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Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…
Markov networks and Bayesian networks are effective graphic representations of the dependencies embedded in probabilistic models. It is well known that independencies captured by Markov networks (called graph-isomorphs) have a finite…
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete…
In this paper, we extend Meek's conjecture (Meek 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the…
We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search…
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…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
This paper studies the problem of detecting anomalous graphs using a machine learning model trained on only normal graphs, which has many applications in molecule, biology, and social network data analysis. We present a self-discriminative…
Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution {induced} by a structural causal model, and additional data from (in the best case) \textit{only…
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…
We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded…
We present a new approach for recognition of complex graphic symbols in technical documents. Graphic symbol recognition is a well known challenge in the field of document image analysis and is at heart of most graphic recognition systems.…
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. We say that a graph $G$ is $d$-distinguishing critical, if…
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of…
Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a…
Max-linear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…
We introduce a new graph polynomial that encodes interesting properties of graphs, for example, the number of matchings and the number of perfect matchings. Most importantly, for bipartite graphs the polynomial encodes the number of…