Related papers: Bounding Search Space Size via (Hyper)tree Decompo…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
We present a new branch-and-bound type search method for mixed integer linear optimization problems based on the concept of offshoots (introduced in this paper). While similar to a classic branch-and-bound method, it allows for changing the…
Hypertree decompositions provide a way to evaluate Conjunctive Queries (CQs) in polynomial time, where the exponent of this polynomial is determined by the width of the decomposition. In theory, the goal of efficient CQ evaluation therefore…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
We study the tractability of conjunctive query answering for queries with unbounded arity. It is well known that tractability of the problem can be characterised in terms of the queries treewidth under the assumption of bounded arity. We…
The paper evaluates the power of best-first search over AND/OR search spaces for solving the Most Probable Explanation (MPE) task in Bayesian networks. The main virtue of the AND/OR representation of the search space is its sensitivity to…
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…
Several novel frameworks for hyperparameter search have emerged in the last decade, but most rely on strict, often normal, distributional assumptions, limiting search model flexibility. This paper proposes a novel optimization framework…
Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require $\Omega(2^{n})$ expansions, where $n$ is the number of states within the final $f$ bound. Existing algorithms…
In recent years, to improve the evolutionary algorithms used to solve optimization problems involving a large number of decision variables, many attempts have been made to simplify the problem solution space of a given problem for the…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
In recent years, deep neural networks have had great success in machine learning and pattern recognition. Architecture size for a neural network contributes significantly to the success of any neural network. In this study, we optimize the…
Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…