Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

Performing model selection between Gibbs random fields is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical or numerical methods. Furthermore, such unobserved fields cannot be integrated out and the likelihood evaluztion is a doubly intractable problem. This forms a central issue to pick the model that best fits an observed data. We introduce a new approximate version of the Bayesian Information Criterion. We partition the lattice into continuous rectangular blocks and we approximate the probability measure of the hidden Gibbs field by the product of some Gibbs distributions over the blocks. On that basis, we estimate the likelihood and derive the Block Likelihood Information Criterion (BLIC) that answers model choice questions such as the selection of the dependency structure or the number of latent states. We study the performances of BLIC for those questions. In addition, we present a comparison with ABC algorithms to point out that the novel criterion offers a better trade-off between time efficiency and reliable results

Bayesian mapping of brain regions using compound Markov random field priors

Human brain mapping, i.e. the detection of functional regions and their connections, has experienced enormous progress through the use of functional magnetic resonance imaging (fMRI). The massive spatio-temporal data sets generated by this imaging technique impose challenging problems for statistical analysis. Many approaches focus on adequate modeling of the temporal component. Spatial aspects are often considered only in a separate postprocessing step, if at all, or modeling is based on Gaussian random fields. A weakness of Gaussian spatial smoothing is possible underestimation of activation peaks or blurring of sharp transitions between activated and non-activated regions. In this paper we suggest Bayesian spatio-temporal models, where spatial adaptivity is improved through inhomogeneous or compound Markov random field priors. Inference is based on an approximate MCMC technique. Performance of our approach is investigated through a simulation study, including a comparison to models based on Gaussian as well as more robust spatial priors in terms of pixelwise and global MSEs. Finally we demonstrate its use by an application to fMRI data from a visual stimulation experiment for assessing activation in visual cortical areas

Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images

In All Likelihood, Deep Belief Is Not Enough

Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is given by the likelihood. One class of statistical models which has recently gained increasing popularity and has been applied to a variety of complex data are deep belief networks. Analyses of these models, however, have been typically limited to qualitative analyses based on samples due to the computationally intractable nature of the model likelihood. Motivated by these circumstances, the present article provides a consistent estimator for the likelihood that is both computationally tractable and simple to apply in practice. Using this estimator, a deep belief network which has been suggested for the modeling of natural image patches is quantitatively investigated and compared to other models of natural image patches. Contrary to earlier claims based on qualitative results, the results presented in this article provide evidence that the model under investigation is not a particularly good model for natural image

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning