Related papers: Decomposing Gaussians with Unknown Covariance
Suppose we observe a random vector $X$ from some distribution $P$ in a known family with unknown parameters. We ask the following question: when is it possible to split $X$ into two parts $f(X)$ and $g(X)$ such that neither part is…
The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…
Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is…
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
Efficient signal representation is essential for the functioning of living and artificial systems operating under resource constraints. A widely recognized framework for deriving such representations is the information bottleneck method,…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
Gaussian Processes (GP) are widely used for probabilistic modeling and inference for nonparametric regression. However, their computational complexity scales cubicly with the sample size rendering them unfeasible for large data sets. To…