4,620 research outputs found
Gravity-Inspired Graph Autoencoders for Directed Link Prediction
Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged
as powerful node embedding methods. In particular, graph AE and VAE were
successfully leveraged to tackle the challenging link prediction problem,
aiming at figuring out whether some pairs of nodes from a graph are connected
by unobserved edges. However, these models focus on undirected graphs and
therefore ignore the potential direction of the link, which is limiting for
numerous real-life applications. In this paper, we extend the graph AE and VAE
frameworks to address link prediction in directed graphs. We present a new
gravity-inspired decoder scheme that can effectively reconstruct directed
graphs from a node embedding. We empirically evaluate our method on three
different directed link prediction tasks, for which standard graph AE and VAE
perform poorly. We achieve competitive results on three real-world graphs,
outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management
(CIKM 2019
Clustering in Complex Directed Networks
Many empirical networks display an inherent tendency to cluster, i.e. to form
circles of connected nodes. This feature is typically measured by the
clustering coefficient (CC). The CC, originally introduced for binary,
undirected graphs, has been recently generalized to weighted, undirected
networks. Here we extend the CC to the case of (binary and weighted) directed
networks and we compute its expected value for random graphs. We distinguish
between CCs that count all directed triangles in the graph (independently of
the direction of their edges) and CCs that only consider particular types of
directed triangles (e.g., cycles). The main concepts are illustrated by
employing empirical data on world-trade flows
Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses
We investigate the relationship between the structure of a discrete graphical
model and the support of the inverse of a generalized covariance matrix. We
show that for certain graph structures, the support of the inverse covariance
matrix of indicator variables on the vertices of a graph reflects the
conditional independence structure of the graph. Our work extends results that
have previously been established only in the context of multivariate Gaussian
graphical models, thereby addressing an open question about the significance of
the inverse covariance matrix of a non-Gaussian distribution. The proof
exploits a combination of ideas from the geometry of exponential families,
junction tree theory and convex analysis. These population-level results have
various consequences for graph selection methods, both known and novel,
including a novel method for structure estimation for missing or corrupted
observations. We provide nonasymptotic guarantees for such methods and
illustrate the sharpness of these predictions via simulations.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1162 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
A challenging problem in estimating high-dimensional graphical models is to
choose the regularization parameter in a data-dependent way. The standard
techniques include -fold cross-validation (-CV), Akaike information
criterion (AIC), and Bayesian information criterion (BIC). Though these methods
work well for low-dimensional problems, they are not suitable in high
dimensional settings. In this paper, we present StARS: a new stability-based
method for choosing the regularization parameter in high dimensional inference
for undirected graphs. The method has a clear interpretation: we use the least
amount of regularization that simultaneously makes a graph sparse and
replicable under random sampling. This interpretation requires essentially no
conditions. Under mild conditions, we show that StARS is partially sparsistent
in terms of graph estimation: i.e. with high probability, all the true edges
will be included in the selected model even when the graph size diverges with
the sample size. Empirically, the performance of StARS is compared with the
state-of-the-art model selection procedures, including -CV, AIC, and BIC, on
both synthetic data and a real microarray dataset. StARS outperforms all these
competing procedures
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