相关论文: Inductive Geometric Matrix Midranges

In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given…

In recent years, Transformer-based auto-attention mechanisms have been successfully applied to the analysis of a variety of context-reliant data types, from texts to images and beyond, including data from non-Euclidean geometries. In this…

Moir\'e materials such as magic angle twisted bilayer graphene (MATBG) exhibit remarkable phenomenology, but present significant challenges for certain experimental methods, particularly scanning probes such as scanning tunneling microscopy…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…

We introduce a novel algorithm for approximating the logarithm of the determinant of a symmetric positive definite (SPD) matrix. The algorithm is randomized and approximates the traces of a small number of matrix powers of a specially…

Extrinsic Gaussian process regression methods, such as wrapped Gaussian process, have been developed to analyze manifold data. However, there is a lack of intrinsic Gaussian process methods for studying complex data with manifold-valued…

Longitudinal or panel data can be represented as a matrix with rows indexed by units and columns indexed by time. We consider inferential questions associated with the missing data version of panel data induced by staggered adoption. We…

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…

The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially for huge data sets and online learning. While this recursive algorithm is popular for computation and memory efficiency, quantifying…

Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in…

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…

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…

Traditional methods employed in matrix volatility forecasting often overlook the inherent Riemannian manifold structure of symmetric positive definite matrices, treating them as elements of Euclidean space, which can lead to suboptimal…

We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…

Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…

We introduce Thurstonian Boltzmann Machines (TBM), a unified architecture that can naturally incorporate a wide range of data inputs at the same time. Our motivation rests in the Thurstonian view that many discrete data types can be…