources

arXiv2022

Multiplicative functions resembling the Möbius funciton

A multiplicative function $f$ is said to be resembling the Möbius function if $f$ is supported on the square-free integers, and $f(p)=\pm 1$ for each prime $p$. We prove $O$- and $Ω$-results for the summatory function $\sum_{n\leq x} f(n)$ for a class of these $f$ studied by Aymone, and the point is that these $O$-results demonstrate cancellations better than the square-root saving. It is proved in particular that the summatory function is $O(x^{1/3+\varepsilon})$ under the Riemann Hypothesis. On the other hand it is proved to be $Ω(x^{1/4})$ unconditionally. It is interesting to compare these with the corresponding results for the Möbius function.

math.NT↗

arXiv2022

Fast Object Placement Assessment

Object placement assessment (OPA) aims to predict the rationality score of a composite image in terms of the placement (e.g., scale, location) of inserted foreground object. However, given a pair of scaled foreground and background, to enumerate all the reasonable locations, existing OPA model needs to place the foreground at each location on the background and pass the obtained composite image through the model one at a time, which is very time-consuming. In this work, we investigate a new task named as fast OPA. Specifically, provided with a scaled foreground and a background, we only pass them through the model once and predict the rationality scores for all locations. To accomplish this task, we propose a pioneering fast OPA model with several innovations (i.e., foreground dynamic filter, background prior transfer, and composite feature mimicking) to bridge the performance gap between slow OPA model and fast OPA model. Extensive experiments on OPA dataset show that our proposed fast OPA model performs on par with slow OPA model but runs significantly faster.

cs.CV↗

arXiv2021

Bayesian Variable Selection for Cox Regression Model with Spatially Varying Coefficients with Applications to Louisiana Respiratory Cancer Data

The Cox regression model is a commonly used model in survival analysis. In public health studies, clinical data are often collected from medical service providers of different locations. There are large geographical variations in the covariate effects on survival rates from particular diseases. In this paper, we focus on the variable selection issue for the Cox regression model with spatially varying coefficients. We propose a Bayesian hierarchical model which incorporates a horseshoe prior for sparsity and a point mass mixture prior to determine whether a regression coefficient is spatially varying. An efficient two-stage computational method is used for posterior inference and variable selection. It essentially applies the existing method for maximizing the partial likelihood for the Cox model by site independently first, and then applying an MCMC algorithm for variable selection based on results of the first stage. Extensive simulation studies are carried out to examine the empirical performance of the proposed method. Finally, we apply the proposed methodology to analyzing a real data set on respiratory cancer in Louisiana from the SEER program.

stat.AP↗

arXiv2021

Time Fused Coefficient SIR Model with Application to COVID-19 Epidemic in the United States

In this paper, we propose a Susceptible-Infected-Removal (SIR) model with time fused coefficients. In particular, our proposed model discovers the underlying time homogeneity pattern for the SIR model's transmission rate and removal rate via Bayesian shrinkage priors. MCMC sampling for the proposed method is facilitated by the nimble package in R. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. We further apply the proposed methodology to analyze different levels of COVID-19 data in the United States.

stat.AP↗