Lower bounds on private estimation of Gaussian covariance matrices.
problem Private estimation of Gaussian covariance matrices under various parameter regimes.
method Stein-Haff identity and fingerprinting lemma extensions.
result Lower bounds match existing upper bounds in the widest known parameters.
Neural networks speed up covariance estimation in spatial Gaussian processes.
problem Efficiently estimating covariance parameters in spatial Gaussian processes.
method Training neural networks to approximate maximum likelihood estimates.
result Neural network estimates are as accurate as ML methods but much faster.
Improved global minimum-variance portfolios using cross-validation for high-dimensional covariance estimation.
problem Ill-conditioned sample covariance matrix in high-dimensional data leads to suboptimal portfolios.
method Cross-validation technique to select tuning parameters for efficient covariance matrix estimation methods.
result Data-driven tuning parameters improve out-of-sample performance of global minimum-variance portfolios.
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.
A-BLINK speeds up Gaussian process covariance estimation.
problem Slow covariance matrix inversion in Gaussian processes.
method Two pre-trained neural networks learn Kriging weights and spatial variance.
result Significant computational speedups and posterior inference.
Improved 2-bit covariance estimator with reduced operator norm error and no tuning needed.
problem Improving 2-bit covariance estimation with reduced operator norm error and no tuning needed.
method Proposed a new 2-bit covariance matrix estimator using triangular dithering scales.
result Improved operator norm error rate that depends on effective rank of covariance matrix, closing theoretical gap.
Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.
A streaming algorithm estimates quadratic covariation from financial data efficiently.
problem Estimating quadratic covariation from ultra-high-frequency financial data with limited memory.
method Formulated multi-scale, realized kernel, pre-averaging, and modulated realized covariance estimators with fixed bandwidth.
result Fixed bandwidth estimators require higher bandwidth for positive semidefiniteness.
Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample cov…
DPERC efficiently estimates covariance matrices for mixed data with missing values.
problem Estimating covariance matrices for datasets with missing values and mixed features.
method Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC).
result DPERC outperforms other methods in estimating covariance matrices for mixed data with missing values.
Study on Matérn covariance approximations on grids, finding issues with high-frequency aliasing.
problem Issues with high-frequency aliasing in SPDE approximations of Matérn covariance functions.
method Analysis of aliased spectral densities and numerical simulations.
result SPDE approximations assign too much power at high frequencies and do not improve accuracy as grid spacing decreases.
Proposes a robust method for predicting missing outcomes in covariate shift adaptation.
problem Predicting missing outcomes in test data with covariate shift.
method Doubly robust estimator for covariate shift adaptation via importance weighting, incorporating an additional estimator for the regression function.
result Shows robustness against density-ratio estimation errors, maintaining consistency if either estimator is consistent.
Paper proposes an online covariance estimator for sketched Newton methods.
problem Estimating the limiting covariance matrix of sketched Newton methods.
method Proposes a fully online covariance matrix estimator from Newton iterates.
result Establishes the consistency and convergence rate of the proposed estimator.
Paper proposes an online estimator for covariance matrix of SGD iterates.
problem Quantifying variability and randomness of SGD-based estimates in online learning.
method Proposes a fully online estimator for covariance matrix of ASGD using SGD iterates.
result Establishes consistency of the online estimator and shows comparable convergence rate to offline methods.
ConvNets improve nonstationary covariance estimation for large-scale spatial data.
problem Estimating nonstationary spatial covariance functions on large scales.
method Convolutional Neural Networks (ConvNets) for subregion identification and selection.
result Enhanced accuracy in parameter estimation using ConvNet-based partitioning.
The paper proposes AIS for Bayesian inversion of multioutput signals with covariance estimation.
problem Performing uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals.
method Adaptive Importance Sampling (AIS) scheme, split variables, frequentist approach for noise covariance, prior density over covariance matrix.
result Estimation of model parameters and covariance matrix of noise.
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance function parameters increases with the dimension. Even evaluation of the likelihood fu…
This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.
problem Estimating chaotic dynamics and parameters from observations.
method Local ensemble Kalman filters with covariance and local domain localisation.
result Rigorously updating global parameters using a local domain ensemble Kalman filter.
GP-LVM improves covariance estimation in finance.
problem Stability of covariance estimates in small sample sizes.
method Gaussian Process Latent Variable Model (GP-LVM) for non-linear covariance estimation.
result GP-LVM reduces estimation errors and provides interpretable parameters.
Paper estimates Hurst parameter from implied volatilities.
problem Estimating Hurst parameter from implied volatilities.
method Uses covariance between asset return and realized volatility, and applies limit theorems for stochastic volatility models.
result Direct relation between covariance and slope of at-the-money implied volatility established.
Simple private estimators for mean and covariance outperform existing methods.
problem Private estimation of mean and covariance at small sample sizes.
method Differentially private estimators for multivariate sub-Gaussian data.
result Asymptotic error rates match theoretical bounds and outperform previous methods.
EiGLasso speeds up sparse Kronecker-sum covariance estimation.
problem Sparse Kronecker-sum inverse covariance estimation challenges in scalability and parameter identification.
method Newton's method combined with eigendecomposition of sample and feature graphs, approximating Hessian for speed.
result Two to three orders-of-magnitude speed-up on simulated and real-world data.
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate appr…
Proposes a new method to estimate variable importance in black box models, mitigating correlation effects.
problem Correlation between covariates affects the interpretation of variable importance parameters.
method Develops a modified LOCO (Leave Out COvariates) method and uses semiparametric models for estimation.
result Shows how to estimate a modified LOCO method that mitigates correlation effects.
Paper estimates GMMs with unknown covariances using sparse regularization.
problem Estimating GMMs with unknown diagonal covariances from samples.
method Employed Beurling-LASSO (BLASSO) for sparse estimation of component means, covariances, and weights.
result Established non-asymptotic recovery guarantees with nearly parametric convergence rates.
A new method for covariate shift adaptation using nearest neighbors.
problem Mitigating distribution shift between source and target datasets.
method Directly work on unlabeled target data, labeled by nearest neighbors in source data.
result Optimal choice of k=1 simplifies hyper-parameter tuning and improves efficiency. Method estimates multiple related Gaussian distributions using Laplacian regularization.
problem Jointly estimate multiple related zero-mean Gaussian distributions.
method Laplacian regularized stratified model fitting with hyper-parameters to encourage covariance closeness.
result The method performs well, especially in low data regimes, as demonstrated in finance, radar, and weather.
This study evaluates shrinkage estimators for improving mean and covariance in portfolio optimization.
problem Estimation errors in expected returns and covariance matrix in mean-variance model.
method Examined five shrinkage estimators for expected returns and eleven for covariance matrix across six datasets.
result GMV model with Ledoit Wolf COV2 outperforms traditional methods in most scenarios.
Novel approach for SEM in small samples with p>n.
problem Small sample size and p>n issues in factor-based SEM. method Reformulates covariance structure into self-covariance and cross-covariance, defines a feasible set with relative error constraint.
result Improved stability and directional information in small-sample settings.
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The methods developed here are useful for missing data impu…
BSL package simplifies Bayesian synthetic likelihood for complex models.
problem Estimating posterior distributions for models with intractable likelihoods.
method Approximates likelihood via model simulation and density estimation, using penalized covariance and semi-parametric approaches.
result Reduces the need for model simulations and improves efficiency compared to ABC.
In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a sm…
Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.
problem Efficiency in estimating treatment or policy effects in causal inference.
method Outcome-adapted AutoDML estimator that uses a shared covariate representation that is predictive of the outcome but not the Riesz representer.
result Outcome-adapted AutoDML estimator is asymptotically more efficient than baseline AutoDML.
Localized debiased machine learning simplifies estimating quantile treatment effects.
problem Estimating quantile treatment effects in causal inference with many covariates and flexible relationships.
method Localized debiased machine learning (LDML) avoids learning the full nuisance function by estimating only at a single initial guess.
result LDML enables practically-feasible and theoretically-grounded efficient estimation of quantile treatment effects.
This article addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random variable whose covariance encodes the spatial cha…
REBMIX package generates, estimates, clusters and classifies multivariate normal mixtures.
problem Generating, estimating, clustering and classifying multivariate normal mixtures with unrestricted variance-covariance matrices.
method Random generation, estimation of components, weights, and parameters, prediction of cluster and class membership.
result Demonstrates the REBMIX package's capabilities for multivariate normal mixtures.
New algorithm estimates Gaussian means and covariances efficiently and privately.
problem Estimating Gaussian parameters privately and efficiently.
method Differentially private preconditioner to transform arbitrary Gaussian samples.
result First polynomial-time, sample-efficient estimator for arbitrary Gaussian distributions.
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.
Novel approach to robustly estimate inverse covariance matrix for multivariate data.
problem Estimating the inverse covariance matrix for multivariate data robustly against distributional uncertainty.
method Distributionally robust optimization framework tailored to graphical lasso, with closed-form radius.
result The radius of the Wasserstein ambiguity set is directly related to the regularization parameter and can be computed in closed-form.
SPICE estimates sparse linear dynamic networks without hyperparameters.
problem Estimating topology and dynamics of sparse linear dynamic networks.
method SPICE (Sparse Iterative Covariance Estimation) method in an iterative framework.
result Directly reveals the underlying topology of the network.
Paper extends Bayesian Cramér-Rao bound with geometric considerations.
problem Estimation of covariance matrices with geometric structures.
method Intrinsic Bayesian Cramér-Rao bound with Riemannian geometry.
result Performance bounds for covariance matrix estimation.
Optimizes ellipsoids for uncertainty regions in parameter estimation.
problem Learning minimal volume uncertainty ellipsoids for parameter estimation.
method Differentiable optimization approach using neural networks to approximate optimal ellipsoids.
result Approximately computed ellipsoids are smaller and more accurate than existing methods.
Paper develops a method to construct confidence regions for model parameters using batch means method.
problem Constructing confidence regions for model parameters in stochastic gradient descent.
method Batch means method to cancel out covariance matrix, using Polyak-Ruppert averaging.
result Established process-level functional central limit theorem for stochastic gradient descent estimators.
Study shows sample complexity for logistic regression with normal covariates.
problem Estimating parameters of logistic regression with normal design.
method Analyzes sample complexity in terms of dimension and inverse temperature.
result Shows two change-points in sample complexity curve based on inverse temperature.
New method selects variables for GP regression using sparse projection.
problem Identifying environmental factors affecting metal corrosion.
method Sparse projection of input variables, gradient descent optimization, non-convex marginal likelihood.
result Proposed method outperforms benchmarks in variable selection accuracy.
Unified approach to linear regression using covariance fitting for optimal weights.
problem Finding optimal weights for linear regression models when weights are unknown.
method Covariance fitting SPICE-methodology to obtain data-adaptive weights.
result Tuned versions of known regularized estimators are unified under a common approach.
New method corrects bias in datasets using cumulative distribution functions.
problem Varying domains and biased datasets lead to differences between training and target distributions.
method Empirical cumulative distribution function estimates of the target distribution, rigorously generalized.
result Method is more robust, not reliant on parameter tuning, and performs similarly to state-of-the-art techniques.
In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO penalty (Zou, 2006) hav…