5,344 research outputs found
Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis
Factor analysis aims to determine latent factors, or traits, which summarize
a given data set. Inter-battery factor analysis extends this notion to multiple
views of the data. In this paper we show how a nonlinear, nonparametric version
of these models can be recovered through the Gaussian process latent variable
model. This gives us a flexible formalism for multi-view learning where the
latent variables can be used both for exploratory purposes and for learning
representations that enable efficient inference for ambiguous estimation tasks.
Learning is performed in a Bayesian manner through the formulation of a
variational compression scheme which gives a rigorous lower bound on the log
likelihood. Our Bayesian framework provides strong regularization during
training, allowing the structure of the latent space to be determined
efficiently and automatically. We demonstrate this by producing the first (to
our knowledge) published results of learning from dozens of views, even when
data is scarce. We further show experimental results on several different types
of multi-view data sets and for different kinds of tasks, including exploratory
data analysis, generation, ambiguity modelling through latent priors and
classification.Comment: 49 pages including appendi
Fast joint detection-estimation of evoked brain activity in event-related fMRI using a variational approach
In standard clinical within-subject analyses of event-related fMRI data, two
steps are usually performed separately: detection of brain activity and
estimation of the hemodynamic response. Because these two steps are inherently
linked, we adopt the so-called region-based Joint Detection-Estimation (JDE)
framework that addresses this joint issue using a multivariate inference for
detection and estimation. JDE is built by making use of a regional bilinear
generative model of the BOLD response and constraining the parameter estimation
by physiological priors using temporal and spatial information in a Markovian
modeling. In contrast to previous works that use Markov Chain Monte Carlo
(MCMC) techniques to approximate the resulting intractable posterior
distribution, we recast the JDE into a missing data framework and derive a
Variational Expectation-Maximization (VEM) algorithm for its inference. A
variational approximation is used to approximate the Markovian model in the
unsupervised spatially adaptive JDE inference, which allows fine automatic
tuning of spatial regularisation parameters. It follows a new algorithm that
exhibits interesting properties compared to the previously used MCMC-based
approach. Experiments on artificial and real data show that VEM-JDE is robust
to model mis-specification and provides computational gain while maintaining
good performance in terms of activation detection and hemodynamic shape
recovery
Time Series Analysis of fMRI Data: Spatial Modelling and Bayesian Computation
Time series analysis of fMRI data is an important area of medical statistics
for neuroimaging data. The neuroimaging community has embraced mean-field
variational Bayes (VB) approximations, which are implemented in Statistical
Parametric Mapping (SPM) software. While computationally efficient, the quality
of VB approximations remains unclear even though they are commonly used in the
analysis of neuroimaging data. For reliable statistical inference, it is
important that these approximations be accurate and that users understand the
scenarios under which they may not be accurate.
We consider this issue for a particular model that includes spatially-varying
coefficients. To examine the accuracy of the VB approximation we derive
Hamiltonian Monte Carlo (HMC) for this model and conduct simulation studies to
compare its performance with VB. As expected we find that the computation time
required for VB is considerably less than that for HMC. In settings involving a
high or moderate signal-to-noise ratio (SNR) we find that the two approaches
produce very similar results suggesting that the VB approximation is useful in
this setting. On the other hand, when one considers a low SNR, substantial
differences are found, suggesting that the approximation may not be accurate in
such cases and we demonstrate that VB produces Bayes estimators with larger
mean squared error (MSE). A real application related to face perception is also
carried out. Overall, our work clarifies the usefulness of VB for the
spatiotemporal analysis of fMRI data, while also pointing out the limitation of
VB when the SNR is low and the utility of HMC in this case
Adaptive Non-uniform Compressive Sampling for Time-varying Signals
In this paper, adaptive non-uniform compressive sampling (ANCS) of
time-varying signals, which are sparse in a proper basis, is introduced. ANCS
employs the measurements of previous time steps to distribute the sensing
energy among coefficients more intelligently. To this aim, a Bayesian inference
method is proposed that does not require any prior knowledge of importance
levels of coefficients or sparsity of the signal. Our numerical simulations
show that ANCS is able to achieve the desired non-uniform recovery of the
signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce
the number of required measurements significantly.Comment: 6 pages, 8 figures, Conference on Information Sciences and Systems
(CISS 2017) Baltimore, Marylan
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