Inbeom Lee,Siyi Deng,Yang Ning
Inbeom Lee
Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which c...
The Dyson equalizer: adaptive noise stabilization for low-rank signal detection and recovery [0.03%]
戴森校正器：低秩信号检测和恢复的自适应噪声稳定技术
Boris Landa,Yuval Kluger
Boris Landa
Detecting and recovering a low-rank signal in a noisy data matrix is a fundamental task in data analysis. Typically, this task is addressed by inspecting and manipulating the spectrum of the observed data, e.g. thresholding the singular val...
Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise [0.03%]
双随机规范化图拉普拉斯矩阵：收敛于流形拉普拉斯矩阵和异常值噪声下的鲁棒性
Xiuyuan Cheng,Boris Landa
Xiuyuan Cheng
Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically nor...
Phase transition and higher order analysis of Lq regularization under dependence [0.03%]
Lq正则化在依赖条件下的相变及高阶分析
Hanwen Huang,Peng Zeng,Qinglong Yang
Hanwen Huang
We study the problem of estimating a [Formula: see text]-sparse signal [Formula: see text] from a set of noisy observations [Formula: see text] under the model [Formula: see text], where [Formula: see text] is the measurement matrix the row...
On statistical inference with high-dimensional sparse CCA [0.03%]
高维稀疏 canonical correlation分析的统计推断方法研究
Nilanjana Laha,Nathan Huey,Brent Coull et al.
Nilanjana Laha et al.
We consider asymptotically exact inference on the leading canonical correlation directions and strengths between two high-dimensional vectors under sparsity restrictions. In this regard, our main contribution is developing a novel represent...
Byol Kim,Rina Foygel Barber
Byol Kim
Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e.g. removal of a single data point) may affect the outputs of a regression algorithm. Knowing an algorithm's stability pr...
Yariv Aizenbud,Ariel Jaffe,Meng Wang et al.
Yariv Aizenbud et al.
Modeling the distribution of high-dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nod...
Linear convergence of the subspace constrained mean shift algorithm: from Euclidean to directional data [0.03%]
约束子空间均值漂移算法的线性收敛性：从欧几里得数据到方向数据
Yikun Zhang,Yen-Chi Chen
Yikun Zhang
This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special...
An analysis of classical multidimensional scaling with applications to clustering [0.03%]
经典多维尺度分析及其在聚类中的应用研究
Anna Little,Yuying Xie,Qiang Sun
Anna Little
Classical multidimensional scaling is a widely used dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedd...
Tamir Bendory,Ariel Jaffe,William Leeb et al.
Tamir Bendory et al.
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled and noisy observations. We focus on the low SNR regime, and show that a signal in ℝ M is uniquely de...