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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…
Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor…
Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati…
Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…
In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We focus on the notion of regular fraction and we introduce methods to check whether a given symmetric orthogonal array can…
As a generalization of the classical linear factor model, generalized latent factor models are useful for analyzing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to…
Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…
Factor analysis models explain dependence among observed variables by a smaller number of unobserved factors. A main challenge in confirmatory factor analysis is determining whether the factor loading matrix is identifiable from the…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
Unidimensional factor models justify some of the most consequential summaries in science -- single scores, single ranks, and single leaderboards -- yet unidimensionality is usually assessed indirectly by fitting and evaluating models on…
Purpose: Factor analysis (FA) has become part and parcel in metabolic syndrome (MBS) research. Both exploration- and confirmation-driven factor analyzes are rampant. However, factor analytic results on MBS differ widely. A situation that is…
In (exploratory) factor analysis, the loading matrix is identified only up to orthogonal rotation. For identifiability, one thus often takes the loading matrix to be lower triangular with positive diagonal entries. In Bayesian inference, a…
Data-fusion involves the integration of multiple related datasets. The statistical file-matching problem is a canonical data-fusion problem in multivariate analysis, where the objective is to characterise the joint distribution of a set of…
This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations - they are free…
A polymorphic analysis is an analysis whose input and output contain parameters which serve as placeholders for information that is unknown before analysis but provided after analysis. In this paper, we present a polymorphic groundness…
The R package GFA provides a full pipeline for factor analysis of multiple data sources that are represented as matrices with co-occurring samples. It allows learning dependencies between subsets of the data sources, decomposed into latent…
The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…