We propose a novel estimation approach for the covariance matrix based on the -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…
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48 results for “covariance factors”
Partial covariance factorizes in path diagrams, simplifying analysis.
problem Understanding partial covariance in complex diagrams.
method Factorization of partial covariance over nodes and edges.
result Simpson's paradox cannot occur in singly-connected diagrams.
Proposes FarmHazard model for hazard regression with correlated covariates.
problem Model selection challenges in high-dimensional data with correlated covariates.
method Factor-Augmented Regularized Model for Hazard Regression (FarmHazard) that learns latent factors and idiosyncratic components.
result Proves model selection and estimation consistency under mild conditions.
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.
Russian-Doll Risk Modelsq-fin.PM
We give a simple explicit algorithm for building multi-factor risk models. It dramatically reduces the number of or altogether eliminates the risk factors for which the factor covariance matrix needs to be computed. This is achieved via a nested "Russian-doll" embedding: the factor covariance matrix itself is modeled v…
Shrinkage = Factor Modelq-fin.PM
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…
Factor Models for Alpha Streamsq-fin.PM
We propose a framework for constructing factor models for alpha streams. Our motivation is threefold. 1) When the number of alphas is large, the sample covariance matrix is singular. 2) Its out-of-sample stability is challenging. 3) Optimization of investment allocation into alpha streams can be tractable for a factor …
In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are extracted from least square, principal, iterative principal component, alpha or i…
We analyze linear factor models for asset pricing panels.
problem Characterizing cross-sectional and inter-temporal properties of returns and factors.
method Conditional means and covariances, review of Kozak and Nagel (2024) conditions.
result Low-dimensional factor portfolios can span efficient portfolios in unbalanced panels.
Investigates the long-only minimum variance portfolio in factor models.
problem Understanding the long-only minimum variance portfolio in factor models.
method Investigates the long-only global minimum variance portfolio in a factor model of returns, providing explicit and geometric descriptions for different factor models.
result Provides rigorous and explicit descriptions of the long-only solution in terms of covariance matrix parameters and geometric descriptions for multiple factors.
Deep learning improves covariance matrix estimation for better portfolio risk management.
problem Improving the accuracy of covariance matrix estimation for portfolio risk management.
method Formulated as a learning problem, used deep learning to automatically discover risk factors.
result 1.9% higher explained variance and reduced portfolio risk.
Paper proposes a new method for sparse covariance Cholesky factor estimation.
problem Estimating sparse covariance matrices for ordered data.
method Matrix loss penalization approach for sparse Cholesky factor estimation.
result The proposed method outperforms existing regression-based approaches in simulations and real data.
Paper proposes a new algorithm for graph learning with covariance constraints.
problem Graphical models and factor analysis not jointly leveraged in graph learning processes.
method Penalized maximum likelihood estimation of an elliptical distribution with Riemannian optimization.
result Effectiveness of the proposed approach demonstrated on real-world data sets.
A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for a covariate present in a sample to both repeat itself and excite related ones…
Meta learns low-rank covariance factors for better uncertainty estimation.
problem Sub-optimal covariance matrices in multi-task settings.
method Meta learns diagonal or diagonal plus low-rank factors using an attentive set encoder.
result Efficiently constructed task-specific covariance matrices improve uncertainty estimation.
factor analysismath.OC
New method for factor analysis using nuclear and norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, norm, and KL divergence. Used alternating minimization algorithm.
result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
Method regularizes Cholesky factors to detect nonstationarity in longitudinal data.
problem Detecting nonstationarity in large covariance matrices of longitudinal data.
method Fused-Lasso regularization on Cholesky factors.
result Regularization leads to smooth subdiagonals, indicating nonstationarity.
GLSKF improves tensor completion by capturing both global and local variations.
problem Tensor completion with missing entries, especially in data with spatial or temporal side information.
method Integrates smoothness-constrained low-rank factorization with a locally correlated residual process.
result GLSKF achieves superior performance and scalability on real-world datasets.
New method models covariates and responses without parametric assumptions using manifold learning.
problem Losing explanatory power for responses in standard factor models applied to covariates alone.
method Anisotropic diffusion maps for learning low-dimensional embeddings.
result Kalman filtering in diffusion-map coordinates improves joint covariate-response prediction.
Estimates linear model from noisy covariates and instruments using spectral regularization.
problem Estimating a linear model from many noisy covariates and instruments.
method Two-stage least squares with spectral regularization of canonical correlations.
result Upper and lower bounds on estimation error, proving optimality of the method with noisy data.
This paper investigates factors influencing SGD minima.
problem Understanding the factors that influence the minima found by SGD.
method Examined learning rate, batch size, Hessian, and gradient covariance; used stochastic differential equations to model SGD.
result The ratio of batch size to learning rate is a main factor in SGD dynamics.
New method for estimating financial covariance matrices efficiently.
problem Noisy covariance matrix estimation in high-dimensional financial data.
method Cluster financial time series into groups, apply shrinkage to ensure positive definiteness.
result Proposed methods provide reliable estimates and outperform other estimators.
In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at random based on the random projection method. Randomness of factors has the con…
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
New method estimates covariance in multi-view data with better accuracy and uncertainty.
problem Estimating covariance in multi-view data with shared and view-specific latent factors.
method Spectral decompositions and conditional conjugate priors for factor loadings and residual variances.
result Proves favorable asymptotic properties and excellent performance in simulations and real data.
Develops a fast algorithm for fitting multilevel factor models.
problem Fitting multilevel factor models with covariance structure.
method Novel expectation-maximization algorithm tailored for multilevel factor models.
result Shows efficient computation of inverse of positive definite MLR matrix.
Study analyzes bond price covariation robustly under no-arbitrage conditions.
problem Identifying the number of statistically relevant factors in the bond market.
method Nonparametric analysis of realized covariations in a general no-arbitrage setting.
result A high number of factors is needed to describe term structure evolution and term structure of volatility varies over time.
New method for inference on covariates in NMF with random effects.
problem Formal inference for covariate effects in NMF with non-negativity constraints.
method NMF-RE model with random effects, ridge updates, df-based cap, asymptotic linearization, wild bootstrap.
result Valid inference on covariates with non-negativity constraint, avoiding degeneracy.
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
ITSPACE improves covariance alignment faster than other methods.
problem Optimizing covariance matrices for machine learning tasks.
method Proximal majorization-minimization method that directly optimizes the Bures-Wasserstein objective.
result ITSPACE achieves lower BW gap solutions faster than other methods.
Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, w…
Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the sh…
MSFA clusters high-dimensional spatial data using spline-based covariance structures.
problem Clustering high-dimensional spatial data with flexible covariance structures.
method Mixture of spatial factor analyzers with spline-based covariance and matrix variate factor analyzers for dimensionality reduction.
result Proposed models accurately infer and differentiate distinct spatial patterns in tensor-variate data.
Proposes CoDEAL for estimating heterogeneous treatment effects in panel data models.
problem Estimating heterogeneous treatment effects in causal panel data models with covariate effects.
method Covariate-Adjusted Deep Causal Learning (CoDEAL) integrating neural networks and autoencoders.
result Establishes theoretical guarantees and demonstrates compelling performance in simulations and real data.
We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order…
Proposes a new Gaussian factor for probabilistic inference with degenerate settings.
problem Handling linear dependencies among random variables in Gaussian networks.
method Introduces a parametrised factor that relaxes the positive-definite constraint of the covariance matrix.
result Accurately accommodates degeneracies in probabilistic inference without significant computational overhead.
Paper solves a key problem in learning from high-dimensional covariance matrices.
problem Computing normalizing factors for Riemannian Gaussian distributions on high-dimensional covariance matrices.
method Equivalence with random matrix theory and log-normal matrix ensembles to approximate normalizing factors.
result Efficient approximation of normalizing factors with decreasing error as dimension increases.
Improves predictions by integrating forward-looking views into dynamic factor models.
problem Poor forecasts from historical data when dynamics change.
method Combines historical data with forward-looking views using a dynamic factor model.
result Derives optimal portfolio strategies influenced by both myopic and intertemporal factors.
Paper proposes a fast algorithm to recover causal DAGs with latent variables.
problem Discovering causal relationships in the presence of latent variables.
method Cholesky factorization of covariance matrix with optimization for latent variables.
result The algorithm significantly outperforms previous methods in synthetic and real-world datasets.
Proposes FATTNN for tensor-on-tensor regression with improved prediction and reduced computation.
problem Tensor-on-tensor regression with complex tensor structures and nonlinear relationships.
method Integrates tensor factor models into deep neural networks to handle nonlinearity and reduce data dimensionality.
result Significant improvements in prediction accuracy and computational efficiency over traditional methods.
Paper optimizes private PCA for covariance estimation in statistics.
problem Private estimation of covariance matrices and principal components.
method Developed differentially private estimators for spiked covariance model.
result Established minimax rates of convergence for principal components and covariance matrix estimation.
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors…
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing a class of nonparametric covariance regression models, which allow an unknown p …
Optimally tackles covariate shift in RKHS-based nonparametric regression.
problem Covariate shift in nonparametric regression over RKHS.
method Two families of covariate shift problems defined using likelihood ratios. Minimax rate-optimal estimators for KRR and reweighted KRR.
result KRR is minimax rate-optimal and strictly sub-optimal compared to naive estimator under covariate shift.
High-dimensional covariance matrix estimators on simulated portfolios with complex structuresq-fin.CP
Study high-dimensional covariance matrix estimators for complex portfolios, improving financial metrics.
problem Estimating covariance matrices in high-dimensional portfolios with nested and one-factor structures.
method Combining random matrix theory, free probability, deterministic equivalents, and two-step covariance estimators.
result Two-step estimators improve financial metrics in complex and one-factor covariance models.
Proposes a hybrid deep learning network for better heart failure survival prediction.
problem Improving survival prediction in heart failure patients.
method Joint analysis of cardiac motion features and clinical risk factors using a hybrid deep learning network.
result Optimal integration of clinical risk factors into deep prediction networks.
A new model for dynamic covariance recovery in neuroimaging data.
problem Estimating time-varying covariances in high-dimensional neuroimaging data.
method Nonconvex factorization into sparse spatial and smooth temporal components, combined with spectral initialization and gradient descent.
result The proposed method achieves linear convergence and superior performance compared to existing approaches.
We investigate a solution for the problems related to the application of multivariate GARCH models to markets with a large number of stocks by restricting the form of the conditional covariance matrix. The model is a factor model and uses only six free GARCH parameters. One factor can be interpreted as the market compo…