ISEE method efficiently estimates large precision matrices in Gaussian graphical models.
problem Estimating large precision matrices in ultra-large Gaussian graphical models.
method ISEE method combines sparse modeling and large covariance matrix estimation.
result ISEE method can recover graphical structure with significant probability and efficient estimation of link strengths.
New method estimates multivariate Gaussian fields using sparse precision matrix.
problem Estimating covariance matrices for large multivariate Gaussian fields.
method Sparse Precision Matrix Selection (SPS) algorithm for multivariate GRFs.
result Theoretical rates of convergence for estimated covariance and parameters validated.
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
problem Challenges in inferring conditional dependence relationships in high-dimensional compositional data.
method Composition adaptive regularized estimation (CARE) method for sparse basis precision matrix.
result CARE estimator achieves minimax optimality in high dimensions, performing as well as if the basis were observed.
A new R package for high-dimensional regression and precision matrix estimation.
problem High-dimensional linear regression and precision matrix estimation challenges.
method flare package implements various regression methods and extensions for sparse precision matrix estimation.
result The flare package is efficient and scalable for large problems.
Bayesian method improves portfolio management with limited data.
problem Estimating covariance or precision matrix for large portfolios is challenging.
method Bayesian graphical LASSO for precision matrix estimation.
result The Bayesian approach outperforms non-Bayesian methods in stability and precision matrix estimation.
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gau…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables p→∞ and the sample size n→∞ so that p/n→c∈(0,+∞). The precision matrix is estimated directly, wit…
Characterizes RFF regression in large n,p,N setting, providing precise learning phases and double descent curve.
problem Characterizes RFF regression in large n,p,N setting. method Characterizes the exact asymptotics of random Fourier feature (RFF) regression in the realistic setting of large n,p,N. result Characterizes two qualitatively different phases of learning and the corresponding double descent test error curve.
Paper presents a deep learning method for estimating asset return precision matrices in noisy financial markets.
problem Estimating precision matrices of asset returns in low signal-to-noise ratio environments.
method Non-linear factor model within deep learning framework, consistent estimator with error covariance estimator.
result Superior accuracy in simulations and empirical data.
Generalized Precision Matrix for scalable estimation of nonparametric Markov networks.
problem Estimating conditional independence structure in general distributions for all data types.
method Generalized Precision Matrix (GPM) for mixed-type variables, regularized score matching framework for scalability.
result Validated theoretical results and demonstrated scalability in various settings.
Improved covariance estimation for various metrics outperforms existing methods.
problem Estimating covariance and precision matrices for a wide range of metrics.
method Random matrix theory for improved estimation.
result Significantly outperforms sample covariance matrix and state-of-the-art methods.
Noise-cleaning fMRI brain activity matrices for better precision estimation.
problem Denoise precision matrices of fMRI time series to estimate true matrices.
method Comparison of various noise-cleaning algorithms on synthetic and real fMRI data.
result Optimal Rotationally Invariant Estimator outperforms others in fMRI data.
Proposes a method for forecasting large-scale interval-valued time series.
problem Modeling and forecasting large-scale interval-valued time series.
method Feature extraction procedure involving auto-segmentation, clustering, and precision matrix estimation.
result The method enhances forecasting performance for large-scale interval-valued time series.
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
A new method uses SPDEs to efficiently model random fields on complex domains.
problem Efficient representation of random fields on complex domains for engineering and machine learning.
method Uses SPDEs to develop a scalable framework for statFEM and GP regression.
result Can model anisotropic, non-stationary random fields with arbitrary smoothness.
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.
A new test for graph structure in graphical models using U-statistics.
problem Distinguishing between true and false associations in precision matrix estimates.
method Applying U-statistics to covariance matrix bounds and using Weyl's theorem.
result Conservative test threshold for a wider class of distributions.
MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.
problem Dequantization bottleneck in LLM inference on modern AI accelerators.
method MSD decomposes high-precision activations into multiple low-precision components for direct multiplication with quantized weights.
result MSD avoids INT8-to-BF16 weight conversion, reducing dequantization cycles and HBM traffic.
The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
problem Estimating sparse precision matrices in high-dimensional settings.
method Tempered posterior with fully specified horseshoe prior.
result Concentration results and theoretical oracle inequality for posterior.
Machine learning improves high-dimensional matrix estimation.
problem Efficient estimation of high-dimensional matrices.
method Integrates machine learning with classical optimization algorithms for high-dimensional matrix estimation.
result The reparameterized LADMM achieves faster convergence and higher accuracy.
Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information on either users or items, and assumes a common variance for all users. We extend…
Paper develops differentially private methods for estimating precision matrices.
problem Estimating precision matrices from sensitive data while maintaining privacy.
method Differential privacy framework, ridge estimator, graphical lasso estimator, ADMM algorithm.
result The proposed methods provide utility in estimating precision matrices from private data.
New bounds improve minimax estimation of banded precision matrices.
problem Estimating banded precision matrices with optimal rates.
method Inverting wider blocks of empirical covariance matrices to estimate subblocks of precision matrices.
result Minimax rate matches for banded covariance matrices, improving previous bounds.
Estimates precision matrix with confounding, improving over baselines.
problem Precision matrix estimation with extraneous confounding.
method Joint nonparametric estimator inspired by neuroscientific research.
result Consistent and efficient estimation of precision matrix with improved performance over baselines.
New algorithm solves high-dimensional regression and precision matrix estimation problems efficiently.
problem High-dimensional multivariate regression and precision matrix estimation.
method Gradient descent with hard thresholding for nonconvex optimization.
result Algorithm achieves optimal statistical rate with provable convergence.
Study compares different covariance estimation methods for portfolio allocation.
problem Comparing methods for estimating covariance and precision matrices in portfolio allocation.
method Gaussian Graphical Model (GGM), Shrinkage, Thresholding, Random Matrix Theory (RMT) methods.
result GGM methods outperform other methods in predictive ability for portfolio allocation.
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive …
Proposes a method to classify with matrix-valued predictors using penalized likelihood.
problem Classification with matrix-valued predictors.
method Penalized likelihood method with Kronecker product decomposition for precision matrix estimation.
result Outperforms competitors in classification accuracy, even when assumptions are violated.
Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from labeled training data. We make two contributions. First, we show how to reparameterize…
A new optimization algorithm for Gaussian Variational Inference on precision matrices.
problem Complex models with positive definite constraints on covariance matrices.
method Manifold Gaussian Variational Bayes (MGVBP) with natural gradient updates.
result Empirically validated as a feasible and efficient solution for VI in complex models.
Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
problem Limitations of inverse covariance matrix in non-Gaussian settings.
method Exploits local dependence function to define generalized precision matrix (GPM) for multivariate t-Student distribution.
result GPM leads to statistically significant lower out-of-sample variances in minimum-variance portfolios.
Algorithm compresses large matrices by approximating them as low rank and low precision factors.
problem Efficiently storing and processing large matrices with billions of elements.
method Randomized sketching and quantization of matrix columns to achieve low rank and low precision factorization.
result Achieves compression ratios as low as one bit per matrix coordinate while maintaining or improving performance.
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.
Mixed-precision CA-SGD for generalized linear models on GPUs
problem SGD communication bottleneck
method Mixed-precision CA-SGD
result Matches FP32 SGD loss within 0.5% on various problems
Detects anomalies in Gaussian graphical models using contrastive estimation.
problem Detecting structural changes in Gaussian graphical models.
method Two-step approach: background precision matrix estimation and contrastive foreground precision estimation using ADMM.
result Significant improvement in precision and recall for detecting structural changes.
Improved method for estimating precision matrices without knowing variable order.
problem Estimating precision matrices without knowing the order of variables.
method Combining multiple permutations and thresholding for sparse structure.
result Consistent property established under weak conditions, superior performance in simulations and real data.
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.
The paper analyzes data augmentation for precision matrix estimation in high dimensions.
problem Precision matrix estimation in high-dimensional settings.
method Linear shrinkage estimators and data augmentation methods.
result Concentration bounds for the quadratic error of estimators.
Clusterpath estimator simplifies graphical model interpretation for large datasets.
problem Difficulty in interpreting graphical models with many variables.
method Clusterpath estimator that groups variables for block-structured precision matrix.
result CGGM outperforms other methods in variable clustering and practical applications.
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that severa…
The paper examines how kernel approximations affect Gaussian process regression in large data applications.
problem Effect of kernel approximations on Gaussian process regression in large data applications.
method Unified framework to analyze Gaussian process regression under computational and epistemic misspecification.
result Theoretical analysis of Gaussian process regression under various misspecifications.
New method quantifies classifier uncertainty, revealing large variability in performance metrics.
problem Uncertainty in classifier performance metrics due to small data sets.
method Probability model of the confusion matrix to quantify uncertainty.
result Large uncertainties in classification performance metrics can lead to misleading conclusions.
A new RPCA method is faster and more scalable than AltProj.
problem Recovering low-rank matrices from data matrices with sparse parts.
method Factorization-based RPCA model with complexity O(kdn). result Our method is about 4 times faster than AltProj and more scalable.
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
problem Learning a sparse undirected graph from multivariate data under Laplacian-related constraints.
method Modifications to penalized log-likelihood approaches to enforce total positivity and lasso/adaptive lasso penalties using ADMM.
result The proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches.
Trans-Glasso uses transfer learning to estimate precision matrices from related studies.
problem Challenges in precision matrix estimation with limited target samples.
method Two-step transfer learning: multi-task learning followed by differential network estimation.
result Trans-Glasso achieves minimax optimality under certain conditions and outperforms baseline methods in simulations and real-world applications.
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
problem Selecting an appropriate regularization parameter for sparse precision matrix estimation.
method Developed a closed-form matrix-valued regularization parameter based on the sampling distribution of optimality conditions.
result The proposed method achieves comparable estimation accuracy and superior support recovery to cross-validation, with significant runtime improvements.
Study on estimating covariance and precision matrices along specific subspaces.
problem Estimating covariance and precision matrices along prescribed subspaces or directions.
method Analysis of finite sample covariance, focusing on components corresponding to desired subspaces or directions.
result Estimation accuracy depends almost exclusively on components corresponding to desired subspaces or directions.
A new algorithm improves GLasso for sparse precision matrix estimation.
problem Efficiently estimating sparse precision matrices in high-dimensional data.
method A new reparametrization and iterative block coordinate descent algorithm.
result Improved performance comparable to DP-GLasso with a simpler optimization target.