Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected *contrast* between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce an *pooled posterior* distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the pooled posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop, without resorting to lower bound approximations of the EIG. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach.

We propose a new procedure named PASOA, for Bayesian experimental design, that performs sequential design optimization by simultaneously providing accurate estimates of successive posterior distributions for parameter inference. The sequential design process is carried out via a contrastive estimation principle, using stochastic optimization and Sequential Monte Carlo (SMC) samplers to maximise the Expected Information Gain (EIG). As larger information gains are obtained for larger distances between successive posterior distributions, this EIG objective may worsen classical SMC performance. To handle this issue, tempering is proposed to have both a large information gain and an accurate SMC sampling, that we show is crucial for performance. This novel combination of stochastic optimization and tempered SMC allows to jointly handle design optimization and parameter inference. We provide a proof that the obtained optimal design estimators benefit from some consistency property. Numerical experiments confirm the potential of the approach, which outperforms other recent existing procedures.

We extend Bayesian Synthetic Likelihood (BSL) methods to non-Gaussian approximations of the likelihood function. In this setting, we introduce Mixtures of Experts (MoEs), a class of neural network models, as surrogate likelihoods that exhibit desirable approximation theoretic properties. Moreover, MoEs can be estimated using Expectation-Maximization algorithm-based approaches, such as the Gaussian Locally Linear Mapping model estimators that we implement. Further, we provide theoretical evidence towards the ability of our procedure to estimate and approximate a wide range of likelihood functions. Through simulations, we demonstrate the superiority of our approach over existing BSL variants in terms of both posterior approximation accuracy and computational efficiency.

The full acceptance of Deep Learning (DL) models in the clinical field is rather low with respect to the quantity of high-performing solutions reported in the literature. End users are particularly reluctant to rely on the opaque predictions of DL models. Uncertainty quantification methods have been proposed in the literature as a potential solution, to reduce the black-box effect of DL models and increase the interpretability and the acceptability of the result by the final user. In this review, we propose an overview of the existing methods to quantify uncertainty associated with DL predictions. We focus on applications to medical image analysis, which present specific challenges due to the high dimensionality of images and their variable quality, as well as constraints associated with real-world clinical routine. Moreover, we discuss the concept of structural uncertainty, a corpus of methods to facilitate the alignment of segmentation uncertainty estimates with clinical attention. We then discuss the evaluation protocols to validate the relevance of uncertainty estimates. Finally, we highlight the open challenges for uncertainty quantification in the medical field.

Lidar (Light Detection and Ranging) has become an essential part of the remote sensing toolbox used for biosphere monitoring. In particular, Lidar provides the opportunity to map forest leaf area with unprecedented accuracy, while leaf area has remained an important source of uncertainty affecting models of gas exchanges between the vegetation and the atmosphere. Unmanned Aerial Vehicles (UAV) are easy to mobilize and therefore allow frequent revisits to track the response of vegetation to climate change. However, miniature sensors embarked on UAVs usually provide point clouds of limited density, which are further affected by a strong decrease in density from top to bottom of the canopy due to progressively stronger occlusion. In such a context, discriminating leaf points from wood points presents a significant challenge due in particular to strong class imbalance and spatially irregular sampling intensity. Here we introduce a neural network model based on the Pointnet ++ architecture which makes use of point geometry only (excluding any spectral information). To cope with local data sparsity, we propose an innovative sampling scheme which strives to preserve local important geometric information. We also propose a loss function adapted to the severe class imbalance. We show that our model outperforms state-of-the-art alternatives on UAV point clouds. We discuss future possible improvements, particularly regarding much denser point clouds acquired from below the canopy.

With the advent of recent deep learning techniques, computerized methods for automatic lesion segmentation have reached performances comparable to those of medical practitioners. However, little attention has been paid to the detection of subtle physiological changes caused by evolutive pathologies, such as neurodegenerative diseases. In this work, we leverage deep learning models to detect anomalies in brain diffusion tensor imaging (DTI) parameter maps of recently diagnosed and untreated (de novo) patients with Parkinson's disease (PD). For this purpose, we trained auto-encoders on parameter maps of healthy controls (n = 56) and tested them on those of de novo PD patients (n = 129). We considered large reconstruction errors between the original and reconstructed images to be anomalies that, when quantified, allow discerning between de novo PD patients and healthy controls. The most discriminating brain macro-region was found to be the white matter with a ROC-AUC 68.3 (IQR 5.4) and the best subcortical structure, the GPi (ROC-AUC 62.6 IQR 5.4). Our results indicate that our deep learning-based model can detect potentially pathological regions in de novo PD patients, without requiring any expert delineation. This may enable extracting neuroimaging biomarkers of PD in the future, but further testing on larger cohorts is needed. Such models can be seamlessly extended with additional parameter maps and applied to study the physio-pathology of other neurological diseases.

Standard parameter estimation from vascular magnetic resonance fingerprinting (MRF) data is based on matching the MRF signals to their best counterparts in a grid of coupled simulated signals and parameters, referred to as a dictionary. To reach a good accuracy, the matching requires an informative dictionary whose cost, in terms of design, storage and exploration, is rapidly prohibitive for even moderate numbers of parameters. In this work, we propose an alternative dictionary-based statistical learning (DB-SL) approach made of three steps: 1) a quasi-random sampling strategy to produce efficiently an informative dictionary, 2) an inverse statistical regression model to learn from the dictionary a correspondence between fingerprints and parameters, and 3) the use of this mapping to provide both parameter estimates and their confidence indices. The proposed DB-SL approach is compared to both the standard dictionary-based matching (DBM) method and to a dictionary-based deep learning (DB-DL) method. Performance is illustrated first on synthetic signals including scalable and standard MRF signals with spatial undersampling noise. Then, vascular MRF signals are considered both through simulations and real data acquired in tumor bearing rats. Overall, the two learning methods yield more accurate parameter estimates than matching and to a range not limited to the dictionary boundaries. DB-SL in particular resists to higher noise levels and provides in addition confidence indices on the estimates at no additional cost. DB-SL appears as a promising method to reduce simulation needs and computational requirements, while modeling sources of uncertainty and providing both accurate and interpretable results.

When analyzing brain tumors, two tasks are intrinsically linked, spatial localization, and physiological characterization of the lesioned tissues. Automated data-driven solutions exist, based on image segmentation techniques or physiological parameters analysis, but for each task separately, the other being performedmanually or with user tuning operations. In this paper, the availability of quantitative magnetic resonance (MR) parameters is combined with advancedmultivariate statistical tools to design a fully automated method that jointly performs both localization and characterization. Non trivial interactions between relevant physiologicalparameters are capturedthanks to recent generalized Student distributions that provide a larger variety of distributional shapes compared to the more standard Gaussian distributions. Probabilisticmixtures of the former distributions are then consideredto account for the different tissue types and potential heterogeneity of lesions. Discriminative multivariate features are extracted from this mixture modeling and turned into individual lesion signatures. The signatures are subsequently pooled together to build a statistical fingerprintmodel of the different lesion types that captures lesion characteristics while accounting for inter-subject variability. The potential of this generic procedure is demonstrated on a data set of 53 rats, with 36 rats bearing 4 different brain tumors, for which 5 quantitative MR parameters were acquired.

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.

As an emerging area, data science is facing great opportunities as well as challenges. Often arguments exist: What is data science? Why data science? We have information science already, why do we need data science? Do we need analytics science? Is analytics new? What is the difference between statistics and data analytics? What makes a data scientist? We believe that a special session on Trends and Controversy about data science and advanced analytics could bring insights from different mindsets for the healthy development of the science and society. Accordingly, this T&C special session will host talks by invitation to outline different views about today and future of data science. Invited speakers can contribute a paper (in the same format as the main conference submissions but could be less than 10 pages) to the special session, which will be handled by program co-chairs and accepted into the main conference proceeding probably by addressing comments from the program cochairs.

In this paper, we address the problems of modeling the acoustic space generated by a full-spectrum sound source and using the learned model for the localization and separation of multiple sources that simultaneously emit sparse-spectrum sounds. We lay theoretical and methodological grounds in order to introduce the binaural manifold paradigm. We perform an in-depth study of the latent low-dimensional structure of the high-dimensional interaural spectral data, based on a corpus recorded with a human-like audiomotor robot head. A nonlinear dimensionality reduction technique is used to show that these data lie on a two-dimensional (2D) smooth manifold parameterized by the motor states of the listener, or equivalently, the sound-source directions. We propose a probabilistic piecewise affine mapping model (PPAM) specifically designed to deal with high-dimensional data exhibiting an intrinsic piecewise linear structure. We derive a closed-form expectation-maximization (EM) procedure for estimating the model parameters, followed by Bayes inversion for obtaining the full posterior density function of a sound-source direction. We extend this solution to deal with missing data and redundancy in real-world spectrograms, and hence for 2D localization of natural sound sources such as speech. We further generalize the model to the challenging case of multiple sound sources and we propose a variational EM framework. The associated algorithm, referred to as variational EM for source separation and localization (VESSL) yields a Bayesian estimation of the 2D locations and time-frequency masks of all the sources. Comparisons of the proposed approach with several existing methods reveal that the combination of acoustic-space learning with Bayesian inference enables our method to outperform state-of-the-art methods.

In this paper we report the set-up and results of the Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) organized in conjunction with the MICCAI 2012 and 2013 conferences. Twenty state-of-the-art tumor segmentation algorithms were applied to a set of 65 multi-contrast MR scans of low- and high-grade glioma patients-manually annotated by up to four raters-and to 65 comparable scans generated using tumor image simulation software. Quantitative evaluations revealed considerable disagreement between the human raters in segmenting various tumor sub-regions (Dice scores in the range 74%-85%), illustrating the difficulty of this task. We found that different algorithms worked best for different sub-regions (reaching performance comparable to human inter-rater variability), but that no single algorithm ranked in the top for all sub-regions simultaneously. Fusing several good algorithms using a hierarchical majority vote yielded segmentations that consistently ranked above all individual algorithms, indicating remaining opportunities for further methodological improvements. The BRATS image data and manual annotations continue to be publicly available through an online evaluation system as an ongoing benchmarking resource.

Standard detection of evoked brain activity in functional MRI (fMRI) relies on a fixed and known shape of the impulse response of the neurovascular coupling, namely the hemo-dynamic response function (HRF). To cope with this issue, the joint detection-estimation (JDE) framework has been proposed. This formalism enables to estimate a HRF per region but for doing so, it assumes a prior brain partition (or parcellation) regarding hemodynamic territories. This partition has to be accurate enough to recover accurate HRF shapes but has also to overcome the detection-estimation issue: the lack of hemodynamics information in the non-active positions. An hemodynamically-based parcellation method is proposed, consisting first of a feature extraction step, followed by a Gaussian Mixture-based parcellation, which considers the injection of the activation levels in the parcellation process, in order to overcome the detection-estimation issue and find the underlying hemodynamics.

The sound-source separation and localization (SSL) problems are addressed within a unified formulation. Firstly, a mapping between white-noise source locations and binaural cues is estimated. Secondly, SSL is solved via Bayesian inversion of this mapping in the presence of multiple sparse-spectrum emitters (such as speech), noise and reverberations. We propose a variational EM algorithm which is described in detail together with initialization and convergence issues. Extensive real-data experiments show that the method outperforms the state-of-the-art both in separation and localization (azimuth and elevation).

In many neuroscience applications, the Arterial Spin Labeling (ASL) fMRI modality arises as a preferable choice to the standard BOLD modality due to its ability to provide a quantitative measure of the Cerebral Blood Flow (CBF). Such a quantification is central but generally performed without consideration of a specific modeling of the perfusion component in the signal often handled via standard GLM approaches using the BOLD canonical response function as regressor. In this work, we propose a novel Bayesian hierarchical model of the ASL signal which allows activation detection and both the extraction of a perfusion and a hemodynamic component. Validation on synthetic and real data sets from event-related ASL show the ability of our model to address the source separation and double deconvolution problems inherent to ASL data analysis.

In this paper we address the problem of aligning visual (V) and auditory (A) data using a sensor that is composed of a camera-pair and a microphone-pair. The original contribution of the paper is a method for AV data aligning through estimation of the 3D positions of the microphones in the visual-centred coordinate frame defined by the stereo camera-pair. We exploit the fact that these two distinct data sets are conditioned by a common set of parameters, namely the (unknown) 3D trajectory of an AV object, and derive an EM-like algorithm that alternates between the estimation of the microphone-pair position and the estimation of the AV object trajectory. The proposed algorithm has a number of built-in features: it can deal with A and V observations that are misaligned in time, it estimates the reliability of the data, it is robust to outliers in both modalities, and it has proven theoretical convergence. We report experiments with both simulated and real data.

In standard within-subject analyses of event-related functional magnetic resonance imaging (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 model. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to sample 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 automatic fine-tuning of spatial regularization parameters. It provides a new algorithm that exhibits interesting properties in terms of estimation error and computational cost compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model misspecification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery.

Modern GPUs enable widely affordable personal computers to carry out massively parallel computation tasks. NVIDIA's CUDA technology provides a wieldy parallel computing platform. Many state-of-the-art algorithms arising from different fields have been redesigned based on CUDA to achieve computational speedup. Differential evolution (DE), as a very promising evolutionary algorithm, is highly suitable for parallelization owing to its data-parallel algorithmic structure. However, most existing CUDA-based DE implementations suffer from excessive low-throughput memory access and less efficient device utilization. This work presents an improved CUDA-based DE to optimize memory and device utilization: several logically-related kernels are combined into one composite kernel to reduce global memory access; kernel execution configuration parameters are automatically determined to maximize device occupancy; streams are employed to enable concurrent kernel execution to maximize device utilization. Experimental results on several numerical problems demonstrate superior computational time efficiency of the proposed method over two recent CUDA-based DE and the sequential DE across varying problem dimensions and algorithmic population sizes.

We address the issue of jointly detecting brain activity and estimating brain hemodynamics from functional MRI data. To this end, we adopt the so-called Joint-Detection-Estimation (JDE) framework introduced in [1] and augmented in [2]. An inherent difficulty is to find the right spatial scale at which brain hemodynamics estimation makes sense. The voxel level is clearly not appropriate as estimating a full hemodynamic response function (HRF) from a single voxel time course may suffer from a poor signal-to-noise-ratio and lead to potentially misleading results (non-physiological HRF shapes). More robust estimation can be obtained by considering groups of voxels (i.e. parcels) with some functional homogeneity properties. Current JDE approaches are therefore based on an initial parcellation but with no guarantee of its optimality or goodness. In this work, we propose a joint parcellation-detection-estimation (JPDE) procedure that incorporates an additional parcel estimation step solving this way both the parcellation choice and robust HRF estimation issues. As in [3], inference is carried out in a Bayesian setting using variational approximation techniques for computational efficiency.

Harmony search (HS), as an emerging metaheuristic technique mimicking the improvisation behavior of musicians, has demonstrated strong efficacy in solving various numerical and real-world optimization problems. This work presents a harmony search with differential mutation based pitch adjustment (HSDM) algorithm, which improves the original pitch adjustment operator of HS using the self-referential differential mutation scheme that features differential evolution - another celebrated metaheuristic algorithm. In HSDM, the differential mutation based pitch adjustment can dynamically adapt the properties of the landscapes being explored at different searching stages. Meanwhile, the pitch adjustment operator's execution probability is allowed to vary randomly between 0 and 1, which can maintain both wild and fine exploitation throughout the searching course. HSDM has been evaluated and compared to the original HS and two recent HS variants using 16 numerical test problems of various searching landscape complexities at 10 and 30 dimensions. HSDM almost always demonstrates superiority on all test problems.

In this paper we address the problem of detecting and localizing objects that can be both seen and heard, e.g., people. This may be solved within the framework of data clustering. We propose a new multimodal clustering algorithm based on a Gaussian mixture model, where one of the modalities (visual data) is used to supervise the clustering process. This is made possible by mapping both modalities into the same metric space. To this end, we fully exploit the geometric and physical properties of an audio-visual sensor based on binocular vision and binaural hearing. We propose an EM algorithm that is theoretically well justified, intuitive, and extremely efficient from a computational point of view. This efficiency makes the method implementable on advanced platforms such as humanoid robots. We describe in detail tests and experiments performed with publicly available data sets that yield very interesting results.

SUMMARY: Among classical methods for module detection, SpaCEM(3) provides ad hoc algorithms that were shown to be particularly well adapted to specific features of biological data: high-dimensionality, interactions between components (genes) and integrated treatment of missingness in observations. The software, currently in its version 2.0, is developed in C++ and can be used either via command line or with the GUI under Linux and Windows environments. AVAILABILITY: The SpaCEM(3) software, a documentation and datasets are available from http://spacem3.gforge.inria.fr/.

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space. A solution may consist in considering multiple clustering tasks independently for each modality. The main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent. In this letter, we show that multimodal clustering can be addressed within a novel framework: conjugate mixture models. These models exploit the explicit transformations that are often available between an unobserved parameter space (objects) and each of the observation spaces (sensors). We formulate the problem as a likelihood maximization task and derive the associated conjugate expectation-maximization algorithm. The convergence properties of the proposed algorithm are thoroughly investigated. Several local and global optimization techniques are proposed in order to increase its convergence speed. Two initialization strategies are proposed and compared. A consistent model selection criterion is proposed. The algorithm and its variants are tested and evaluated within the task of 3D localization of several speakers using both auditory and visual data.

This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely, the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyze in detail the associated consequences in terms of estimation of the registration parameters, and propose an optimal method for estimating the rotational and translational parameters based on semidefinite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and compare it both theoretically and experimentally with other robust methods for point registration.

In this paper, we propose an algorithm that recovers binocular disparities in accordance with the surface properties of the scene under consideration. To do so, we estimate the disparity as well as the normals in the disparity space, by setting the two tasks in a unified framework. A novel joint probabilistic model is defined through two random fields to favor both intra field (within neighboring disparities and neighboring normals) and inter field (between disparities and normals) consistency. Geometric contextual information is introduced in the models for both normals and disparities, which is optimized using an appropriate alternating maximization procedure. We illustrate the performance of our approach on synthetic and real data.

UNLABELLED: Clustering of genes into groups sharing common characteristics is a useful exploratory technique for a number of subsequent computational analysis. A wide range of clustering algorithms have been proposed in particular to analyze gene expression data, but most of them consider genes as independent entities or include relevant information on gene interactions in a suboptimal way. We propose a probabilistic model that has the advantage to account for individual data (e.g., expression) and pairwise data (e.g., interaction information coming from biological networks) simultaneously. Our model is based on hidden Markov random field models in which parametric probability distributions account for the distribution of individual data. Data on pairs, possibly reflecting distance or similarity measures between genes, are then included through a graph, where the nodes represent the genes, and the edges are weighted according to the available interaction information. As a probabilistic model, this model has many interesting theoretical features. In addition, preliminary experiments on simulated and real data show promising results and points out the gain in using such an approach. AVAILABILITY: The software used in this work is written in C++ and is available with other supplementary material at http://mistis.inrialpes.fr/people/forbes/transparentia/supplementary.html.

Accurate tissue and structure segmentation of magnetic resonance (MR) brain scans is critical in several applications. In most approaches this task is handled through two sequential steps. We propose to carry out cooperatively both tissue and subcortical structure segmentation by distributing a set of local and cooperative Markov random field (MRF) models Tissue segmentation is performed by partitioning the volume into subvolumes where local MRFs are estimated in cooperation with their neighbors to ensure consistency. Local estimation fits precisely to the local intensity distribution and thus handles nonuniformity of intensity without any bias field modelization. Similarly, subcortical structure segmentation is performed via local MRF models that integrate localization constraints provided by a priori fuzzy description of brain anatomy. Subcortical structure segmentation is not reduced to a subsequent processing step but joined with tissue segmentation: the two procedures cooperate to gradually and conjointly improve model accuracy. We propose a framework to implement this distributed modeling integrating cooperation, coordination, and local model checking in an efficient way. Its evaluation was performed using both phantoms and real 3 T brain scans, showing good results and in particular robustness to nonuniformity and noise with a low computational cost. This original combination of local MRF models, including anatomical knowledge, appears as a powerful and promising approach for MR brain scan segmentation.

In this paper we carry out cooperatively both disparity and object boundary estimation by setting the two tasks in a unified Markovian framework. We introduce a new joint probabilistic model that allows to estimate disparities through a Markov random field model. Boundary estimation then cooperates with disparity estimation to gradually and jointly improve accuracy. The feedback from boundary estimation to disparity estimation is made through the use of an auxiliary field referred to as a displacement field. This field suggests the corrections that need to be applied at disparity discontinuities in order that they align with object boundaries. The joint model reduces to a Markov random field model when considering disparities while it reduces to a Markov chain when focusing on the displacement field. The performance of our approach is illustrated on real stereo images sets, demonstrating the power of this cooperative framework.

This paper describes the acquisition and content of a new multi-modal database. Some tools for making use of the data streams are also presented. The Computational Audio-Visual Analysis (CAVA) database is a unique collection of three synchronised data streams obtained from a binaural microphone pair, a stereoscopic camera pair and a head tracking device. All recordings are made from the perspective of a person; i.e. what would a human with natural head movements see and hear in a given environment. The database is intended to facilitate research into humans' ability to optimise their multi-modal sensory input and fills a gap by providing data that enables human centred audio-visual scene analysis. It also enables 3D localisation using either audio, visual, or audio-visual cues. A total of 50 sessions, with varying degrees of visual and auditory complexity, were recorded. These range from seeing and hearing a single speaker moving in and out of field of view, to moving around a 'cocktail party' style situation, mingling and joining different small groups of people chatting.

International audience

We address the issue of classifying complex data. We focus on three main sources of complexity, namely the high dimensionality of the observed data, the dependencies between these observations and the general nature of the noise model underlying their distribution. We investigate the recent Triplet Markov Fields and propose new models in this class designed for such data and in particular allowing very general noise models. In addition, our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework. One advantage of our models is that whatever the initial complexity of the noise model, parameter estimation can be carried out using state-of-the-art Bayesian clustering techniques under the usual simplifying assumptions. As generative models, they can be seen as an alternative, in the supervised case, to discriminative Conditional Random Fields. Identifiability issues underlying the models in the non supervised case, are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity.

Issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables. Approximations are required, and most of them are based either on simulation methods or on deterministic variational methods. While variational methods provide fast and reasonable approximate estimates in many scenarios, simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost. In this work, we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden Markov random fields (HMRFs). These algorithms can be viewed as stochastic perturbations of variational expectation maximization (VEM) algorithms, which are not tractable for HMRF. We focus more specifically on one of these perturbations and we prove their (almost sure) convergence to the same limit set as the limit set of VEM. In addition, experiments on synthetic and real-world images show that the algorithm performance is very close and sometimes better than that of other existing simulation-based and variational EM-like algorithms.

International audience

Hidden Markov random fields appear naturally in problems such as image segmentation, where an unknown class assignment has to be estimated from the observations at each pixel. Choosing the probabilistic model that best accounts for the observations is an important first step for the quality of the subsequent estimation and analysis. A commonly used selection criterion is the Bayesian Information Criterion (BIC) of Schwarz (1978), but for hidden Markov random fields, its exact computation is not tractable due to the dependence structure induced by the Markov model. We propose approximations of BIC based on the mean field principle of statistical physics. The mean field theory provides approximations of Markov random fields by systems of independent variables leading to tractable computations. Using this principle, we first derive a class of criteria by approximating the Markov distribution in the usual BIC expression as a penalized likelihood. We then rewrite BIC in terms of normalizing constants, also called partition functions, instead of Markov distributions. It enables us to use finer mean field approximations and to derive other criteria using optimal lower bounds for the normalizing constants. To illustrate the performance of our partition function-based approximation of BIC as a model selection criterion, we focus on the preliminary issue of choosing the number of classes before the segmentation task. Experiments on simulated and real data point out our criterion as promising: It takes spatial information into account through the Markov model and improves the results obtained with BIC for independent mixture models.