Probabilistic Priors Research Articles

Facies‐constrained transdimensional amplitude versus angle inversion using machine learning assisted priors

ABSTRACTWe present a methodology for seismic inversion that generates high‐resolution models of facies and elastic properties from pre‐stack data. Our inversion algorithm uses a transdimensional approach where, in addition to the layer properties, the number of layers is treated as unknown. In other words, the data itself determine the correct model parameterization, that is, the number of layers. The reversible jump Markov Chain Monte Carlo method is an effective tool to solve such transdimensional problems as it generates models of reservoir properties along with uncertainty estimates. However, current implementations of the reversible jump Markov Chain Monte Carlo algorithms do not account for the non‐Gaussian and multimodal nature of model parameters. The target elastic reservoir properties generally have multimodal and non‐parametric distribution at each location of the model. The number of modes is equal to the number of facies. Taking these factors into account, we extend the reversible jump Markov Chain Monte Carlo algorithm to simultaneously invert for discrete facies and continuous elastic reservoir properties. The proposed extension to the algorithm iteratively samples the facies, by moving from one mode to another, and elastic properties by sampling within the same mode. The integration of facies classification within the inversion reduces non‐uniqueness, improves convergence speed and produces geologically consistent results. The workflow uses machine learning to generate probabilistic priors for the model parameters. We validate our approach by applying it to a synthetic dataset generated from a well log with two facies and then to a complex synthetic two‐dimensional model involving three facies having overlapping elastic property distribution. Finally, we apply our algorithm to a field dataset acquired over an unconventional reservoir. Our algorithm demonstrates the usefulness of incorporating facies information in seismic inversion and also the feasibility of inverting for facies from seismic data.

Integrating Semantic Awareness and Probabilistic Priors for Object Search in Indoor Environments

Integrating Semantic Awareness and Probabilistic Priors for Object Search in Indoor Environments

Entropy-Based Estimation of Event-Related De/Synchronization in Motor Imagery Using Vector-Quantized Patterns.

Assessment of brain dynamics elicited by motor imagery (MI) tasks contributes to clinical and learning applications. In this regard, Event-Related Desynchronization/Synchronization (ERD/S) is computed from Electroencephalographic signals, which show considerable variations in complexity. We present an Entropy-based method, termed VQEnt, for estimation of ERD/S using quantized stochastic patterns as a symbolic space, aiming to improve their discriminability and physiological interpretability. The proposed method builds the probabilistic priors by assessing the Gaussian similarity between the input measured data and their reduced vector-quantized representation. The validating results of a bi-class imagine task database (left and right hand) prove that VQEnt holds symbols that encode several neighboring samples, providing similar or even better accuracy than the other baseline sample-based algorithms of Entropy estimation. Besides, the performed ERD/S time-series are close enough to the trajectories extracted by the variational percentage of EEG signal power and fulfill the physiological MI paradigm. In BCI literate individuals, the VQEnt estimator presents the most accurate outcomes at a lower amount of electrodes placed in the sensorimotor cortex so that reduced channel set directly involved with the MI paradigm is enough to discriminate between tasks, providing an accuracy similar to the performed by the whole electrode set.

Group adaptive matching pursuit with intra-group correlation learning for sparse signal recovery

In this paper, a Bayesian model is adopted for sparse signal recovery where sparsity is enforced on the reconstructed coefficients via probabilistic priors. In particular, we focus on a group spike-and-slab prior and a kernel matrix which capture both the underlying group structure and the element correlation within groups. A novel greedy based group adaptive matching pursuit (GAMP) algorithm is introduced, which integrates both prior parameter learning and intra-group correlation parameter learning into one single problem. The proposed approach improves the reconstruction accuracy and offers strong robustness to signal-to-noise ratio. We consider a fast implementation method of GAMP which applies the preconditioned conjugate gradient method. Simulations, MNIST dataset based experiments and multi-static radar imaging application are used to verify the superior performance of the proposed method over existing techniques.

Adaptive Bayesian label fusion using kernel-based similarity metrics in hippocampus segmentation.

The effectiveness of brain magnetic resonance imaging (MRI) as a useful evaluation tool strongly depends on the performed segmentation of associated tissues or anatomical structures. We introduce an enhanced brain segmentation approach of Bayesian label fusion that includes the construction of adaptive target-specific probabilistic priors using atlases ranked by kernel-based similarity metrics to deal with the anatomical variability of collected MRI data. In particular, the developed segmentation approach appraises patch-based voxel representation to enhance the voxel embedding in spaces with increased tissue discrimination, as well as the construction of a neighborhood-dependent model that addresses the label assignment of each region with a different patch complexity. To measure the similarity between the target and training atlases, we propose a tensor-based kernel metric that also includes the training labeling set. We evaluate the proposed approach, adaptive Bayesian label fusion using kernel-based similarity metrics, in the specific case of hippocampus segmentation of five benchmark MRI collections, including ADNI dataset, resulting in an increased performance (assessed through the Dice index) as compared to other recent works.

Student's t Source and Mixing Models for Multichannel Audio Source Separation

This paper presents a Bayesian framework for under-determined audio source separation in multichannel reverberant mixtures. We model the source signals as Student's t latent random variables in a time-frequency domain. The specific structure of musical signals in this domain is exploited by means of a nonnegative matrix factorization model. Conversely, we design the mixing model in the time domain. In addition to leading to an exact representation of the convolutive mixing process, this approach allows us to develop simple probabilistic priors for the mixing filters. Indeed, as those filters correspond to room responses they exhibit a simple characteristic structure in the time domain that can be used to guide their estimation. We also rely on the Student's t distribution for modeling the impulse response of the mixing filters. From this model, we develop a variational inference algorithm in order to perform source separation. The experimental evaluation demonstrates the potential of this approach for separating multichannel reverberant mixtures.

Game-theoretic modeling of players’ ambiguities on external factors

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players’ preferences on return-distribution vectors, essentially mappings from states of the world to distributions of returns to be received by players. There are two ways in which equilibria for this preference game can be defined. Also, when the preferences possess ever more features, we can gradually add more structures to the game. These include real-valued functions over return-distribution vectors, sets of probabilistic priors over states of the world, and eventually the traditional expected-utility framework involving one single prior. We establish equilibrium existence results, show the upper hemi-continuity of equilibrium sets over changing ambiguity attitudes, and uncover relations between the two versions of equilibria. Some attention is paid to the enterprising game, in which players exhibit ambiguity-seeking attitudes while betting optimistically on the favorable resolution of ambiguities. The two solution concepts are unified at this game’s pure equilibria, whose existence is guaranteed when strategic complementarities are present. The current framework can be applied to settings like auctions involving ambiguity on competitors’ assessments of item worths.

Game-Theoretic Modeling of Players’ Ambiguities on External Factors

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on return-distribution vectors, essentially mappings from states of the world to distributions of returns to be received by players. There are two ways in which equilibria for this preference game can be defined. Also, when the preferences possess ever more features, we can gradually add more structures to the game. These include real-valued functions over return-distribution vectors, sets of probabilistic priors over states of the world, and eventually the traditional expected-utility framework involving one single prior. We establish equilibrium existence results, show the upper hemi-continuity of equilibrium sets over changing ambiguity attitudes, and uncover relations between the two versions of equilibria. Some attention is paid to the enterprising game, in which players exhibit ambiguity-seeking attitudes while betting optimistically on the favorable resolution of ambiguities. The two solution concepts are unified at this game's pure equilibria, whose existence is guaranteed when strategic complementarities are present. The current framework can be applied to settings like auctions involving ambiguity on competitors' assessments of item worths.

Discovering spatio-temporal dependencies based on time-lag in intelligent transportation data

Learning spatio-temporal dependency structure is meaningful to characterize causal or statistical relationships. In many real-world applications, dependency structure is often characterized by time-lag between variables. For example, traffic system and climate, time lag is a key feature of hidden temporal dependencies, and plays an essential role in interpreting the cause of discovered temporal dependencies. However, traditional dependencies learning algorithms only use the same time stamp data of variables. In this paper, we propose a method for mining dependencies by considering the time lag. The proposed approach is based on a decomposition of the coefficients into products of two-level hierarchical coefficients, where one represents feature-level and the other represents time-level. Specially, we capture the prior information of time lag in intelligent transportation data. We construct a probabilistic formulation by applying some probabilistic priors to these hierarchical coefficients, and devise an expectation-maximization (EM) algorithm to learn the model parameters. We evaluate our model on both synthetic and real-world highway traffic datasets. Experimental results show the effectiveness of our method.

Multichannel Audio Source Separation With Probabilistic Reverberation Priors

Incorporating prior knowledge about the sources and/or the mixture is a way to improve under-determined audio source separation performance. A great number of informed source separation techniques concentrate on taking priors on the sources into account, but fewer works have focused on constraining the mixing model. In this paper, we address the problem of underdetermined multichannel audio source separation in reverberant conditions. We target a semi-informed scenario where some room parameters are known. Two probabilistic priors on the frequency response of the mixing filters are proposed. Early reverberation is characterized by an autoregressive model while according to statistical room acoustics results, late reverberation is represented by an autoregressive moving average model. Both reverberation models are defined in the frequency domain. They aim to transcribe the temporal characteristics of the mixing filters into frequency-domain correlations. Our approach leads to a maximum a posteriori estimation of the mixing filters which is achieved thanks to the expectation-maximization algorithm. We experimentally show the superiority of this approach compared with a maximum likelihood estimation of the mixing filters.

The average baboon brain: MRI templates and tissue probability maps from 89 individuals

The baboon (Papio) brain is a remarkable model for investigating the brain. The current work aimed at creating a population-average baboon (Papio anubis) brain template and its left/right hemisphere symmetric version from a large sample of T1-weighted magnetic resonance images collected from 89 individuals. Averaging the prior probability maps output during the segmentation of each individual also produced the first baboon brain tissue probability maps for gray matter, white matter and cerebrospinal fluid. The templates and the tissue probability maps were created using state-of-the-art, freely available software tools and are being made freely and publicly available: http://www.nitrc.org/projects/haiko89/ or http://lpc.univ-amu.fr/spip.php?article589. It is hoped that these images will aid neuroimaging research of the baboon by, for example, providing a modern, high quality normalization target and accompanying standardized coordinate system as well as probabilistic priors that can be used during tissue segmentation.

Iterative Convex Refinement for Sparse Recovery

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, and existing solutions involve simplifying assumptions and/or relaxations. We propose an approach called Iterative Convex Refinement (ICR) that aims to solve the aforementioned optimization problem directly allowing for greater generality in the sparse structure. Essentially, ICR solves a sequence of convex optimization problems such that sequence of solutions converges to a sub-optimal solution of the original hard optimization problem. We propose two versions of our algorithm: a.) an unconstrained version, and b.) with a non-negativity constraint on sparse coefficients, which may be required in some real-world problems. Experimental validation is performed on both synthetic data and for a real-world image recovery problem, which illustrates merits of ICR over state of the art alternatives.

Spatial location priors for Gaussian model based reverberant audio source separation

Abstract We consider the Gaussian framework for reverberant audio source separation, where the sources are modeled in the time-frequency domain by their short-term power spectra and their spatial covariance matrices. We propose two alternative probabilistic priors over the spatial covariance matrices which are consistent with the theory of statistical room acoustics and we derive expectation-maximization algorithms for maximum a posteriori (MAP) estimation. We argue that these algorithms provide a statistically principled solution to the permutation problem and to the risk of overfitting resulting from conventional maximum likelihood (ML) estimation. We show experimentally that in a semi-informed scenario where the source positions and certain room characteristics are known, the MAP algorithms outperform their ML counterparts. This opens the way to rigorous statistical treatment of this family of models in other scenarios in the future.

Continuous Shape Estimation of Continuum Robots Using X-ray Images.

We present a new method for continuously and accurately estimating the shape of a continuum robot during a medical procedure using a small number of X-ray projection images (e.g., radiographs or fluoroscopy images). Continuum robots have curvilinear structure, enabling them to maneuver through constrained spaces by bending around obstacles. Accurately estimating the robot's shape continuously over time is crucial for the success of procedures that require avoidance of anatomical obstacles and sensitive tissues. Online shape estimation of a continuum robot is complicated by uncertainty in its kinematic model, movement of the robot during the procedure, noise in X-ray images, and the clinical need to minimize the number of X-ray images acquired. Our new method integrates kinematics models of the robot with data extracted from an optimally selected set of X-ray projection images. Our method represents the shape of the continuum robot over time as a deformable surface which can be described as a linear combination of time and space basis functions. We take advantage of probabilistic priors and numeric optimization to select optimal camera configurations, thus minimizing the expected shape estimation error. We evaluate our method using simulated concentric tube robot procedures and demonstrate that obtaining between 3 and 10 images from viewpoints selected by our method enables online shape estimation with errors significantly lower than using the kinematic model alone or using randomly spaced viewpoints.

Line spectrum estimation with probabilistic priors

For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises distribution that can parameterize the entire range of prior certainty of the frequencies. An efficient alternating projections method is used to solve the resulting optimization problem. The estimator is evaluated numerically and compared with other estimators and the Cramér-Rao bound.

The 6th Computational Structural Bioinformatics Workshop

The rapid accumulation of macromolecular structures presents a unique set of challenges and opportunities in the analysis, comparison, modeling, and prediction of macromolecular structures and interactions. The 6th Computational Structural Bioinformatics Workshop (CSBW) was held in Philadelphia on October 4, 2012. This issue includes eleven papers selected from the work presented at the CSBW of 2012. In "Four-body atomic potential for modeling protein-ligand binding affinity: application to enzyme-inhibitor binding energy prediction", a predictive model of free-energy was built to evaluate the binding between a protein and a ligand. In "Unbiased, scalable sampling of protein loop conformations from probabilistic priors", a new Markov chain Monte Carlo algorithm was proposed to generate unbiased conformations of closed protein loops from probabilistic priors. In "Enhancement of accuracy and efficiency for RNA secondary structure prediction by sequence segmentation and MapReduce", authors demonstrate an enhanced method by cutting a long RNA sequence into smaller chunks at strategically selected points, and distributing the tasks to multiple processors. In "A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction", the authors present an evolutionary search algorithm to obtain a discrete representation of the protein energy surface in terms of an ensemble of conformations representing local energy minima. In "Estimating loop length from Cryo-EM images at medium resolutions", the authors developed a computational geometry method to simplify the points along the skeleton to measure loop length in 3D images. The paper "A conservation and rigidity based method for detecting critical protein residues" presents a method that combines the rigidity and the evolutionary conservation in detection of the critical residues. In "A conservation and biophysics guided stochastic approach to refining docked multimeric proteins", the authors introduce a refinement method that accepts complexes consisting of any number of monomeric units. In "Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method," the authors present a robotics-inspired tree-based method to sample energetically-credible conformational pathways connecting diverse functional states in multimodal proteins. The paper "An aggregate analysis of many predicted structures to reduce errors in protein structure comparison caused by conformational flexibility" applies protein structure prediction algorithms to enhance the classification of homologous proteins according to their binding preferences. In "DINC: A new AutoDock-based protocol for docking large ligands", an enhanced method was demonstrated for docking large ligands. The paper "Modeling protein conformational transitions by a combination of coarse-grained normal mode analysis and robotics-inspired methods" presents an efficient approach involving robotics concepts.

Unbiased, scalable sampling of protein loop conformations from probabilistic priors.

BackgroundProtein loops are flexible structures that are intimately tied to function, but understanding loop motion and generating loop conformation ensembles remain significant computational challenges. Discrete search techniques scale poorly to large loops, optimization and molecular dynamics techniques are prone to local minima, and inverse kinematics techniques can only incorporate structural preferences in adhoc fashion. This paper presents Sub-Loop Inverse Kinematics Monte Carlo (SLIKMC), a new Markov chain Monte Carlo algorithm for generating conformations of closed loops according to experimentally available, heterogeneous structural preferences.ResultsOur simulation experiments demonstrate that the method computes high-scoring conformations of large loops (>10 residues) orders of magnitude faster than standard Monte Carlo and discrete search techniques. Two new developments contribute to the scalability of the new method. First, structural preferences are specified via a probabilistic graphical model (PGM) that links conformation variables, spatial variables (e.g., atom positions), constraints and prior information in a unified framework. The method uses a sparse PGM that exploits locality of interactions between atoms and residues. Second, a novel method for sampling sub-loops is developed to generate statistically unbiased samples of probability densities restricted by loop-closure constraints.ConclusionNumerical experiments confirm that SLIKMC generates conformation ensembles that are statistically consistent with specified structural preferences. Protein conformations with 100+ residues are sampled on standard PC hardware in seconds. Application to proteins involved in ion-binding demonstrate its potential as a tool for loop ensemble generation and missing structure completion.

Object affordances tune observers' prior expectations about tool-use behaviors.

Learning about the function and use of tools through observation requires the ability to exploit one's own knowledge derived from past experience. It also depends on the detection of low-level local cues that are rooted in the tool's perceptual properties. Best known as ‘affordances’, these cues generate biomechanical priors that constrain the number of possible motor acts that are likely to be performed on tools. The contribution of these biomechanical priors to the learning of tool-use behaviors is well supported. However, it is not yet clear if, and how, affordances interact with higher-order expectations that are generated from past experience – i.e. probabilistic exposure – to enable observational learning of tool use. To address this question we designed an action observation task in which participants were required to infer, under various conditions of visual uncertainty, the intentions of a demonstrator performing tool-use behaviors. Both the probability of observing the demonstrator achieving a particular tool function and the biomechanical optimality of the observed movement were varied. We demonstrate that biomechanical priors modulate the extent to which participants' predictions are influenced by probabilistically-induced prior expectations. Biomechanical and probabilistic priors have a cumulative effect when they ‘converge’ (in the case of a probabilistic bias assigned to optimal behaviors), or a mutually inhibitory effect when they actively ‘diverge’ (in the case of probabilistic bias assigned to suboptimal behaviors).

Finding combinatorial histone code by semi-supervised biclustering

BackgroundCombinatorial histone modification is an important epigenetic mechanism for regulating chromatin state and gene expression. Given the rapid accumulation of genome-wide histone modification maps, there is a pressing need for computational methods capable of joint analysis of multiple maps to reveal combinatorial modification patterns.ResultsWe present the Semi-Supervised Coherent and Shifted Bicluster Identification algorithm (SS-CoSBI). It uses prior knowledge of combinatorial histone modifications to guide the biclustering process. Specifically, co-occurrence frequencies of histone modifications characterized by mass spectrometry are used as probabilistic priors to adjust the similarity measure in the biclustering process. Using a high-quality set of transcriptional enhancers and associated histone marks, we demonstrate that SS-CoSBI outperforms its predecessor by finding histone modification and genomic locus biclusters with higher enrichment of enhancers. We apply SS-CoSBI to identify multiple cell-type-specific combinatorial histone modification states associated with human enhancers. We show enhancer histone modification states are correlated with the expression of nearby genes. Further, we find that enhancers with the histone mark H3K4me1 have higher levels of DNA methylation and decreased expression of nearby genes, suggesting a functional interplay between H3K4me1 and DNA methylation that can modulate enhancer activities.ConclusionsThe analysis presented here provides a systematic characterization of combinatorial histone codes of enhancers across three human cell types using a novel semi-supervised biclustering algorithm. As epigenomic maps accumulate, SS-CoSBI will become increasingly useful for understanding combinatorial chromatin modifications by taking advantage of existing knowledge.Availability and implementationSS-CoSBI is implemented in C. The source code is freely available at http://www.healthcare.uiowa.edu/labs/tan/SS-CoSBI.gz.

Cooperative Object Segmentation and Behavior Inference in Image Sequences

In this paper, we propose a general framework for fusing bottom-up segmentation with top-down object behavior inference over an image sequence. This approach is beneficial for both tasks, since it enables them to cooperate so that knowledge relevant to each can aid in the resolution of the other, thus enhancing the final result. In particular, the behavior inference process offers dynamic probabilistic priors to guide segmentation. At the same time, segmentation supplies its results to the inference process, ensuring that they are consistent both with prior knowledge and with new image information. The prior models are learned from training data and they adapt dynamically, based on newly analyzed images. We demonstrate the effectiveness of our framework via particular implementations that we have employed in the resolution of two hand gesture recognition applications. Our experimental results illustrate the robustness of our joint approach to segmentation and behavior inference in challenging conditions involving complex backgrounds and occlusions of the target object.