Directed acyclic graphs with edge-specific bounds

Directed acyclic graphs with edge-specific bounds.

We give a definition of a bounded edge within the causal directed acyclic graph framework. A bounded edge generalizes the notion of a signed edge and is defined in terms of bounds on a ratio of survivor probabilities. We derive rules concerning the propagation of bounds. Bounds on causal effects in the presence of unmeasured confounding are also derived using bounds related to specific edges on...

Edge Weight Reduction Problems in Directed Acyclic Graphs

Let G be a weighted, direr.ted, acyclic graph in which each edge weight. is not a staticquantity, but can be reduced for a certain cost. In this paper we consider the problem of determining which edg('s to reduce so that the length of the longest paths is minimized and the total cost associated with the reductions does not exceed a given cost. We consider two type-s of edge reductions, linear r...

Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs

Given a graph and pairs siti of terminals, the edge-disjoint paths problem is to determine whether there exist siti paths that do not share any edges. We consider this problem on acyclic digraphs. It is known to be NP-complete and solvable in time n where k is the number of paths. It has been a long-standing open question whether it is fixed-parameter tractable in k. We resolve this question in...

Generic Directed Acyclic Graphs

Copula directed acyclic graphs

We present a new methodology for selecting a Bayesian network for continuous data outside the widely used class of multivariate normal distributions. The use of bivariate copula densities to model connections between pairs of nodes in the network brings in flexibility in the choice of the distribution. Cand D-vines play a central role in dealing with the high-dimensional aspect of the data, due...