Related papers: Entropic covariance models
This paper provides a comprehensive estimation framework for large covariance matrices via a log-det heuristics augmented by a nuclear norm plus $\ell_{1}$-norm penalty. We develop the model framework, which includes high-dimensional…
A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
For a given statistical model, it often happens that it is necessary to intervene the model to reduce the variances of the output variables. In structural equation models, this can be done by changing the values of the path coefficients by…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
The regression problem associated with finding a matrix approximation of the Koopman operator from data is considered. The regression problem is formulated as a convex optimization problem subject to linear matrix inequality (LMI)…
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
A common assumption when sampling $p$-dimensional observations from $K$ distinct group is the equality of the covariance matrices. In this paper, we propose two penalized $M$-estimation approaches for the estimation of the covariance or…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
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…
As observed by Auderset et al. (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter. In…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…