相关论文: A Multinomial Canonical Decomposition Model, with …

We present a method to decompose a set of multivariate real polynomials into linear combinations of univariate polynomials in linear forms of the input variables. The method proceeds by collecting the first-order information of the…

Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a…

Many analyses of multivariate data focus on evaluating the dependence between two sets of variables, rather than the dependence among individual variables within each set. Canonical correlation analysis (CCA) is a classical data analysis…

In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of…

This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a…

This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables…

Generalized linear models, such as logistic regression, are widely used to model the association between a treatment and a binary outcome as a function of baseline covariates. However, the coefficients of a logistic regression model…

Multinomial logistic regression models allow one to predict the risk of a categorical outcome with more than 2 categories. When developing such a model, researchers should ensure the number of participants (n) is appropriate relative to the…

Clinical prediction models (CPMs) are used to predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, with rising emphasis on the prediction of…

We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…

Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…

Causal inference on multiple non-independent outcomes raises serious challenges, because multivariate techniques that properly account for the outcome's dependence structure need to be considered. We focus on the case of binary outcomes…

The availability of multi-modality datasets provides a unique opportunity to characterize the same object of interest using multiple viewpoints more comprehensively. In this work, we investigate the use of canonical correlation analysis…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

Multilabel classification is a relatively recent subfield of machine learning. Unlike to the classical approach, where instances are labeled with only one category, in multilabel classification, an arbitrary number of categories is chosen…

We introduce a novel bias-variance decomposition for a range of strictly convex margin losses, including the logistic loss (minimized by the classic LogitBoost algorithm), as well as the squared margin loss and canonical boosting loss.…

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

We know that the marginals in a multinomial distribution are binomial variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the…

Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about…

Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…