3,432 research outputs found
Variational inference for sparse network reconstruction from count data
In multivariate statistics, the question of finding direct interactions can
be formulated as a problem of network inference - or network reconstruction -
for which the Gaussian graphical model (GGM) provides a canonical framework.
Unfortunately, the Gaussian assumption does not apply to count data which are
encountered in domains such as genomics, social sciences or ecology.
To circumvent this limitation, state-of-the-art approaches use two-step
strategies that first transform counts to pseudo Gaussian observations and then
apply a (partial) correlation-based approach from the abundant literature of
GGM inference. We adopt a different stance by relying on a latent model where
we directly model counts by means of Poisson distributions that are conditional
to latent (hidden) Gaussian correlated variables. In this multivariate Poisson
lognormal-model, the dependency structure is completely captured by the latent
layer. This parametric model enables to account for the effects of covariates
on the counts.
To perform network inference, we add a sparsity inducing constraint on the
inverse covariance matrix of the latent Gaussian vector. Unlike the usual
Gaussian setting, the penalized likelihood is generally not tractable, and we
resort instead to a variational approach for approximate likelihood
maximization. The corresponding optimization problem is solved by alternating a
gradient ascent on the variational parameters and a graphical-Lasso step on the
covariance matrix.
We show that our approach is highly competitive with the existing methods on
simulation inspired from microbiological data. We then illustrate on three
various data sets how accounting for sampling efforts via offsets and
integrating external covariates (which is mostly never done in the existing
literature) drastically changes the topology of the inferred network
Expectation Propagation for Poisson Data
The Poisson distribution arises naturally when dealing with data involving
counts, and it has found many applications in inverse problems and imaging. In
this work, we develop an approximate Bayesian inference technique based on
expectation propagation for approximating the posterior distribution formed
from the Poisson likelihood function and a Laplace type prior distribution,
e.g., the anisotropic total variation prior. The approach iteratively yields a
Gaussian approximation, and at each iteration, it updates the Gaussian
approximation to one factor of the posterior distribution by moment matching.
We derive explicit update formulas in terms of one-dimensional integrals, and
also discuss stable and efficient quadrature rules for evaluating these
integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem
DeepVoxels: Learning Persistent 3D Feature Embeddings
In this work, we address the lack of 3D understanding of generative neural
networks by introducing a persistent 3D feature embedding for view synthesis.
To this end, we propose DeepVoxels, a learned representation that encodes the
view-dependent appearance of a 3D scene without having to explicitly model its
geometry. At its core, our approach is based on a Cartesian 3D grid of
persistent embedded features that learn to make use of the underlying 3D scene
structure. Our approach combines insights from 3D geometric computer vision
with recent advances in learning image-to-image mappings based on adversarial
loss functions. DeepVoxels is supervised, without requiring a 3D reconstruction
of the scene, using a 2D re-rendering loss and enforces perspective and
multi-view geometry in a principled manner. We apply our persistent 3D scene
representation to the problem of novel view synthesis demonstrating
high-quality results for a variety of challenging scenes.Comment: Video: https://www.youtube.com/watch?v=HM_WsZhoGXw Supplemental
material:
https://drive.google.com/file/d/1BnZRyNcVUty6-LxAstN83H79ktUq8Cjp/view?usp=sharing
Code: https://github.com/vsitzmann/deepvoxels Project page:
https://vsitzmann.github.io/deepvoxels
Distributed Reconstruction of Nonlinear Networks: An ADMM Approach
In this paper, we present a distributed algorithm for the reconstruction of
large-scale nonlinear networks. In particular, we focus on the identification
from time-series data of the nonlinear functional forms and associated
parameters of large-scale nonlinear networks. Recently, a nonlinear network
reconstruction problem was formulated as a nonconvex optimisation problem based
on the combination of a marginal likelihood maximisation procedure with
sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative
reweighted lasso algorithm was derived to solve the initial nonconvex
optimisation problem. By exploiting the structure of the objective function of
this reweighted lasso algorithm, a distributed algorithm can be designed. To
this end, we apply the alternating direction method of multipliers (ADMM) to
decompose the original problem into several subproblems. To illustrate the
effectiveness of the proposed methods, we use our approach to identify a
network of interconnected Kuramoto oscillators with different network sizes
(500~100,000 nodes).Comment: To appear in the Preprints of 19th IFAC World Congress 201
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