Related papers: Real birational implicitization for statistical mo…
Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for…
Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel…
In this paper, we show that some fundamental results for smooth mappings (e.g., the Brouwer degree formula, the implicit function and inverse function theorems, the mean value theorem, Sard's theorem, Hadamard's global invertibility…
We recall a higher dimension analog of the classic plane de Jonqui\`eres transformations, as given by Hassanzadeh and Simis. Such a parameterization defines a birational map from $\mathbb{P}^{n-1}$ to a hypersurface in $\mathbb{P}^{n}$, and…
Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
New theoretical results are presented here on the recently introduced model called mixed states MRF. Such models were introduced in the context of image motion analysis and are useful to represent information which can take both discrete…
In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,...,f_n$ of the same degree in a graded algebra $A$. We first compute the degree of this closed image…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras. For G semisimple simply connected, we describe birational sheets in terms of Lusztig-Spaltenstein induction and we prove that…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case…
How to efficiently represent a graph in computer memory is a fundamental data structuring question. In the present paper, we address this question from a combinatorial point of view. A representation of an $n$-vertex graph $G$ is called…
Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…