Related papers: Algorithms for detecting dependencies and rigid su…
Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
This paper is devoted to the generalized differential study of the normal cone mappings associated with a large class of parametric constraint systems (PCS) that appear, in particular, in nonpolyhedral conic programming. Conducting a local…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…
Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
The Macaulay2 package GraphicalModels contains algorithms for the algebraic study of graphical models associated to undirected, directed and mixed graphs, and associated collections of conditional independence statements. Among the…
The cornerstone underpinning deep learning is the guarantee that gradient descent on an objective converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, where there are multiple…
The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes,…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple…
Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive…
Parametric time-dependent systems are of a crucial importance in modeling real phenomena, often characterized by non-linear behaviors too. Those solutions are typically difficult to generalize in a sufficiently wide parameter space while…
Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role…