Related papers: Using Tree-Decomposable Structures to Approximate …
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
A tree decomposition of a graph facilitates computations by grouping vertices into bags that are interconnected in an acyclic structure, hence their importance in a plethora of problems such as query evaluation over databases and inference…
In this paper, optimum decomposition of belief networks is discussed. Some methods of decomposition are examined and a new method - the method of Minimum Total Number of States (MTNS) - is proposed. The problem of optimum belief network…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
In this paper, we consider the problem of distributed inference in tree based networks. In the framework considered in this paper, distributed nodes make a 1-bit local decision regarding a phenomenon before sending it to the fusion center…
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…
Tree projections provide a mathematical framework that encompasses all the various (purely) structural decomposition methods that have been proposed in the literature to single out classes of nearly-acyclic (hyper)graphs, such as the tree…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Application of the turbo principle to multiuser decoding results in an exchange of probability distributions between two sets of constraints. Firstly, constraints imposed by the multiple-access channel, and secondly, individual constraints…
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, "end of minimal chain" and "parent of maximum leaf" a true Tree Calculus is being developed to solve a partial difference equation system and…
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification…
This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as…
`Tree pruning' (TP) is an algorithm for probabilistic inference on binary Markov random fields. It has been recently derived by Dror Weitz and used to construct the first fully polynomial approximation scheme for counting independent sets…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…