1,786 research outputs found
Unsupervised relational inference using masked reconstruction
Problem setting: Stochastic dynamical systems in which local interactions give rise
to complex emerging phenomena are ubiquitous in nature and society. This work
explores the problem of inferring the unknown interaction structure (represented as
a graph) of such a system from measurements of its constituent agents or individual
components (represented as nodes). We consider a setting where the underlying
dynamical model is unknown and where diferent measurements (i.e., snapshots) may
be independent (e.g., may stem from diferent experiments).
Method: Our method is based on the observation that the temporal stochastic evolution manifests itself in local patterns. We show that we can exploit these patterns to
infer the underlying graph by formulating a masked reconstruction task. Therefore, we
propose GINA (Graph Inference Network Architecture), a machine learning approach
to simultaneously learn the latent interaction graph and, conditioned on the interaction graph, the prediction of the (masked) state of a node based only on adjacent
vertices. Our method is based on the hypothesis that the ground truth interaction
graph—among all other potential graphs—allows us to predict the state of a node,
given the states of its neighbors, with the highest accuracy.
Results: We test this hypothesis and demonstrate GINA’s efectiveness on a wide
range of interaction graphs and dynamical processes. We fnd that our paradigm allows
to reconstruct the ground truth interaction graph in many cases and that GINA outperforms statistical and machine learning baseline on independent snapshots as well
as on time series data
Information processing in biology
To survive, organisms must respond appropriately to a variety of challenges posed by a dynamic and uncertain environment. The mechanisms underlying such responses can in general be framed as input-output devices which map environment states (inputs) to associated responses (output. In this light, it is appealing to attempt to model these systems using information theory, a well developed mathematical framework to describe input-output systems.
Under the information theoretical perspective, an organism’s behavior is fully characterized by the repertoire of its outputs under different environmental conditions. Due to natural selection, it is reasonable to assume this input-output mapping has been fine tuned in such a way as to maximize the organism’s fitness. If that is the case, it should be possible to abstract away the mechanistic implementation details and obtain the general principles that lead to fitness under a certain environment. These can then be used inferentially to both generate hypotheses about the underlying implementation as well as predict novel responses under external perturbations.
In this work I use information theory to address the question of how biological systems generate complex outputs using relatively simple mechanisms in a robust manner. In particular, I will examine how communication and distributed processing can lead to emergent phenomena which allow collective systems to respond in a much richer way than a single organism could
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]
An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u
Complex and Adaptive Dynamical Systems: A Primer
An thorough introduction is given at an introductory level to the field of
quantitative complex system science, with special emphasis on emergence in
dynamical systems based on network topologies. Subjects treated include graph
theory and small-world networks, a generic introduction to the concepts of
dynamical system theory, random Boolean networks, cellular automata and
self-organized criticality, the statistical modeling of Darwinian evolution,
synchronization phenomena and an introduction to the theory of cognitive
systems.
It inludes chapter on Graph Theory and Small-World Networks, Chaos,
Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean
Networks, Cellular Automata and Self-Organized Criticality, Darwinian
evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements
of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer,
Complexity Series (2008, second edition 2010
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