Related papers: A Factor-Graph Formulation of CSS Syndrome Decodin…
In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erd\H{o}s-R\'enyi (ER) graph embedded in a larger and sparser ER graph, in the presence of…
In the context of solving large distributed constraint optimization problems (DCOP), belief-propagation and approximate inference algorithms are candidates of choice. However, in general, when the factor graph is very loopy (i.e. cyclic),…
We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on $n$ nodes, having i.i.d. weights $(\phi_u)_{u=1}^n$ (possibly heavy-tailed), partitioned into $q \geq 2$ asymptotically equal-sized clusters. The model…
Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series $\psi(x, y, z; t, 1+\beta)$ that might be interpreted as a continuous deformation of the generating series of rooted hypermaps. They…
We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local…
Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
The name graph state is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the…
A \emph{palindrome} is a word that reads the same forwards and backwards. A \emph{block palindrome factorization} (or \emph{BP-factorization}) is a factorization of a word into blocks that becomes palindrome if each identical block is…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
In this manuscript a factor graph approach is employed to investigate the recursive filtering problem for a mixed linear/nonlinear state-space model, i.e. for a model whose state vector can be partitioned in a linear state variable…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
We describe a method for parameter estimation in bipartite probabilistic graphical models for joint prediction of clinical conditions from the electronic medical record. The method does not rely on the availability of gold-standard labels,…
Bibliographic coupling (BC) and co-citation (CC) are the two most common citation-based coupling measures of similarity between scientific items. One can interpret these measures as second-neighbor relations distinguished by the direction…
Simulation-based calibration checking (SBC) is a practical method to validate computationally-derived posterior distributions or their approximations. In this paper, we introduce a new variant of SBC to alleviate several known problems. Our…
We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…
We address the problem of partitioning a vertex-weighted connected graph into $k$ connected subgraphs that have similar weights, for a fixed integer $k\geq 2$. This problem, known as the \emph{balanced connected $k$-partition problem}…
Product constructions constitute a powerful method for generating quantum CSS codes, yielding celebrated examples such as toric codes and asymptotically good low-density parity check (LDPC) codes. Since a CSS code is fully described by a…
Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…
The framework of statistical inference has been successfully used to detect the meso-scale structures in complex networks, such as community structure, core-periphery (CP) structure. The main principle is that the stochastic block model…