arXiv research

Introduces matrix MLP for learning symmetric positive definite matrices.

Sparse covariance estimation in the vertical-split model achieves exponential improvement over dense estimates.

The abstract introduces a new concept called flagfolds to model multi-dimensional shapes.

Enhances power of covariance matrix tests for high-dimensional data.

New method computes dense partial correlations with applications in graph theory and uncertainty quantification.

Efficiently solves large portfolio optimization problems by reducing and sparsifying covariance matrices.

S-VNNs improve VNNs by sparsifying covariance matrices.

We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.

In 1981 Masur proved the existence of a dense geodesic in the moduli space for a Teichmüller space. We prove an analogue theorem for reduced Outer Space endowed with the Lipschitz metric. We also prove two results possibly of independent interest: we show Brun's unordered algorithm weakly converges and from this prove …

New method speeds up sparse graph neural networks training on dense hardware.

Paper proposes a deep learning method for better covariance matrix forecasting.

We calculate eigenvector overlaps between intersecting time periods of covariance matrices.

Paper explores geometry of covariance matrices using associated bundles.

Paper solves a key problem in learning from high-dimensional covariance matrices.

Simple bounds for covariance and Gram matrices across various settings.

Estimates covariance matrices with correlations between samples.

Diagonal transformations preserve independence structures in non-Gaussian distributions.

Study extends bounds on sample covariance matrices with general dependence.

This paper studies geodesics between covariance matrices of different ranks using the Bures-Wasserstein metric.

Optimizes clustering in Gaussian mixtures with varying covariance matrices.

Proposes a new Sliced-Wasserstein distance for covariance matrices in M/EEG signals.

New estimator learns symmetric dynamics from few observations.

Better signal detection in undersampled data using joint and cross covariances.

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…

New method estimates sparse covariance matrices in logit mixtures.

Method estimates sparse inverse covariance and partial correlation matrices efficiently.

The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…

New GPU kernels boost deep learning speed and memory efficiency.

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-time. Prompted by this observation, we study a convex optimization…

Machine learning creates non-factor covariance matrices for risk models.

Paper introduces a novel method for dynamic covariance estimation with random forests.

A new method reduces the bias in estimating inverse covariance matrices from sketches.

New MCMC method learns sparse preconditioner for high-dimensional problems.

In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random variables. We show that one could introduce the univariate invariant depending solely …

Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that error covariance matrices are known and given. In this paper, we study a general…

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which amounts to evaluating the logarithm of the marginal likelihood (LML) o…

Riemannian geometry has been applied to Brain Computer Interface (BCI) for brain signals classification yielding promising results. Studying electroencephalographic (EEG) signals from their associated covariance matrices allows a mitigation of common sources of variability (electronic, electrical, biological) by constr…

Ranky solves SVD for large sparse matrices in distributed systems.

Paper introduces MSA for weakly supervised covariance alignment in MEG signals.

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using Bayes theorem. With LDA, we estimate a single, pooled covariance m…

Denise learns a function to quickly decompose covariance matrices robustly.

In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computing…

Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background material, this paper introduces a technique we call slicing for obtaining a nonsingular …

The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance matrices are the following…

Lower bounds on private estimation of Gaussian covariance matrices.

Study on random matrices in deep neural networks with IID entries.

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim i…