11,207 research outputs found
A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data
In this paper we propose a unified, probabilistically coherent framework for the analysis of task-related brain activity in multi-subject fMRI experiments. This is distinct from two-stage “group analysis” approaches traditionally considered in the fMRI literature, which separate the inference on the individual fMRI time courses from the inference at the population level. In our modeling approach we consider a spatiotemporal linear regression model and specifically account for the between-subjects heterogeneity in neuronal activity via a spatially informed multi-subject nonparametric variable selection prior. For posterior inference, in addition to Markov chain Monte Carlo sampling algorithms, we develop suitable variational Bayes algorithms. We show on simulated data that variational Bayes inference achieves satisfactory results at more reduced computational costs than using MCMC, allowing scalability of our methods. In an application to data collected to assess brain responses to emotional stimuli our method correctly detects activation in visual areas when visual stimuli are presented
Tensor Monte Carlo: particle methods for the GPU era
Multi-sample, importance-weighted variational autoencoders (IWAE) give
tighter bounds and more accurate uncertainty estimates than variational
autoencoders (VAE) trained with a standard single-sample objective. However,
IWAEs scale poorly: as the latent dimensionality grows, they require
exponentially many samples to retain the benefits of importance weighting.
While sequential Monte-Carlo (SMC) can address this problem, it is
prohibitively slow because the resampling step imposes sequential structure
which cannot be parallelised, and moreover, resampling is non-differentiable
which is problematic when learning approximate posteriors. To address these
issues, we developed tensor Monte-Carlo (TMC) which gives exponentially many
importance samples by separately drawing samples for each of the latent
variables, then averaging over all possible combinations. While the sum
over exponentially many terms might seem to be intractable, in many cases it
can be computed efficiently as a series of tensor inner-products. We show that
TMC is superior to IWAE on a generative model with multiple stochastic layers
trained on the MNIST handwritten digit database, and we show that TMC can be
combined with standard variance reduction techniques
Reducing Reparameterization Gradient Variance
Optimization with noisy gradients has become ubiquitous in statistics and
machine learning. Reparameterization gradients, or gradient estimates computed
via the "reparameterization trick," represent a class of noisy gradients often
used in Monte Carlo variational inference (MCVI). However, when these gradient
estimators are too noisy, the optimization procedure can be slow or fail to
converge. One way to reduce noise is to use more samples for the gradient
estimate, but this can be computationally expensive. Instead, we view the noisy
gradient as a random variable, and form an inexpensive approximation of the
generating procedure for the gradient sample. This approximation has high
correlation with the noisy gradient by construction, making it a useful control
variate for variance reduction. We demonstrate our approach on non-conjugate
multi-level hierarchical models and a Bayesian neural net where we observed
gradient variance reductions of multiple orders of magnitude (20-2,000x)
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