Related papers: Multivariate probability distribution for categori…
Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
Marginal imputation, which consists of imputing each item requiring imputation separately, is often used in surveys. This type of imputation procedures leads to asymptotically unbiased estimators of simple parameters such as population…
Discrete but ordered covariates are quite common in applied statistics, and some regularized fitting procedures have been proposed for proper handling of ordinal predictors in statistical modeling. In this study, we show how quadratic…
Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable.…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
This paper is especially written for students and demonstrates the correct use of nominal and ordinal scaled variables in regression analysis by means of so-called dummy variables. We start out with examples of body mass index (BMI)…
Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of the corresponding conditional probability distributions on the level-sets of a collective variable…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by…
Cross-classified data frequently arise in scientific fields such as education, healthcare, and social sciences. A common modeling strategy is to introduce crossed random effects within a regression framework. However, this approach often…
The ability to estimate joint, conditional and marginal probability distributions over some set of variables is of great utility for many common machine learning tasks. However, estimating these distributions can be challenging,…