4,257 research outputs found
Learning sparse representations of depth
This paper introduces a new method for learning and inferring sparse
representations of depth (disparity) maps. The proposed algorithm relaxes the
usual assumption of the stationary noise model in sparse coding. This enables
learning from data corrupted with spatially varying noise or uncertainty,
typically obtained by laser range scanners or structured light depth cameras.
Sparse representations are learned from the Middlebury database disparity maps
and then exploited in a two-layer graphical model for inferring depth from
stereo, by including a sparsity prior on the learned features. Since they
capture higher-order dependencies in the depth structure, these priors can
complement smoothness priors commonly used in depth inference based on Markov
Random Field (MRF) models. Inference on the proposed graph is achieved using an
alternating iterative optimization technique, where the first layer is solved
using an existing MRF-based stereo matching algorithm, then held fixed as the
second layer is solved using the proposed non-stationary sparse coding
algorithm. This leads to a general method for improving solutions of state of
the art MRF-based depth estimation algorithms. Our experimental results first
show that depth inference using learned representations leads to state of the
art denoising of depth maps obtained from laser range scanners and a time of
flight camera. Furthermore, we show that adding sparse priors improves the
results of two depth estimation methods: the classical graph cut algorithm by
Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page
Generalized structured additive regression based on Bayesian P-splines
Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM's and extensions to generalized structured additive regression based on one or two dimensional P-splines as the main building block. The approach extends previous work by Lang und Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. For the first time, we present Bayesian semiparametric inference for the widely used multinomial logit models. As we will demonstrate through two applications on the forest health status of trees and a space-time analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX
Sharing deep generative representation for perceived image reconstruction from human brain activity
Decoding human brain activities via functional magnetic resonance imaging
(fMRI) has gained increasing attention in recent years. While encouraging
results have been reported in brain states classification tasks, reconstructing
the details of human visual experience still remains difficult. Two main
challenges that hinder the development of effective models are the perplexing
fMRI measurement noise and the high dimensionality of limited data instances.
Existing methods generally suffer from one or both of these issues and yield
dissatisfactory results. In this paper, we tackle this problem by casting the
reconstruction of visual stimulus as the Bayesian inference of missing view in
a multiview latent variable model. Sharing a common latent representation, our
joint generative model of external stimulus and brain response is not only
"deep" in extracting nonlinear features from visual images, but also powerful
in capturing correlations among voxel activities of fMRI recordings. The
nonlinearity and deep structure endow our model with strong representation
ability, while the correlations of voxel activities are critical for
suppressing noise and improving prediction. We devise an efficient variational
Bayesian method to infer the latent variables and the model parameters. To
further improve the reconstruction accuracy, the latent representations of
testing instances are enforced to be close to that of their neighbours from the
training set via posterior regularization. Experiments on three fMRI recording
datasets demonstrate that our approach can more accurately reconstruct visual
stimuli
Region-Referenced Spectral Power Dynamics of EEG Signals: A Hierarchical Modeling Approach
Functional brain imaging through electroencephalography (EEG) relies upon the
analysis and interpretation of high-dimensional, spatially organized time
series. We propose to represent time-localized frequency domain
characterizations of EEG data as region-referenced functional data. This
representation is coupled with a hierarchical modeling approach to multivariate
functional observations. Within this familiar setting, we discuss how several
prior models relate to structural assumptions about multivariate covariance
operators. An overarching modeling framework, based on infinite factorial
decompositions, is finally proposed to balance flexibility and efficiency in
estimation. The motivating application stems from a study of implicit auditory
learning, in which typically developing (TD) children, and children with autism
spectrum disorder (ASD) were exposed to a continuous speech stream. Using the
proposed model, we examine differential band power dynamics as brain function
is interrogated throughout the duration of a computer-controlled experiment.
Our work offers a novel look at previous findings in psychiatry, and provides
further insights into the understanding of ASD. Our approach to inference is
fully Bayesian and implemented in a highly optimized Rcpp package
Probabilistic Meta-Representations Of Neural Networks
Existing Bayesian treatments of neural networks are typically characterized
by weak prior and approximate posterior distributions according to which all
the weights are drawn independently. Here, we consider a richer prior
distribution in which units in the network are represented by latent variables,
and the weights between units are drawn conditionally on the values of the
collection of those variables. This allows rich correlations between related
weights, and can be seen as realizing a function prior with a Bayesian
complexity regularizer ensuring simple solutions. We illustrate the resulting
meta-representations and representations, elucidating the power of this prior.Comment: presented at UAI 2018 Uncertainty In Deep Learning Workshop (UDL AUG.
2018
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