arXiv subjects

Ting Ma

Publications and source records attributed to Ting Ma.

42 records · Page 3Linked to original sources

arXiv2021

Towards Unbiased COVID-19 Lesion Localisation and Segmentation via Weakly Supervised Learning

Despite tremendous efforts, it is very challenging to generate a robust model to assist in the accurate quantification assessment of COVID-19 on chest CT images. Due to the nature of blurred boundaries, the supervised segmentation methods usually suffer from annotation biases. To support unbiased lesion localisation and to minimise the labeling costs, we propose a data-driven framework supervised by only image-level labels. The framework can explicitly separate potential lesions from original images, with the help of a generative adversarial network and a lesion-specific decoder. Experiments on two COVID-19 datasets demonstrate the effectiveness of the proposed framework and its superior performance to several existing methods.

eess.IV↗

arXiv2020

A Note on the Gaussian Minimum Conjecture

Let $n\geq 2$ and $(X_i,1\leq i\leq n)$ be a centered Gaussian random vector. The Gaussian minimum conjecture says that $E\left(\min_{1\leq i\leq n}|X_i|\right)\geq E\left(\min_{1\leq i\leq n}|Y_i|\right)$, where $Y_1,\ldots,Y_n$ are independent centered Gaussian random variables with $E(X_i^2)=E(Y_i^2)$ for any $i=1,\ldots,n$. In this note, we will show that this conjecture holds if and only if $n=2$.

math.PR↗

arXiv2020

A Note on Convergence of Random Variables

In this note, convergence of random variables will be revisited. We will give the answers to 5 questions among the 6 open questions introduced in (Convergence rates in the law of large numbers and new kinds of convergence of random variables, {\it Communication in Statistics - Theory and Methods}, DOI: 10.1080/03610926.2020.1716248), and make some related discussions.

math.PR↗

arXiv2019

Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus

In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on $\T$. First we prove that the convergence rate for stochastic 2D heat equation is of order $α-δ$ in Besov space $\C^{-α}$ for $α\in(0,1)$ and $δ>0$ arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order $α-δ$ in $\C^{-α}$ for $α\in(0,2/9)$ and $δ>0$ arbitrarily small.

math.PR↗

arXiv2019

Convergence rates in the law of large numbers under sublinear expectations

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong $L^p$-convergence version and a strongly quasi sure convergence version of the law of large numbers.

math.PR↗

arXiv2018

On the length of the longest consecutive switches

An unbiased coin is tossed $n$ times independently and sequentially. In this paper, we will study the length of the longest consecutive switches, and prove that the limit behaviors are similar to that of the length of the longest head-run.

math.PR↗