相关论文: On Block Cholesky Decomposition for Sparse Inverse…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large…

Block-structured problems are central to advances in numerical optimization and machine learning. This paper provides the formalization of convergence analysis for two pivotal algorithms in such settings: the block coordinate descent (BCD)…

We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in…

Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g. there are highly correlated groups of variables). To improve prediction accuracy, various methods have been…

Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…

Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a…

We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on…

In this paper, we aim to estimate block-diagonal covariance matrices for Gaussian data in high dimension and in fixed dimension. We first estimate the block-diagonal structure of the covariance matrix by theoretical and practical estimators…

Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited…

Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…

We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…

Two types of low cost-per-iteration gradient descent methods have been extensively studied in parallel. One is online or stochastic gradient descent (OGD/SGD), and the other is randomzied coordinate descent (RBCD). In this paper, we combine…

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.…

Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew…