Related papers: Algebraic tests of general Gaussian latent tree mo…

We define a class of "algebraic" random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner…

The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in…

The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to…

We propose methods to improve the forecasts from generalized autoregressive score (GAS) models (Creal et. al, 2013; Harvey, 2013) by localizing their parameters using decision trees and random forests. These methods avoid the curse of…

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first…

Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…

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 paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…

The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is to expand the currently limited range of random polynomials…

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…

Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…

Model-based trees are used to find subgroups in data which differ with respect to model parameters. In some applications it is natural to keep some parameters fixed globally for all observations while asking if and how other parameters vary…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian…

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…