235 research outputs found
A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data
Deducing the structure of neural circuits is one of the central problems of
modern neuroscience. Recently-introduced calcium fluorescent imaging methods
permit experimentalists to observe network activity in large populations of
neurons, but these techniques provide only indirect observations of neural
spike trains, with limited time resolution and signal quality. In this work we
present a Bayesian approach for inferring neural circuitry given this type of
imaging data. We model the network activity in terms of a collection of coupled
hidden Markov chains, with each chain corresponding to a single neuron in the
network and the coupling between the chains reflecting the network's
connectivity matrix. We derive a Monte Carlo Expectation--Maximization
algorithm for fitting the model parameters; to obtain the sufficient statistics
in a computationally-efficient manner, we introduce a specialized
blockwise-Gibbs algorithm for sampling from the joint activity of all observed
neurons given the observed fluorescence data. We perform large-scale
simulations of randomly connected neuronal networks with biophysically
realistic parameters and find that the proposed methods can accurately infer
the connectivity in these networks given reasonable experimental and
computational constraints. In addition, the estimation accuracy may be improved
significantly by incorporating prior knowledge about the sparseness of
connectivity in the network, via standard L penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multiscale Dictionary Learning for Estimating Conditional Distributions
Nonparametric estimation of the conditional distribution of a response given
high-dimensional features is a challenging problem. It is important to allow
not only the mean but also the variance and shape of the response density to
change flexibly with features, which are massive-dimensional. We propose a
multiscale dictionary learning model, which expresses the conditional response
density as a convex combination of dictionary densities, with the densities
used and their weights dependent on the path through a tree decomposition of
the feature space. A fast graph partitioning algorithm is applied to obtain the
tree decomposition, with Bayesian methods then used to adaptively prune and
average over different sub-trees in a soft probabilistic manner. The algorithm
scales efficiently to approximately one million features. State of the art
predictive performance is demonstrated for toy examples and two neuroscience
applications including up to a million features
Covariate-assisted spectral clustering
Biological and social systems consist of myriad interacting units. The
interactions can be represented in the form of a graph or network. Measurements
of these graphs can reveal the underlying structure of these interactions,
which provides insight into the systems that generated the graphs. Moreover, in
applications such as connectomics, social networks, and genomics, graph data
are accompanied by contextualizing measures on each node. We utilize these node
covariates to help uncover latent communities in a graph, using a modification
of spectral clustering. Statistical guarantees are provided under a joint
mixture model that we call the node-contextualized stochastic blockmodel,
including a bound on the mis-clustering rate. The bound is used to derive
conditions for achieving perfect clustering. For most simulated cases,
covariate-assisted spectral clustering yields results superior to regularized
spectral clustering without node covariates and to an adaptation of canonical
correlation analysis. We apply our clustering method to large brain graphs
derived from diffusion MRI data, using the node locations or neurological
region membership as covariates. In both cases, covariate-assisted spectral
clustering yields clusters that are easier to interpret neurologically.Comment: 28 pages, 4 figures, includes substantial changes to theoretical
result
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