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Compiling Bayesian networks (BNs) to junction trees and performing belief propagation over them is among the most prominent approaches to computing posteriors in BNs. However, belief propagation over junction tree is known to be…
Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in…
Bayesian networks are probabilistic graphical models often used in big data analytics. The problem of exact structure learning is to find a network structure that is optimal under certain scoring criteria. The problem is known to be NP-hard…
This paper identifies and solves a new optimization problem: Given a belief network (BN) and a target ordering on its variables, how can we efficiently derive its minimal I-map whose arcs are consistent with the target ordering? We present…
In this paper, we introduce tiled graphs as models of learning and maturing processes. We show how tiled graphs can combine graphs of learning spaces or antimatroids (partial hypercubes) and maturity models (total orders) to yield models of…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social…
This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is…
Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles.…
This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a…
The perfect phylogeny problem is a classic problem in computational biology, where we seek an unrooted phylogeny that is compatible with a set of qualitative characters. Such a tree exists precisely when an intersection graph associated…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
In social networks the {\sc Strong Triadic Closure} is an assignment of the edges with strong or weak labels such that any two vertices that have a common neighbor with a strong edge are adjacent. The problem of maximizing the number of…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
The paper deals with optimality issues in connection with updating beliefs in networks. We address two processes: triangulation and construction of junction trees. In the first part, we give a simple algorithm for constructing an optimal…
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…
Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…