37,678 research outputs found
A description of within-family resource exchange networks in a Malawian village
In this paper we explore patterns of economic transfers between adults within household and family networks in a village in Malawi’s Rumphi district, using data from the 2006 round of the Malawi Longitudinal Study of Families and Health. We fit Exponential-family Random Graph Models (ERGMs) to assess individual, relational, and higher-order network effects. The network effects of cyclic giving, reciprocity, and in-degree and out-degree distribution suggest a network with a tendency away from the formation of hierarchies or "hubs." Effects of age, sex, working status, education, health status, and kinship relation are also considered.Malawi, Malawi Longitudinal Study of Families and Health, networks, resource exchange, social network
Directed Network Laplacians and Random Graph Models
We consider spectral methods that uncover hidden structures in directed
networks. We develop a general framework that allows us to associate methods
based on optimization formulations with maximum likelihood problems on random
graphs. We focus on two existing spectral approaches that build and analyse
Laplacian-style matrices via the minimization of frustration and trophic
incoherence. These algorithms aim to reveal directed periodic and linear
hierarchies, respectively. We show that reordering nodes using the two
algorithms, or mapping them onto a specified lattice, is associated with new
classes of directed random graph models. Using this random graph setting, we
are able to compare the two algorithms on a given network and quantify which
structure is more likely to be present. We illustrate the approach on synthetic
and real networks, and discuss practical implementation issues
GRASS: Generative Recursive Autoencoders for Shape Structures
We introduce a novel neural network architecture for encoding and synthesis
of 3D shapes, particularly their structures. Our key insight is that 3D shapes
are effectively characterized by their hierarchical organization of parts,
which reflects fundamental intra-shape relationships such as adjacency and
symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a
flat, unlabeled, arbitrary part layout to a compact code. The code effectively
captures hierarchical structures of man-made 3D objects of varying structural
complexities despite being fixed-dimensional: an associated decoder maps a code
back to a full hierarchy. The learned bidirectional mapping is further tuned
using an adversarial setup to yield a generative model of plausible structures,
from which novel structures can be sampled. Finally, our structure synthesis
framework is augmented by a second trained module that produces fine-grained
part geometry, conditioned on global and local structural context, leading to a
full generative pipeline for 3D shapes. We demonstrate that without
supervision, our network learns meaningful structural hierarchies adhering to
perceptual grouping principles, produces compact codes which enable
applications such as shape classification and partial matching, and supports
shape synthesis and interpolation with significant variations in topology and
geometry.Comment: Corresponding author: Kai Xu ([email protected]
Structural Inference of Hierarchies in Networks
One property of networks that has received comparatively little attention is
hierarchy, i.e., the property of having vertices that cluster together in
groups, which then join to form groups of groups, and so forth, up through all
levels of organization in the network. Here, we give a precise definition of
hierarchical structure, give a generic model for generating arbitrary
hierarchical structure in a random graph, and describe a statistically
principled way to learn the set of hierarchical features that most plausibly
explain a particular real-world network. By applying this approach to two
example networks, we demonstrate its advantages for the interpretation of
network data, the annotation of graphs with edge, vertex and community
properties, and the generation of generic null models for further hypothesis
testing.Comment: 8 pages, 8 figure
A sharper threshold for bootstrap percolation in two dimensions
Two-dimensional bootstrap percolation is a cellular automaton in which sites
become 'infected' by contact with two or more already infected nearest
neighbors. We consider these dynamics, which can be interpreted as a monotone
version of the Ising model, on an n x n square, with sites initially infected
independently with probability p. The critical probability p_c is the smallest
p for which the probability that the entire square is eventually infected
exceeds 1/2. Holroyd determined the sharp first-order approximation: p_c \sim
\pi^2/(18 log n) as n \to \infty. Here we sharpen this result, proving that the
second term in the expansion is -(log n)^{-3/2+ o(1)}, and moreover determining
it up to a poly(log log n)-factor. The exponent -3/2 corrects numerical
predictions from the physics literature.Comment: 21 page
Graph-Sparse LDA: A Topic Model with Structured Sparsity
Originally designed to model text, topic modeling has become a powerful tool
for uncovering latent structure in domains including medicine, finance, and
vision. The goals for the model vary depending on the application: in some
cases, the discovered topics may be used for prediction or some other
downstream task. In other cases, the content of the topic itself may be of
intrinsic scientific interest.
Unfortunately, even using modern sparse techniques, the discovered topics are
often difficult to interpret due to the high dimensionality of the underlying
space. To improve topic interpretability, we introduce Graph-Sparse LDA, a
hierarchical topic model that leverages knowledge of relationships between
words (e.g., as encoded by an ontology). In our model, topics are summarized by
a few latent concept-words from the underlying graph that explain the observed
words. Graph-Sparse LDA recovers sparse, interpretable summaries on two
real-world biomedical datasets while matching state-of-the-art prediction
performance
- …