Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
problem Classifying SL(n) covariant matrix-valued valuations on Lp-spaces.
method Established a complete classification for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx), eliminating matrix symmetry assumption.
result Unique characterization of such valuations by the moment matrix in n>2, rotation matrix in 2D.
Paper presents a new framework for covariance matrix estimation with geometric insights.
problem Challenges in covariance matrix estimation, especially in finding suitable models and efficient estimation methods.
method General framework for linear restrictions on different transformations of the covariance matrix, including matrix logarithm and its inverse.
result Yields an M-estimator with M-estimation allowing for straightforward asymptotic and finite sample analysis. New methods estimate covariance for matrix data without assuming fixed size or specific distributions.
problem Estimating covariance for high-dimensional matrix data without distributional assumptions.
method Unified framework for bandable covariance estimation with rank one approximation, robust to heavy-tailed data.
result Proposed estimators are rate-optimal and perform well in simulations and real applications.
This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correl…
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
The paper analyzes how Gaussian kernel parameters affect posterior covariance in Gaussian processes.
problem Understanding the influence of Gaussian kernel parameters on posterior covariance in Gaussian processes.
method Geometric analysis and a posteriori error estimation techniques from adaptive finite element methods.
result The bandwidth parameter and spatial distribution of observations significantly influence posterior covariance and its matrix.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.
Classification of SL(n) covariant valuations on Orlicz spaces.
problem Classifying continuous SL(n) covariant valuations on Orlicz spaces.
method Complete classification without symmetric assumptions, focusing on moment matrix and a new functional in dimension two.
result The moment matrix is the only SL(n) covariant valuation for n≥3, and a new functional appears in dimension two.
CovRegRF estimates covariance matrix from covariates using random forests.
problem Estimating conditional covariances or correlations among multivariate responses.
method Random forest trees with a custom splitting rule to maximize covariance difference.
result Accurate covariance matrix estimates and controlled Type-1 error.
S-VNNs improve VNNs by sparsifying covariance matrices.
problem Spurious correlations in covariance matrices degrade VNNs' performance and efficiency.
method Apply sparsification techniques on sample covariance matrix and integrate into VNN architecture.
result S-VNNs achieve improved performance, stability, and reduced computational time.
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state…
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these markets are given: i) a market with a singular covariance matrix and instantaneous rel…
Improved covariance matrix forecasting for S&P 500 using factor models and shrinkage.
problem Forecasting large covariance matrices of returns in finance.
method Decompose covariance matrix into firm-level factors and sectoral restrictions. Estimate using VHAR models with LASSO.
result Significantly improved forecasting precision compared to benchmarks.
The covariance matrix of a p-dimensional random variable is a fundamental quantity in data analysis. Given n i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of O(np2) operations. When n,p are large, this computation may be prohibitively slow. Moreover, …
A regression algorithm uses Green's function and covariance matrix for predictive distributions.
problem Regression and uncertainty quantification for machine learning.
method Green's function theory, Bayesian approach, covariance matrix of normalized Green's function.
result The covariance matrix provides predictive distributions with mean and confidence intervals.
Study on neural network initialization with shaped infinite depth-and-width networks.
problem Understanding the distribution of random covariance matrices in shaped infinite-depth-and-width networks.
method Introduced the Neural Covariance SDE to model the distribution of the random covariance matrix.
result Identified the precise scaling of the activation function necessary for a non-trivial limit.
New algorithm improves matrix estimation with one-sided covariates.
problem Estimating matrix means with unobserved row covariates.
method Proposes an algorithm for nonparametric matrix estimation with observed column covariates.
result Achieves minimax optimal nonparametric rate in moderately proportioned matrices.
New methods improve portfolio risk minimization by estimating covariance matrix more accurately.
problem Uncertainty in estimating covariance matrix leads to unreliable hedge trades.
method Proposes two new estimators of the inverse covariance matrix using l2 and l1 norms.
result Portfolio formed using proposed estimators achieves substantial risk reduction and improved returns.
DACE estimates covariance from compressed data, improving accuracy.
problem Estimating covariance from large, distributed data.
method Data-aware weighted sampling for unbiased estimation.
result DACE provides more accurate covariance estimation under compression.
We provide a method to prepare covariance matrices for quantum datasets.
problem No concrete protocol for preparing covariance matrices for quantum datasets.
method Amplitude encoding of data, exploiting global phase symmetry to center the dataset.
result Covariance matrix can be prepared for arbitrary quantum datasets or centered classical datasets.
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
problem Difficult inference for multivariate Gaussian Processes with multiple lengthscale parameters.
method Introduces a self-assembled Wishart prior and uses MCMC for Bayesian inference on kernel hyperparameters.
result Demonstrates the effectiveness of the new prior in GP-based learning with empirical results.
Method cleans covariance matrices for better statistical inference.
problem Reducing estimation noise in covariance matrices for better statistical inference.
method Robust yet flexible hierarchical ansatz with bootstrap procedure.
result Lower realized risk in global minimum variance portfolios.
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matri…
Enhanced EEG classification using augmented covariance matrix.
problem Improving motor imagery classification from EEG signals.
method Proposes a new framework based on the augmented covariance matrix derived from an autoregressive model.
result The augmented covariance matrix outperformed state-of-the-art methods.
Covariance graphical lasso applies a lasso penalty on the elements of the covariance matrix. This method is useful because it not only produces sparse estimation of covariance matrix but also discovers marginal independence structures by generating zeros in the covariance matrix. We propose and explore two new algorith…
Paper proposes a deep learning method for better covariance matrix forecasting.
problem Suboptimal predictive performance in traditional matrix volatility forecasting.
method Riemannian-geometry-aware deep learning framework for symmetric positive definite matrices.
result Our method outperforms traditional approaches in predictive accuracy.
Enhanced Transformer models predict ETF portfolio performance by optimizing covariance and semi-covariance matrices.
problem Static covariance estimates fail to capture dynamic market fluctuations and non-linear correlations.
method Transformer-based models for real-time covariance and semi-covariance predictions.
result Portfolios optimized with semi-covariance matrix outperform those with standard covariance matrix, especially in volatile conditions.
The graphical lasso (glasso) is a widely-used fast algorithm for estimating sparse inverse covariance matrices. The glasso solves an L1 penalized maximum likelihood problem and is available as an R library on CRAN. The output from the glasso, a regularized covariance matrix estimate a sparse inverse covariance matrix e…
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
This short note reviews so-called Natural Gradient Descent (NGD) for multivariate Gaussians. The Fisher Information Matrix (FIM) is derived for several different parameterizations of Gaussians. Careful attention is paid to the symmetric nature of the covariance matrix when calculating derivatives. We show that there ar…
The paper improves matrix completion with auxiliary covariates using LS estimation.
problem Matrix completion with noisy data and auxiliary covariates.
method Iterative least squares estimation with statistical properties derived.
result Asymptotic normal distributions of estimators for low-rank matrix and coefficient matrix.
A new GNN architecture called coVariance neural network (VNN) improves stability and transferability of covariance matrix analysis.
problem Stability and transferability issues in covariance matrix analysis.
method Developed coVariance neural network (VNN) that operates on sample covariance matrices.
result VNN is more stable and transferable than PCA-based approaches.
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free es…
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We propose a new input model in which one can query single entries of the covarian…
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
Efficiently solves large portfolio optimization problems by reducing and sparsifying covariance matrices.
problem Large and dense covariance matrices limit efficient portfolio optimization.
method Dimension reduction and increased sparsity based on machine learning predictions.
result Improved portfolio performance and reduced runtime compared to full dense covariance matrices.
We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard approximate factor…
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
Study forecasts volatility and risk in electricity markets using matrix-HAR models.
problem Forecasting volatility and risk in electricity markets.
method Constructed a parsimonious matrix-HAR type model to estimate realized covariation and risk premia in electricity markets.
result Inclusion of longer time horizons and renewable generation information improves forecasts.
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. T…
New method tackles high-dimensional SBL without covariance matrices.
problem Sparse coding problem in high-dimensional settings.
method Parallel solution of multiple linear systems using conjugate gradient algorithm.
result Our method scales better in computation time and memory.
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…
We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded…
LoCoV reduces portfolio optimization errors from sample covariance matrices.
problem Large errors in sample covariance matrix for optimal portfolio weights.
method LoCoV (low dimension covariance voting) algorithm to reduce these errors.
result LoCoV outperforms classical methods in portfolio optimization experiments.
Estimates covariance matrices for matrix-variate data via core covariance geometry.
problem Estimating covariance matrices for matrix-variate data with partial isotropy.
method Fixed-rank core covariance geometry, partial-isotropy rank-r core shrinkage estimator.
result The geometry of the space of rank-r cores is a smooth manifold.
We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a 0−1 Bernoulli random variable. We analyze an unbiased covariance estimator under this mod…
The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical data to estimate it. Even though sample covariance matrix is an unbiased…
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternativ…