Supervised Gromov-Wasserstein Optimal Transport with Metric-Preserving Constraints [0.03%]
带度量保持约束的监督Gromov-Wasserstein最优传输方法
Zixuan Cang,Yaqi Wu,Yanxiang Zhao
Zixuan Cang
We introduce the supervised Gromov-Wasserstein (sGW) optimal transport, an extension of Gromov-Wasserstein that incorporates potential infinity entries in the cost tensor. These infinity entries enable sGW to enforce application-induced con...
Pini Zilber,Boaz Nadler
Pini Zilber
Low rank matrix recovery problems appear in a broad range of applications. In this work we present GNMR-an extremely simple iterative algorithm for low rank matrix recovery, based on a Gauss-Newton linearization. On the theoretical front, w...
Wenyu Chen,Mathias Drton,Ali Shojaie
Wenyu Chen
We consider the problem of learning causal structures in sparse high-dimensional settings that may be subject to the presence of (potentially many) unmeasured confounders, as well as selection bias. Based on structure found in common famili...
The Convex Mixture Distribution: Granger Causality for Categorical Time Series [0.03%]
凸混合分布：分类时间序列的Granger因果关系
Alex Tank,Xiudi Li,Emily B Fox et al.
Alex Tank et al.
We present a framework for learning Granger causality networks for multivariate categorical time series based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective, non-identifiability, a...
Boris Landa,Thomas T C K Zhang,Yuval Kluger
Boris Landa
Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the...
Robert J Webber,Erik H Thiede,Douglas Dow et al.
Robert J Webber et al.
Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simul...
Persistent Cohomology for Data With Multicomponent Heterogeneous Information [0.03%]
具有多组件异构信息的数据的持久上同调
Zixuan Cang,Guo-Wei Wei
Zixuan Cang
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and...
Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise [0.03%]
双随机正态化高斯核对异方差噪声具有鲁棒性
Boris Landa,Ronald R Coifman,Yuval Kluger
Boris Landa
A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix b...
Ariel Jaffe,Noah Amsel,Yariv Aizenbud et al.
Ariel Jaffe et al.
A common assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of a s...
George C Linderman,Stefan Steinerberger
George C Linderman
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success...