Related papers: Positive definite completion problems for directed…
Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to…
The \textsc{Degree Realization} problem with respect to a graph family $\mathcal{F}$ is defined as follows. The input is a sequence $d$ of $n$ positive integers, and the goal is to decide whether there exists a graph $G \in \mathcal{F}$…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
We study the following fundamental realization problem of directed acyclic graphs (dags). Given a sequence S:=(a_1,b_1),...,(a_n, b_n) with a_i, b_i in Z_0^+, does there exist a dag (no parallel arcs allowed) with labeled vertex set V:=…
A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…
We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…
We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological…
We give a signed generalization of Laurent's theorem that characterizes feasible positive semidefinite matrix completion problems in terms of metric polytopes. Based on this result, we give a characterization of the maximum rank completions…
In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…
This work addresses the NP-Hard problem of acyclic directed acyclic graph (DAG) partitioning problem. The acyclic partitioning problem is defined as partitioning the vertex set of a given directed acyclic graph into disjoint and…
Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge,…
In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…
Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample…
We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses randomization. But, it returns the correct answer with high…
Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…
A real symmetric matrix $A$ is said to be completely positive if it can be written as $BB^t$ for some (not necessarily square) nonnegative matrix $B$. A simple graph $G$ is called a completely positive graph if every doubly nonnegative…
A polynomial-time exact algorithm for counting the number of directed acyclic graphs in a Markov equivalence class was recently given by Wien\"obst, Bannach, and Li\'skiewicz (AAAI 2021). In this paper, we consider the more general problem…
We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do…
The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…