arXiv subjects

Giovanni M. Marchetti

Publications and source records attributed to Giovanni M. Marchetti.

8 recordsLinked to original sources

arXiv2026

Causal invariance in graphical models with latent variables

Causal discovery aims to identify causal relationships among variables from observational or interventional data, typically represented by a directed acyclic graph (DAG). The causal invariance principle enables the identification of the causal parents of target variables by exploiting the stability of causal effects across different experimental settings. When some parents are unobserved, however, the induced graph over the observed variables may no longer be a DAG, and it may not be unique, complicating causal inference. For relevant configurations of latent parents, we characterize the induced graph and formalize the conditions under which causal invariance is preserved for the identification of the observed parents. Necessary and sufficient conditions for testing such invariance are formally established for a multivariate Gaussian target.

stat.ME↗

arXiv2017

Generating large Ising models with Markov structure via simple linear relations

We extend the notion of a tree graph to sequences of prime graphs which are cycles and edges and name these non-chordal graphs hollow trees. These structures are especially attractive for palindromic Ising models, which mimic a symmetry of joint Gaussian distributions. We show that for an Ising model all defining independences are captured by zero partial correlations and conditional correlations agree with partial correlations within each prime graph if and only if the model is palindromic and has a hollow-tree structure. This implies that the strength of dependences can be assessed locally. We use the results to find a well-fitting general Ising model with hollow-tree structure for a set of longitudinal data.

stat.ME↗

arXiv2016

Palindromic Bernoulli distributions

We introduce and study a subclass of joint Bernoulli distributions which has the palindromic property. For such distributions the vector of joint probabilities is unchanged when the order of the elements is reversed. We prove for binary variables that the palindromic property is equivalent to zero constraints on all odd-order interaction parameters, be it in parameterizations which are log-linear, linear or multivariate logistic. In particular, we derive the one-to-one parametric transformations for these three types of model specifications and give simple closed forms of maximum likelihood estimates. Some special cases and a case study are described.

stat.ME↗

arXiv2014

Star graphs induce tetrad correlations: for Gaussian as well as for binary variables

Tetrad correlations were obtained historically for Gaussian distributions when tasks are designed to measure an ability or attitude so that a single unobserved variable may generate the observed, linearly increasing dependences among the tasks. We connect such generating processes to a particular type of directed graph, the star graph, and to the notion of traceable regressions. Tetrad correlation conditions for the existence of a single latent variable are derived. These are needed for positive dependences not only in joint Gaussian but also in joint binary distributions. Three applications with binary items are given.

stat.ME↗

arXiv2012

Case-control studies for rare diseases: improved estimation of several risks and of feature dependences

To capture the dependences of a disease on several risk factors, a challenge is to combine model-based estimation with evidence-based arguments. Standard case-control methods allow estimation of the dependences of a rare disease on several regressors via logistic regressions. For case-control studies, the sampling design leads to samples from two different populations and for the set of regressors in every logistic regression, these samples are then mixed and taken as given observations. But, it is the differences in independence structures of regressors for cases and for controls that can improve logistic regression estimates and guide us to the important feature dependences that are specific to the diseased. A case-control study on laryngeal cancer is used as illustration.

stat.ME↗

arXiv2011

Chain graph models of multivariate regression type for categorical data

We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to those of a chain graph model recently defined in the literature. Next we provide a parametrization based on a sequence of generalized linear models with a multivariate logistic link function that captures all independence constraints in any chain graph model of this kind.

stat.ME↗

arXiv2009

Matrix representations and independencies in directed acyclic graphs

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.

math.ST↗

arXiv2008

Parameterizations and fitting of bi-directed graph models to categorical data

We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as the multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.

stat.ML↗