Related papers: Entropic covariance models
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide…
This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
In recent years, several convex programming relaxations have been proposed to estimate the permanent of a non-negative matrix, notably in the works of Gurvits and Samorodnitsky. However, the origins of these relaxations and their…
Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…
Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…
Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…
There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…