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Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…
This paper presents a framework designed to tackle a range of planning problems arise in manipulation, which typically involve complex geometric-physical reasoning related to contact and dynamic constraints. We introduce the Contact Factor…
Exploratory factor analysis is often used in the social sciences to estimate potential measurement models. To do this, several important issues need to be addressed: (1) determining the number of factors, (2) learning constraints in the…
Comprehensible neural network explanations are foundations for a better understanding of decisions, especially when the input data are infused with malicious perturbations. Existing solutions generally mitigate the impact of perturbations…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular…
In matching theory, one of the most fundamental and classical branches of combinatorics, {\em canonical decompositions} of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known…
We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
In this paper we describe a heuristic for decomposing a directed graph into factors according to the direct product (also known as Kronecker, cardinal or tensor product). Given a directed, unweighted graph~$G$ with adjacency matrix…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…
A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by…
Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis…
Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…
A diagram $\mathcal{D} = (G, l)$ over a monoid $M$ is an oriented graph $G = (V, E)$ endowed with a labeling $l\colon E \to M$. A diagram is commutative if and only if for any two oriented paths with the same endpoints, the products in $M$…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…