104,213 research outputs found
Ising Models for Inferring Network Structure From Spike Data
Now that spike trains from many neurons can be recorded simultaneously, there
is a need for methods to decode these data to learn about the networks that
these neurons are part of. One approach to this problem is to adjust the
parameters of a simple model network to make its spike trains resemble the data
as much as possible. The connections in the model network can then give us an
idea of how the real neurons that generated the data are connected and how they
influence each other. In this chapter we describe how to do this for the
simplest kind of model: an Ising network. We derive algorithms for finding the
best model connection strengths for fitting a given data set, as well as faster
approximate algorithms based on mean field theory. We test the performance of
these algorithms on data from model networks and experiments.Comment: To appear in "Principles of Neural Coding", edited by Stefano Panzeri
and Rodrigo Quian Quirog
Combining Bayesian Approaches and Evolutionary Techniques for the Inference of Breast Cancer Networks
Gene and protein networks are very important to model complex large-scale
systems in molecular biology. Inferring or reverseengineering such networks can
be defined as the process of identifying gene/protein interactions from
experimental data through computational analysis. However, this task is
typically complicated by the enormously large scale of the unknowns in a rather
small sample size. Furthermore, when the goal is to study causal relationships
within the network, tools capable of overcoming the limitations of correlation
networks are required. In this work, we make use of Bayesian Graphical Models
to attach this problem and, specifically, we perform a comparative study of
different state-of-the-art heuristics, analyzing their performance in inferring
the structure of the Bayesian Network from breast cancer data
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
On the Convexity of Latent Social Network Inference
In many real-world scenarios, it is nearly impossible to collect explicit
social network data. In such cases, whole networks must be inferred from
underlying observations. Here, we formulate the problem of inferring latent
social networks based on network diffusion or disease propagation data. We
consider contagions propagating over the edges of an unobserved social network,
where we only observe the times when nodes became infected, but not who
infected them. Given such node infection times, we then identify the optimal
network that best explains the observed data. We present a maximum likelihood
approach based on convex programming with a l1-like penalty term that
encourages sparsity. Experiments on real and synthetic data reveal that our
method near-perfectly recovers the underlying network structure as well as the
parameters of the contagion propagation model. Moreover, our approach scales
well as it can infer optimal networks of thousands of nodes in a matter of
minutes.Comment: NIPS, 201
Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm
Information spreads across social and technological networks, but often the
network structures are hidden from us and we only observe the traces left by
the diffusion processes, called cascades. Can we recover the hidden network
structures from these observed cascades? What kind of cascades and how many
cascades do we need? Are there some network structures which are more difficult
than others to recover? Can we design efficient inference algorithms with
provable guarantees?
Despite the increasing availability of cascade data and methods for inferring
networks from these data, a thorough theoretical understanding of the above
questions remains largely unexplored in the literature. In this paper, we
investigate the network structure inference problem for a general family of
continuous-time diffusion models using an -regularized likelihood
maximization framework. We show that, as long as the cascade sampling process
satisfies a natural incoherence condition, our framework can recover the
correct network structure with high probability if we observe
cascades, where is the maximum number of parents of a node and is the
total number of nodes. Moreover, we develop a simple and efficient
soft-thresholding inference algorithm, which we use to illustrate the
consequences of our theoretical results, and show that our framework
outperforms other alternatives in practice.Comment: To appear in the 31st International Conference on Machine Learning
(ICML), 201
Learning to Discover Sparse Graphical Models
We consider structure discovery of undirected graphical models from
observational data. Inferring likely structures from few examples is a complex
task often requiring the formulation of priors and sophisticated inference
procedures. Popular methods rely on estimating a penalized maximum likelihood
of the precision matrix. However, in these approaches structure recovery is an
indirect consequence of the data-fit term, the penalty can be difficult to
adapt for domain-specific knowledge, and the inference is computationally
demanding. By contrast, it may be easier to generate training samples of data
that arise from graphs with the desired structure properties. We propose here
to leverage this latter source of information as training data to learn a
function, parametrized by a neural network that maps empirical covariance
matrices to estimated graph structures. Learning this function brings two
benefits: it implicitly models the desired structure or sparsity properties to
form suitable priors, and it can be tailored to the specific problem of edge
structure discovery, rather than maximizing data likelihood. Applying this
framework, we find our learnable graph-discovery method trained on synthetic
data generalizes well: identifying relevant edges in both synthetic and real
data, completely unknown at training time. We find that on genetics, brain
imaging, and simulation data we obtain performance generally superior to
analytical methods
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