Related papers: Covariance Prediction via Convex Optimization

Analysis of high-dimensional data is currently a popular field of research, thanks to many applications e.g. in genetics (DNA data in genomewide association studies), spectrometry or web analysis. At the same time, the type of problems that…

We study the problem of learning vector-valued linear predictors: these are prediction rules parameterized by a matrix that maps an $m$-dimensional feature vector to a $k$-dimensional target. We focus on the fundamental case with a convex…

Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…

In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…

Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…

We develop a version of variational inference for Bayesian count response regression-type models that possesses attractive attributes such as convexity and closed form updates. The convex solution aspect entails numerically stable fitting…

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…

We consider the problem of selective inference after solving a (randomized) convex statistical learning program in the form of a penalized or constrained loss function. Our first main result is a change-of-measure formula that describes…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…

We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…

Gaussian covariance graph model is a popular model in revealing underlying dependency structures among random variables. A Bayesian approach to the estimation of covariance structures uses priors that force zeros on some off-diagonal…

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…

In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…

In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based models such as SVM is, that the…