273 research outputs found
Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles
While feedback loops are known to play important roles in many complex
systems, their existence is ignored in a large part of the causal discovery
literature, as systems are typically assumed to be acyclic from the outset.
When applying causal discovery algorithms designed for the acyclic setting on
data generated by a system that involves feedback, one would not expect to
obtain correct results. In this work, we show that---surprisingly---the output
of the Fast Causal Inference (FCI) algorithm is correct if it is applied to
observational data generated by a system that involves feedback. More
specifically, we prove that for observational data generated by a simple and
-faithful Structural Causal Model (SCM), FCI is sound and complete, and
can be used to consistently estimate (i) the presence and absence of causal
relations, (ii) the presence and absence of direct causal relations, (iii) the
absence of confounders, and (iv) the absence of specific cycles in the causal
graph of the SCM. We extend these results to constraint-based causal discovery
algorithms that exploit certain forms of background knowledge, including the
causally sufficient setting (e.g., the PC algorithm) and the Joint Causal
Inference setting (e.g., the FCI-JCI algorithm).Comment: Major revision. To appear in Proceedings of the 36 th Conference on
Uncertainty in Artificial Intelligence (UAI), PMLR volume 124, 202
Parameterized Approximation Algorithms for Bidirected Steiner Network Problems
The Directed Steiner Network (DSN) problem takes as input a directed
edge-weighted graph and a set of
demand pairs. The aim is to compute the cheapest network for
which there is an path for each . It is known
that this problem is notoriously hard as there is no
-approximation algorithm under Gap-ETH, even when parametrizing
the runtime by [Dinur & Manurangsi, ITCS 2018]. In light of this, we
systematically study several special cases of DSN and determine their
parameterized approximability for the parameter .
For the bi-DSN problem, the aim is to compute a planar
optimum solution in a bidirected graph , i.e., for every edge
of the reverse edge exists and has the same weight. This problem
is a generalization of several well-studied special cases. Our main result is
that this problem admits a parameterized approximation scheme (PAS) for . We
also prove that our result is tight in the sense that (a) the runtime of our
PAS cannot be significantly improved, and (b) it is unlikely that a PAS exists
for any generalization of bi-DSN, unless FPT=W[1].
One important special case of DSN is the Strongly Connected Steiner Subgraph
(SCSS) problem, for which the solution network needs to strongly
connect a given set of terminals. It has been observed before that for SCSS
a parameterized -approximation exists when parameterized by [Chitnis et
al., IPEC 2013]. We give a tight inapproximability result by showing that for
no parameterized -approximation algorithm exists under
Gap-ETH. Additionally we show that when restricting the input of SCSS to
bidirected graphs, the problem remains NP-hard but becomes FPT for
Markov Properties for Graphical Models with Cycles and Latent Variables
We investigate probabilistic graphical models that allow for both cycles and
latent variables. For this we introduce directed graphs with hyperedges
(HEDGes), generalizing and combining both marginalized directed acyclic graphs
(mDAGs) that can model latent (dependent) variables, and directed mixed graphs
(DMGs) that can model cycles. We define and analyse several different Markov
properties that relate the graphical structure of a HEDG with a probability
distribution on a corresponding product space over the set of nodes, for
example factorization properties, structural equations properties,
ordered/local/global Markov properties, and marginal versions of these. The
various Markov properties for HEDGes are in general not equivalent to each
other when cycles or hyperedges are present, in contrast with the simpler case
of directed acyclic graphical (DAG) models (also known as Bayesian networks).
We show how the Markov properties for HEDGes - and thus the corresponding
graphical Markov models - are logically related to each other.Comment: 131 page
Impact of network structure on the capacity of wireless multihop ad hoc communication
As a representative of a complex technological system, so-called wireless
multihop ad hoc communication networks are discussed. They represent an
infrastructure-less generalization of todays wireless cellular phone networks.
Lacking a central control authority, the ad hoc nodes have to coordinate
themselves such that the overall network performs in an optimal way. A
performance indicator is the end-to-end throughput capacity.
Various models, generating differing ad hoc network structure via differing
transmission power assignments, are constructed and characterized. They serve
as input for a generic data traffic simulation as well as some semi-analytic
estimations. The latter reveal that due to the most-critical-node effect the
end-to-end throughput capacity sensitively depends on the underlying network
structure, resulting in differing scaling laws with respect to network size.Comment: 30 pages, to be published in Physica
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