Related papers: Learning about probabilistic inference and forecas…
Constructions in type-driven compositional distributional semantics associate large collections of matrices of size $D$ to linguistic corpora. We develop the proposal of analysing the statistical characteristics of this data in the…
Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…
Scholars frequently use covariate balance tests to test the validity of natural experiments and related designs. Unfortunately, when measured covariates are unrelated to potential outcomes, balance is uninformative about key identification…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
The matrix-variate normal distribution is a popular model for high-dimensional transposable data because it decomposes the dependence structure of the random matrix into the Kronecker product of two covariance matrices: one for each of the…
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…
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…
In order to trust the predictions of a machine learning algorithm, it is necessary to understand the factors that contribute to those predictions. In the case of probabilistic and uncertainty-aware models, it is necessary to understand not…
Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…
We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of…
Covariance matrices of random vectors contain information that is crucial for modelling. Specific structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now,…
This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
Random correlation matrices are studied for both theoretical interestingness and importance for applications. The author of [6] is interested in their interpretation as covariance matrices of purely random signals, the authors of [16]…