Xiaoqi Yang

Zesheng Hong, Yubiao Yue, Yubin Chen et al.

Computer-aided diagnostics has benefited from the development of deep learning-based computer vision techniques in these years. Traditional supervised deep learning methods assume that the test sample is drawn from the identical distribution as the training data. However, it is possible to encounter out-of-distribution samples in real-world clinical scenarios, which may cause silent failure in deep learning-based medical image analysis tasks. Recently, research has explored various out-of-distribution (OOD) detection situations and techniques to enable a trustworthy medical AI system. In this survey, we systematically review the recent advances in OOD detection in medical image analysis. We first explore several factors that may cause a distributional shift when using a deep-learning-based model in clinic scenarios, with three different types of distributional shift well defined on top of these factors. Then a framework is suggested to categorize and feature existing solutions, while the previous studies are reviewed based on the methodology taxonomy. Our discussion also includes evaluation protocols and metrics, as well as the challenge and a research direction lack of exploration.

Luwei Bai, Yaohua Hu, Hao Wang et al.

In this paper, we consider a class of non-convex and non-smooth sparse optimization problems, which encompass most existing nonconvex sparsity-inducing terms. We show the second-order optimality conditions only depend on the nonzeros of the stationary points. We propose two damped iterative reweighted algorithms including the iteratively reweighted $\ell_1$ algorithm (DIRL$_1$) and the iteratively reweighted $\ell_2$ (DIRL$_2$) algorithm, to solve these problems. For DIRL$_1$, we show the reweighted $\ell_1$ subproblem has support identification property so that DIRL$_1$ locally reverts to a gradient descent algorithm around a stationary point. For DIRL$_2$, we show the solution map of the reweighted $\ell_2$ subproblem is differentiable and Lipschitz continuous everywhere. Therefore, the map of DIRL$_1$ and DIRL$_2$ and their inverse are Lipschitz continuous, and the strict saddle points are their unstable fixed points. By applying the stable manifold theorem, these algorithms are shown to converge only to local minimizers with randomly initialization when the strictly saddle point property is assumed.

Xin Li, Yaohua Hu, Chong Li et al.

In this paper, we discuss the statistical properties of the $\ell_q$ optimization methods $(0<q\leq 1)$, including the $\ell_q$ minimization method and the $\ell_q$ regularization method, for estimating a sparse parameter from noisy observations in high-dimensional linear regression with either a deterministic or random design. For this purpose, we introduce a general $q$-restricted eigenvalue condition (REC) and provide its sufficient conditions in terms of several widely-used regularity conditions such as sparse eigenvalue condition, restricted isometry property, and mutual incoherence property. By virtue of the $q$-REC, we exhibit the stable recovery property of the $\ell_q$ optimization methods for either deterministic or random designs by showing that the $\ell_2$ recovery bound $O(ε^2)$ for the $\ell_q$ minimization method and the oracle inequality and $\ell_2$ recovery bound $O(λ^{\frac{2}{2-q}}s)$ for the $\ell_q$ regularization method hold respectively with high probability. The results in this paper are nonasymptotic and only assume the weak $q$-REC. The preliminary numerical results verify the established statistical property and demonstrate the advantages of the $\ell_q$ regularization method over some existing sparse optimization methods.