273 research outputs found
Nonparanormal Graph Quilting with Applications to Calcium Imaging
Probabilistic graphical models have become an important unsupervised learning
tool for detecting network structures for a variety of problems, including the
estimation of functional neuronal connectivity from two-photon calcium imaging
data. However, in the context of calcium imaging, technological limitations
only allow for partially overlapping layers of neurons in a brain region of
interest to be jointly recorded. In this case, graph estimation for the full
data requires inference for edge selection when many pairs of neurons have no
simultaneous observations. This leads to the Graph Quilting problem, which
seeks to estimate a graph in the presence of block-missingness in the empirical
covariance matrix. Solutions for the Graph Quilting problem have previously
been studied for Gaussian graphical models; however, neural activity data from
calcium imaging are often non-Gaussian, thereby requiring a more flexible
modeling approach. Thus, in our work, we study two approaches for nonparanormal
Graph Quilting based on the Gaussian copula graphical model, namely a maximum
likelihood procedure and a low-rank based framework. We provide theoretical
guarantees on edge recovery for the former approach under similar conditions to
those previously developed for the Gaussian setting, and we investigate the
empirical performance of both methods using simulations as well as real data
calcium imaging data. Our approaches yield more scientifically meaningful
functional connectivity estimates compared to existing Gaussian graph quilting
methods for this calcium imaging data set
Sparse Median Graphs Estimation in a High Dimensional Semiparametric Model
In this manuscript a unified framework for conducting inference on complex
aggregated data in high dimensional settings is proposed. The data are assumed
to be a collection of multiple non-Gaussian realizations with underlying
undirected graphical structures. Utilizing the concept of median graphs in
summarizing the commonality across these graphical structures, a novel
semiparametric approach to modeling such complex aggregated data is provided
along with robust estimation of the median graph, which is assumed to be
sparse. The estimator is proved to be consistent in graph recovery and an upper
bound on the rate of convergence is given. Experiments on both synthetic and
real datasets are conducted to illustrate the empirical usefulness of the
proposed models and methods
Joint Estimation of Multiple Graphical Models from High Dimensional Time Series
In this manuscript we consider the problem of jointly estimating multiple
graphical models in high dimensions. We assume that the data are collected from
n subjects, each of which consists of T possibly dependent observations. The
graphical models of subjects vary, but are assumed to change smoothly
corresponding to a measure of closeness between subjects. We propose a kernel
based method for jointly estimating all graphical models. Theoretically, under
a double asymptotic framework, where both (T,n) and the dimension d can
increase, we provide the explicit rate of convergence in parameter estimation.
It characterizes the strength one can borrow across different individuals and
impact of data dependence on parameter estimation. Empirically, experiments on
both synthetic and real resting state functional magnetic resonance imaging
(rs-fMRI) data illustrate the effectiveness of the proposed method.Comment: 40 page
Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships
One of the main goals of current systems neuroscience is to understand how neuronal populations integrate sensory information to inform behavior. However, estimating stimulus or behavioral information that is encoded in high-dimensional neuronal populations is challenging. We propose a method based on parametric copulas which allows modeling joint distributions of neuronal and behavioral variables characterized by different statistics and timescales. To account for temporal or spatial changes in dependencies between variables, we model varying copula parameters by means of Gaussian Processes (GP). We validate the resulting Copula-GP framework on synthetic data and on neuronal and behavioral recordings obtained in awake mice. We show that the use of a parametric description of the high-dimensional dependence structure in our method provides better accuracy in mutual information estimation in higher dimensions compared to other non-parametric methods. Moreover, by quantifying the redundancy between neuronal and behavioral variables, our model exposed the location of the reward zone in an unsupervised manner (i.e., without using any explicit cues about the task structure). These results demonstrate that the Copula-GP framework is particularly useful for the analysis of complex multidimensional relationships between neuronal, sensory and behavioral variables
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