Related papers: Complexity of Inference in Graphical Models
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and…
A drawing of a graph is 1-planar if each edge participates in at most one crossing and adjacent edges do not cross. Up to symmetry, each crossing in a 1-planar drawing belongs to one out of six possible crossing types, where a type…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
We give an analog of the Myhill-Nerode methods from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems: * We provide an algorithm for testing whether a hypergraph has…
A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the `usual suspects'. Our results imply…
Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth,…
We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities. Credal networks are here interpreted as encoding strong independence relations among variables. We first present a…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
In a decision problem, observations are said to be material if they must be taken into account to perform optimally. Decision problems have an underlying (graphical) causal structure, which may sometimes be used to evaluate certain…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call $(\mathrm{tw},\omega)$-bounded. While $(\mathrm{tw},\omega)$-bounded graph classes are…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
Tree ensemble models like random forests and gradient boosting machines are widely used in machine learning due to their excellent predictive performance. However, a high-performance ensemble consisting of a large number of decision trees…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
We prove that finding a $k$-edge induced subgraph is fixed-parameter tractable, thereby answering an open problem of Leizhen Cai. Our algorithm is based on several combinatorial observations, Gauss' famous \emph{Eureka} theorem [Andrews,…
For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two…
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph…
Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a graphical model in order to define a new code.…
The Pathwidth Theorem states that if a class of graphs has unbounded pathwidth, then it contains all trees as graph minors. We prove a similar result for dense graphs. More precisely, we give a finite family of tree-like patterns and prove…