Related papers: Cholesky-based multivariate Gaussian regression
A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
Algorithms come with multiple variants which are obtained by changing the mathematical approach from which the algorithm is derived. These variants offer a wide spectrum of performance when implemented on a multicore platform and we seek to…
This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
This paper takes a different approach for the distributed linear parameter estimation over a multi-agent network. The parameter vector is considered to be stochastic with a Gaussian distribution. The sensor measurements at each agent are…
In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision…