27,174 research outputs found
Evolutionary dynamics on any population structure
Evolution occurs in populations of reproducing individuals. The structure of
a biological population affects which traits evolve. Understanding evolutionary
game dynamics in structured populations is difficult. Precise results have been
absent for a long time, but have recently emerged for special structures where
all individuals have the same number of neighbors. But the problem of
determining which trait is favored by selection in the natural case where the
number of neighbors can vary, has remained open. For arbitrary selection
intensity, the problem is in a computational complexity class which suggests
there is no efficient algorithm. Whether there exists a simple solution for
weak selection was unanswered. Here we provide, surprisingly, a general formula
for weak selection that applies to any graph or social network. Our method uses
coalescent theory and relies on calculating the meeting times of random walks.
We can now evaluate large numbers of diverse and heterogeneous population
structures for their propensity to favor cooperation. We can also study how
small changes in population structure---graph surgery---affect evolutionary
outcomes. We find that cooperation flourishes most in societies that are based
on strong pairwise ties.Comment: 68 pages, 10 figure
High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
We consider the problem of high-dimensional Gaussian graphical model
selection. We identify a set of graphs for which an efficient estimation
algorithm exists, and this algorithm is based on thresholding of empirical
conditional covariances. Under a set of transparent conditions, we establish
structural consistency (or sparsistency) for the proposed algorithm, when the
number of samples n=omega(J_{min}^{-2} log p), where p is the number of
variables and J_{min} is the minimum (absolute) edge potential of the graphical
model. The sufficient conditions for sparsistency are based on the notion of
walk-summability of the model and the presence of sparse local vertex
separators in the underlying graph. We also derive novel non-asymptotic
necessary conditions on the number of samples required for sparsistency
A Statistical Mechanical Load Balancer for the Web
The maximum entropy principle from statistical mechanics states that a closed
system attains an equilibrium distribution that maximizes its entropy. We first
show that for graphs with fixed number of edges one can define a stochastic
edge dynamic that can serve as an effective thermalization scheme, and hence,
the underlying graphs are expected to attain their maximum-entropy states,
which turn out to be Erdos-Renyi (ER) random graphs. We next show that (i) a
rate-equation based analysis of node degree distribution does indeed confirm
the maximum-entropy principle, and (ii) the edge dynamic can be effectively
implemented using short random walks on the underlying graphs, leading to a
local algorithm for the generation of ER random graphs. The resulting
statistical mechanical system can be adapted to provide a distributed and local
(i.e., without any centralized monitoring) mechanism for load balancing, which
can have a significant impact in increasing the efficiency and utilization of
both the Internet (e.g., efficient web mirroring), and large-scale computing
infrastructure (e.g., cluster and grid computing).Comment: 11 Pages, 5 Postscript figures; added references, expanded on
protocol discussio
Representation Learning on Graphs: A Reinforcement Learning Application
In this work, we study value function approximation in reinforcement learning
(RL) problems with high dimensional state or action spaces via a generalized
version of representation policy iteration (RPI). We consider the limitations
of proto-value functions (PVFs) at accurately approximating the value function
in low dimensions and we highlight the importance of features learning for an
improved low-dimensional value function approximation. Then, we adopt different
representation learning algorithm on graphs to learn the basis functions that
best represent the value function. We empirically show that node2vec, an
algorithm for scalable feature learning in networks, and the Variational Graph
Auto-Encoder constantly outperform the commonly used smooth proto-value
functions in low-dimensional feature space
Equilibria in the Tangle
We analyse the Tangle --- a DAG-valued stochastic process where new vertices
get attached to the graph at Poissonian times, and the attachment's locations
are chosen by means of random walks on that graph. These new vertices, also
thought of as "transactions", are issued by many players (which are the nodes
of the network), independently. The main application of this model is that it
is used as a base for the IOTA cryptocurrency system (www.iota.org). We prove
existence of "almost symmetric" Nash equilibria for the system where a part of
players tries to optimize their attachment strategies. Then, we also present
simulations that show that the "selfish" players will nevertheless cooperate
with the network by choosing attachment strategies that are similar to the
"recommended" one.Comment: 33 pages, 11 figure
Benchmarking Network Embedding Models for Link Prediction: Are We Making Progress?
Network embedding methods map a network's nodes to vectors in an embedding
space, in such a way that these representations are useful for estimating some
notion of similarity or proximity between pairs of nodes in the network. The
quality of these node representations is then showcased through results of
downstream prediction tasks. Commonly used benchmark tasks such as link
prediction, however, present complex evaluation pipelines and an abundance of
design choices. This, together with a lack of standardized evaluation setups
can obscure the real progress in the field. In this paper, we aim to shed light
on the state-of-the-art of network embedding methods for link prediction and
show, using a consistent evaluation pipeline, that only thin progress has been
made over the last years. The newly conducted benchmark that we present here,
including 17 embedding methods, also shows that many approaches are
outperformed even by simple heuristics. Finally, we argue that standardized
evaluation tools can repair this situation and boost future progress in this
field
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