8,718 research outputs found
Network Inference with Hidden Units
We derive learning rules for finding the connections between units in
stochastic dynamical networks from the recorded history of a ``visible'' subset
of the units. We consider two models. In both of them, the visible units are
binary and stochastic. In one model the ``hidden'' units are continuous-valued,
with sigmoidal activation functions, and in the other they are binary and
stochastic like the visible ones. We derive exact learning rules for both
cases. For the stochastic case, performing the exact calculation requires, in
general, repeated summations over an number of configurations that grows
exponentially with the size of the system and the data length, which is not
feasible for large systems. We derive a mean field theory, based on a
factorized ansatz for the distribution of hidden-unit states, which offers an
attractive alternative for large systems. We present the results of some
numerical calculations that illustrate key features of the two models and, for
the stochastic case, the exact and approximate calculations
Network Inference from Consensus Dynamics
We consider the problem of identifying the topology of a weighted, undirected
network from observing snapshots of multiple independent consensus
dynamics. Specifically, we observe the opinion profiles of a group of agents
for a set of independent topics and our goal is to recover the precise
relationships between the agents, as specified by the unknown network . In order to overcome the under-determinacy of the problem at hand, we
leverage concepts from spectral graph theory and convex optimization to unveil
the underlying network structure. More precisely, we formulate the network
inference problem as a convex optimization that seeks to endow the network with
certain desired properties -- such as sparsity -- while being consistent with
the spectral information extracted from the observed opinions. This is
complemented with theoretical results proving consistency as the number of
topics grows large. We further illustrate our method by numerical experiments,
which showcase the effectiveness of the technique in recovering synthetic and
real-world networks.Comment: Will be presented at the 2017 IEEE Conference on Decision and Control
(CDC
Network Inference from Co-Occurrences
The recovery of network structure from experimental data is a basic and
fundamental problem. Unfortunately, experimental data often do not directly
reveal structure due to inherent limitations such as imprecision in timing or
other observation mechanisms. We consider the problem of inferring network
structure in the form of a directed graph from co-occurrence observations. Each
observation arises from a transmission made over the network and indicates
which vertices carry the transmission without explicitly conveying their order
in the path. Without order information, there are an exponential number of
feasible graphs which agree with the observed data equally well. Yet, the basic
physical principles underlying most networks strongly suggest that all feasible
graphs are not equally likely. In particular, vertices that co-occur in many
observations are probably closely connected. Previous approaches to this
problem are based on ad hoc heuristics. We model the experimental observations
as independent realizations of a random walk on the underlying graph, subjected
to a random permutation which accounts for the lack of order information.
Treating the permutations as missing data, we derive an exact
expectation-maximization (EM) algorithm for estimating the random walk
parameters. For long transmission paths the exact E-step may be computationally
intractable, so we also describe an efficient Monte Carlo EM (MCEM) algorithm
and derive conditions which ensure convergence of the MCEM algorithm with high
probability. Simulations and experiments with Internet measurements demonstrate
the promise of this approach.Comment: Submitted to IEEE Transactions on Information Theory. An extended
version is available as University of Wisconsin Technical Report ECE-06-
Gene-network inference by message passing
The inference of gene-regulatory processes from gene-expression data belongs
to the major challenges of computational systems biology. Here we address the
problem from a statistical-physics perspective and develop a message-passing
algorithm which is able to infer sparse, directed and combinatorial regulatory
mechanisms. Using the replica technique, the algorithmic performance can be
characterized analytically for artificially generated data. The algorithm is
applied to genome-wide expression data of baker's yeast under various
environmental conditions. We find clear cases of combinatorial control, and
enrichment in common functional annotations of regulated genes and their
regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics
2007, Kyot
Gene-network inference by message passing
The inference of gene-regulatory processes from gene-expression data belongs
to the major challenges of computational systems biology. Here we address the
problem from a statistical-physics perspective and develop a message-passing
algorithm which is able to infer sparse, directed and combinatorial regulatory
mechanisms. Using the replica technique, the algorithmic performance can be
characterized analytically for artificially generated data. The algorithm is
applied to genome-wide expression data of baker's yeast under various
environmental conditions. We find clear cases of combinatorial control, and
enrichment in common functional annotations of regulated genes and their
regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics
2007, Kyot
Gene-network inference by message passing
The inference of gene-regulatory processes from gene-expression data belongs
to the major challenges of computational systems biology. Here we address the
problem from a statistical-physics perspective and develop a message-passing
algorithm which is able to infer sparse, directed and combinatorial regulatory
mechanisms. Using the replica technique, the algorithmic performance can be
characterized analytically for artificially generated data. The algorithm is
applied to genome-wide expression data of baker's yeast under various
environmental conditions. We find clear cases of combinatorial control, and
enrichment in common functional annotations of regulated genes and their
regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics
2007, Kyot
Modeling Information Propagation with Survival Theory
Networks provide a skeleton for the spread of contagions, like, information,
ideas, behaviors and diseases. Many times networks over which contagions
diffuse are unobserved and need to be inferred. Here we apply survival theory
to develop general additive and multiplicative risk models under which the
network inference problems can be solved efficiently by exploiting their
convexity. Our additive risk model generalizes several existing network
inference models. We show all these models are particular cases of our more
general model. Our multiplicative model allows for modeling scenarios in which
a node can either increase or decrease the risk of activation of another node,
in contrast with previous approaches, which consider only positive risk
increments. We evaluate the performance of our network inference algorithms on
large synthetic and real cascade datasets, and show that our models are able to
predict the length and duration of cascades in real data.Comment: To appear at ICML '1
Impact of lag information on network inference
Extracting useful information from data is a fundamental challenge across
disciplines as diverse as climate, neuroscience, genetics, and ecology. In the
era of ``big data'', data is ubiquitous, but appropriated methods are needed
for gaining reliable information from the data. In this work we consider a
complex system, composed by interacting units, and aim at inferring which
elements influence each other, directly from the observed data. The only
assumption about the structure of the system is that it can be modeled by a
network composed by a set of units connected with un-weighted and
un-directed links, however, the structure of the connections is not known. In
this situation the inference of the underlying network is usually done by using
interdependency measures, computed from the output signals of the units. We
show, using experimental data recorded from randomly coupled electronic
R{\"o}ssler chaotic oscillators, that the information of the lag times obtained
from bivariate cross-correlation analysis can be useful to gain information
about the real connectivity of the system
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