Related papers: Complexity of Inference in Graphical Models
We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…
We consider a robust analog of the planted clique problem. In this analog, a set $S$ of vertices is chosen and all edges in $S$ are included; then, edges between $S$ and the rest of the graph are included with probability $\frac{1}{2}$,…
Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such…
The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs…
We prove that the tree-width of graphs in a hereditary class defined by a finite set $F$ of forbidden induced subgraphs is bounded if and only if $F$ includes a complete graph, a complete bipartite graph, a tripod (a forest in which every…
In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free…
We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
The complexity of the problem of deciding properties expressible in FO logic on graphs -- the FO model checking problem (parameterized by the respective FO formula), is well-understood on so-called sparse graph classes, but much less…
The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability…
Tree-shaped graphical models are widely used for their tractability. However, they unfortunately lack expressive power as they require committing to a particular sparse dependency structure. We propose a novel class of generative models…
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…