Unsupervised nonparametric detection of unknown objects in noisy images based on percolation theory

Robust nonparametric detection of objects in noisy images

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathema…

Multiple testing, uncertainty and realistic pictures

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an exp…

Clustering Via Finite Nonparametric ICA Mixture Models

We propose an extension of non-parametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. We formulate an objective function in terms of penalized smoothed Kullback Leibler distance and introduce the nonlinear smoothed majorization-minimization independent component analysis (NSMM-ICA) algorithm for optimizing this function and estimating the model parameters. We have implemented a practical version of this algorithm, which utilizes the FastICA algorithm, in the R packa…

图像的深度非参数条件独立性检验

Deep Nonparametric Conditional Independence Tests for Images

针对图像等高维变量，提出深度非参数条件独立性检验（DNCITs），结合嵌入映射与非参数检验，并在模拟、UKB脑影像数据及混杂控制研究中验证其有效性，提供R包实现。

非参数因子分析及拓展研究

Nonparametric Factor Analysis and Beyond

该研究突破无监督表示学习可辨识性依赖加性独立噪声或无噪声假设的局限，提出非参数含噪场景下潜变量辨识的通用框架，证明相关可辨识性结论，开发对应估计方法并验证有效，可为真实场景潜变量处理提供新思路。