2,664 research outputs found
Visual Similarity Perception of Directed Acyclic Graphs: A Study on Influencing Factors
While visual comparison of directed acyclic graphs (DAGs) is commonly
encountered in various disciplines (e.g., finance, biology), knowledge about
humans' perception of graph similarity is currently quite limited. By graph
similarity perception we mean how humans perceive commonalities and differences
in graphs and herewith come to a similarity judgment. As a step toward filling
this gap the study reported in this paper strives to identify factors which
influence the similarity perception of DAGs. In particular, we conducted a
card-sorting study employing a qualitative and quantitative analysis approach
to identify 1) groups of DAGs that are perceived as similar by the participants
and 2) the reasons behind their choice of groups. Our results suggest that
similarity is mainly influenced by the number of levels, the number of nodes on
a level, and the overall shape of the graph.Comment: Graph Drawing 2017 - arXiv Version; Keywords: Graphs, Perception,
Similarity, Comparison, Visualizatio
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
Ancestral Causal Inference
Constraint-based causal discovery from limited data is a notoriously
difficult challenge due to the many borderline independence test decisions.
Several approaches to improve the reliability of the predictions by exploiting
redundancy in the independence information have been proposed recently. Though
promising, existing approaches can still be greatly improved in terms of
accuracy and scalability. We present a novel method that reduces the
combinatorial explosion of the search space by using a more coarse-grained
representation of causal information, drastically reducing computation time.
Additionally, we propose a method to score causal predictions based on their
confidence. Crucially, our implementation also allows one to easily combine
observational and interventional data and to incorporate various types of
available background knowledge. We prove soundness and asymptotic consistency
of our method and demonstrate that it can outperform the state-of-the-art on
synthetic data, achieving a speedup of several orders of magnitude. We
illustrate its practical feasibility by applying it on a challenging protein
data set.Comment: In Proceedings of Advances in Neural Information Processing Systems
29 (NIPS 2016
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
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