Hierarchical Probabilistic Framework Research Articles

Bayesian Nonlocal Patch Tensor Factorization for Hyperspectral Image Super-Resolution.

The synthesis of high-resolution (HR) hyperspectral image (HSI) by fusing a low-resolution HSI with a corresponding HR multispectral image has emerged as a prevalent HSI super-resolution (HSR) scheme. Recent researches have revealed that tensor analysis is an emerging tool for HSR. However, most off-the-shelf tensor-based HSR algorithms tend to encounter challenges in rank determination and modeling capacity. To address these issues, we construct nonlocal patch tensors (NPTs) and characterize low-rank structures with coupled Bayesian tensor factorization. It is worth emphasizing that the intrinsic global spectral correlation and nonlocal spatial similarity can be simultaneously explored under the proposed model. Moreover, benefiting from the technique of automatic relevance determination, we propose a hierarchical probabilistic framework based on Canonical Polyadic (CP) factorization, which incorporates a sparsity-inducing prior over the underlying factor matrices. We further develop an effective expectation-maximization-type optimization scheme for framework estimation. In contrast to existing works, the proposed model can infer the latent CP rank of NPT adaptively without tuning parameters. Extensive experiments on synthesized and real datasets illustrate the intrinsic capability of our model in rank determination as well as its superiority in fusion performance.

Detecting sex-linked genes using genotyped individuals sampled in natural populations.

We propose a method, SDpop, able to infer sex-linkage caused by recombination suppression typical of sex chromosomes. The method is based on the modeling of the allele and genotype frequencies of individuals of known sex in natural populations. It is implemented in a hierarchical probabilistic framework, accounting for different sources of error. It allows statistical testing for the presence or absence of sex chromosomes, and detection of sex-linked genes based on the posterior probabilities in the model. Furthermore, for gametologous sequences, the haplotype and level of nucleotide polymorphism of each copy can be inferred, as well as the divergence between them. We test the method using simulated data, as well as data from both a relatively recent and an old sex chromosome system (the plant Silene latifolia and humans) and show that, for most cases, robust predictions are obtained with 5 to 10 individuals per sex.

A hierarchical Bayesian approach for calibration of stochastic material models

AbstractThis article recasts the traditional challenge of calibrating a material constitutive model into a hierarchical probabilistic framework. We consider a Bayesian framework where material parameters are assigned distributions, which are then updated given experimental data. Importantly, in true engineering setting, we are not interested in inferring the parameters for a single experiment, but rather inferring the model parameters over the population of possible experimental samples. In doing so, we seek to also capture the inherent variability of the material from coupon-to-coupon, as well as uncertainties around the repeatability of the test. In this article, we address this problem using a hierarchical Bayesian model. However, a vanilla computational approach is prohibitively expensive. Our strategy marginalizes over each individual experiment, decreasing the dimension of our inference problem to only the hyperparameter—those parameter describing the population statistics of the material model only. Importantly, this marginalization step, requires us to derive an approximate likelihood, for which, we exploit an emulator (built offline prior to sampling) and Bayesian quadrature, allowing us to capture the uncertainty in this numerical approximation. Importantly, our approach renders hierarchical Bayesian calibration of material models computational feasible. The approach is tested in two different examples. The first is a compression test of simple spring model using synthetic data; the second, a more complex example using real experiment data to fit a stochastic elastoplastic model for 3D-printed steel.

Infrastructure-Free Hierarchical Mobile Robot Global Localization in Repetitive Environments

Repetitive or ambiguous environment, where structures are highly similar and distinct geometric features are not sufficient, is one of the critical and challenging scenarios for mobile robots to perform global localization or simultaneous localization and mapping (SLAM) tasks. The robots are easy to get lost or mismatched to wrong places in such environments. The existing solutions either rely heavily on pre-installed infrastructures which are inflexible and expensive or rely on single sensor-based global localization methods whose initialization module is not capable enough to provide distinctive information. Thus, this article proposes a hierarchical probabilistic framework that addresses the problem of infrastructure-free mobile robot global localization in GPS-challenged repetitive environments by leveraging both the measured magnetic field (MF) and Light Detection and Ranging (LiDAR) information. The proposed hierarchical system mainly consists of: 1) coarse localization: MF-based localization and 2) fine localization: LiDAR-based localization (LBL). The ambient MF functions as a substitute for the GPS signal, which is considered not available or severely challenged in indoor/semi-indoor local environments. Based on the pre-built MF database, multiple coarse candidate robot poses can first be determined by the proposed initial pose estimation algorithm, which incorporates multivariate Gaussian observation model and random sample consensus (RANSAC) algorithm. Then, using the obtained multiple candidate poses as initialization, the robot can be localized more accurately by LiDAR-based fine localization. Extensive real-world experiments demonstrate that the proposed system achieves over 95% localization success rate and takes less than 2.0-m average traveling distance to localize the mobile robot.

An ensemble methodology for hierarchical probabilistic electric vehicle load forecasting at regular charging stations

Transportation electrification is a valid option for supporting decarbonization efforts but, at the same time, the growing number of electric vehicles will produce new and unpredictable load conditions for the electrical networks. Accurate electric vehicle load forecasting becomes essential to reduce adverse effects of electric vehicle integration into the grid. In this paper, a methodology dedicated to probabilistic electric vehicle load forecasting for different geographic regions is presented. The hierarchical approach is applied to decompose the problem into sub-problems at low-level regions, which are resolved through standard probabilistic models such as gradient boosted regression trees, quantile regression forests and quantile regression neural networks, coupled with principal component analysis to reduce the dimensionality of the sub-problems. The hierarchical perspective is then finalized to forecast the aggregate load at a high-level geographic region through an ensemble methodology based on a penalized linear quantile regression model. This paper brings, as relevant contributions, the development of hierarchical probabilistic forecasting framework, its comparison with non-hierarchical frameworks, and the assessment of the role of data dimensionality refduction. Extensive experimental results based on actual electric vehicle load data are presented which confirm that the hierarchical approaches increase the skill of probabilistic forecasts up to 9.5% compared with non-hierarchical approaches.

Probabilistic Topic Model for Context-Driven Visual Attention Understanding

Modern computer vision techniques have to deal with vast amounts of visual data, which implies a computational effort that has often to be accomplished in broad and challenging scenarios. The interest in efficiently solving these image and video applications has led researchers to develop methods to expertly drive the corresponding processing to conspicuous regions that either depend on the context or are based on specific requirements. In this paper, we propose a general hierarchical probabilistic framework, independent of the application scenario, and relied on the most outstanding psychological studies about attention and eye movements which support that guidance is not based directly on the information provided by early visual processes but on a contextual representation that arose from them. The approach defines the task of context-driven visual attention as a mixture of latent sub-tasks, which are, in turn, modeled as a combination of specific distributions associated to low-, mid-, and high-level spatio-temporal features. Learning from fixations gathered from human observers, we incorporate an intermediate level between feature extraction and visual attention estimation that enables to obtain comprehensively guiding representations. The experiments show how our proposal successfully learns particularly adapted hierarchical explanations of visual attention in diverse video genres, outperforming several leading models in the literature.

Hierarchical Probabilistic Fusion Framework for Matching and Merging of 3-D Occupancy Maps

Fusing 3-D maps generated by multiple robots in real/semi-real time distributed mapping systems are addressed in this paper. A 3-D occupancy grid-based approach for mapping is utilized to satisfy the real/semi-real time and distributed operating constraints. This paper proposes a novel hierarchical probabilistic fusion framework, which consists of uncertainty modeling, map matching, transformation evaluation, and map merging. Before the fusion of maps, the map features and their uncertainties are explicitly modeled and integrated. For map matching, a two-level probabilistic map matching (PMM) algorithm is developed to include high-level structural and low-level voxel features. In the PMM, the structural uncertainty is first used to generate a coarse matching between the maps and its result is then used to improve the voxel level map matching, resulting in a more efficient and accurate matching between maps with a larger convergence basin. The relative transformation output from PMM algorithm is then evaluated based on the Mahalanobis distance, and the relative entropy filter is used subsequently to integrate the map dissimilarities more accurately, completing the map fusion process. The proposed approach is evaluated using map data collected from both simulated and real environments, and the results validate the accuracy, efficiency, and the support for larger convergence basin of the proposed 3-D occupancy map fusion framework.

Hierarchical Probabilistic Framework for Fetal R-Peak Detection, Using ECG Waveform and Heart Rate Information

The abdominal fetal electrocardiogram (fECG) can provide valuable information about fetal well-being. However, fetal R-peak detection in abdominal fECG recordings is challenging due to the low signal-to-noise ratio (SNR) and the nonstationary nature of the fECG waveform in the abdominal recordings. In this paper, we propose a multichannel hierarchical probabilistic framework for fetal R-peak detection that combines predictive models of the ECG waveform and the heart rate. The performance of our method was evaluated on set-A of the 2013 Physionet/Computing in Cardiology Challenge and compared to the performance of several methods that have been proposed in the literature. The hierarchical probabilistic framework presented in this study outperforms other methods for fetal R-peak detection with a mean overall detection accuracy for set-A of 99.6%. Even for recordings with low SNR our method enables reliable fetal R-peak detection (Ac 99.4%).

Inference of Distribution of Fitness Effects and Proportion of Adaptive Substitutions from Polymorphism Data.

The distribution of fitness effects (DFE) encompasses the fraction of deleterious, neutral, and beneficial mutations. It conditions the evolutionary trajectory of populations, as well as the rate of adaptive molecular evolution (α). Inferring DFE and α from patterns of polymorphism, as given through the site frequency spectrum (SFS) and divergence data, has been a longstanding goal of evolutionary genetics. A widespread assumption shared by previous inference methods is that beneficial mutations only contribute negligibly to the polymorphism data. Hence, a DFE comprising only deleterious mutations tends to be estimated from SFS data, and α is then predicted by contrasting the SFS with divergence data from an outgroup. We develop a hierarchical probabilistic framework that extends previous methods to infer DFE and α from polymorphism data alone. We use extensive simulations to examine the performance of our method. While an outgroup is still needed to obtain an unfolded SFS, we show that both a DFE, comprising both deleterious and beneficial mutations, and α can be inferred without using divergence data. We also show that not accounting for the contribution of beneficial mutations to polymorphism data leads to substantially biased estimates of the DFE and α. We compare our framework with one of the most widely used inference methods available and apply it on a recently published chimpanzee exome data set.

Vascular tree tracking and bifurcation points detection in retinal images using a hierarchical probabilistic model

Background and ObjectiveRetinal vascular tree extraction plays an important role in computer-aided diagnosis and surgical operations. Junction point detection and classification provide useful information about the structure of the vascular network, facilitating objective analysis of retinal diseases. MethodsIn this study, we present a new machine learning algorithm for joint classification and tracking of retinal blood vessels. Our method is based on a hierarchical probabilistic framework, where the local intensity cross sections are classified as either junction or vessel points. Gaussian basis functions are used for intensity interpolation, and the corresponding linear coefficients are assumed to be samples from class-specific Gamma distributions. Hence, a directed Probabilistic Graphical Model (PGM) is proposed and the hyperparameters are estimated using a Maximum Likelihood (ML) solution based on Laplace approximation. ResultsThe performance of proposed method is evaluated using precision and recall rates on the REVIEW database. Our experiments show the proposed approach reaches promising results in bifurcation point detection and classification, achieving 88.67% precision and 88.67% recall rates. ConclusionsThis technique results in a classifier with high precision and recall when comparing it with Xu’s method.

Modeling eye movement patterns to characterize perceptual skill in image-based diagnostic reasoning processes

Experts have a remarkable capability of locating, perceptually organizing, identifying, and categorizing objects in images specific to their domains of expertise. In this article, we present a hierarchical probabilistic framework to discover the stereotypical and idiosyncratic viewing behaviors exhibited with expertise-specific groups. Through these patterned eye movement behaviors we are able to elicit the domain-specific knowledge and perceptual skills from the subjects whose eye movements are recorded during diagnostic reasoning processes on medical images. Analyzing experts’ eye movement patterns provides us insight into cognitive strategies exploited to solve complex perceptual reasoning tasks. An experiment was conducted to collect both eye movement and verbal narrative data from three groups of subjects with different levels or no medical training (eleven board-certified dermatologists, four dermatologists in training and thirteen undergraduates) while they were examining and describing 50 photographic dermatological images. We use a hidden Markov model to describe each subject’s eye movement sequence combined with hierarchical stochastic processes to capture and differentiate the discovered eye movement patterns shared by multiple subjects within and among the three groups. Independent experts’ annotations of diagnostic conceptual units of thought in the transcribed verbal narratives are time-aligned with discovered eye movement patterns to help interpret the patterns’ meanings. By mapping eye movement patterns to thought units, we uncover the relationships between visual and linguistic elements of their reasoning and perceptual processes, and show the manner in which these subjects varied their behaviors while parsing the images. We also show that inferred eye movement patterns characterize groups of similar temporal and spatial properties, and specify a subset of distinctive eye movement patterns which are commonly exhibited across multiple images. Based on the combinations of the occurrences of these eye movement patterns, we are able to categorize the images from the perspective of experts’ viewing strategies in a novel way. In each category, images share similar lesion distributions and configurations. Our results show that modeling with multi-modal data, representative of physicians’ diagnostic viewing behaviors and thought processes, is feasible and informative to gain insights into physicians’ cognitive strategies, as well as medical image understanding.

EXOPLANET POPULATION INFERENCE AND THE ABUNDANCE OF EARTH ANALOGS FROM NOISY, INCOMPLETE CATALOGS

No true extrasolar Earth analog is known. Hundreds of planets have been found around Sun-like stars that are either Earth-sized but on shorter periods, or else on year-long orbits but somewhat larger. Under strong assumptions, exoplanet catalogs have been used to make an extrapolated estimate of the rate at which Sun-like stars host Earth analogs. These studies are complicated by the fact that every catalog is censored by non-trivial selection effects and detection efficiencies, and every property (period, radius, etc.) is measured noisily. Here we present a general hierarchical probabilistic framework for making justified inferences about the population of exoplanets, taking into account survey completeness and, for the first time, observational uncertainties. We are able to make fewer assumptions about the distribution than previous studies; we only require that the occurrence rate density be a smooth function of period and radius (employing a Gaussian process). By applying our method to synthetic catalogs, we demonstrate that it produces more accurate estimates of the whole population than standard procedures based on weighting by inverse detection efficiency. We apply the method to an existing catalog of small planet candidates around G dwarf stars (Petigura et al. 2013). We confirm a previous result that the radius distribution changes slope near Earth's radius. We find that the rate density of Earth analogs is about 0.02 (per star per natural logarithmic bin in period and radius) with large uncertainty. This number is much smaller than previous estimates made with the same data but stronger assumptions.

A Hierarchical Probabilistic Framework for Recognizing Learners’ Interaction Experience Trends and Emotions

We seek to model the users’ experience within an interactive learning environment. More precisely, we are interested in assessing the relationship between learners’ emotional reactions and three trends in the interaction experience, namely,flow: the optimal interaction (a perfect immersion within the task),stuck: the nonoptimal interaction (a difficulty to maintain focused attention), andoff-task: the noninteraction (a dropout from the task). We propose a hierarchical probabilistic framework using a dynamic Bayesian network to model this relationship and to simultaneously recognize the probability of experiencing each trend as well as the emotional responses occurring subsequently. The framework combines three modalitydiagnostic variablesthat sense the learner’s experience including physiology, behavior, and performance,predictive variablesthat represent the current context and the learner’s profile, and adynamic structurethat tracks the evolution of the learner’s experience. An experimental study, with a specifically designed protocol for eliciting the targeted experiences, was conducted to validate our approach. Results revealed that multiple concurrent emotions can be associated with the experiences of flow, stuck, and off-task and that the same trend can be expressed differently from one individual to another. The evaluation of the framework showed promising results in predicting learners’ experience trends and emotional responses.

Hierarchical pose estimation for human gait analysis

Articulated structures like the human body have many degrees of freedom. This makes an evaluation of the configuration's likelihood very challenging. In this work we propose new linked hierarchical graphical models which are able to efficiently evaluate likelihoods of articulated structures by sharing visual primitives. Instead of evaluating all configurations of the human body separately we take advantage of the fact that different configurations of the human body share body parts, and body parts, in turn, share visual primitives. A hierarchical Markov random field is used to integrate the sharing of visual primitives in a probabilistic framework. We propose a scalable hierarchical representation of the human body and show that this representation is especially well suited for human gait analysis from a frontal camera perspective. Furthermore, the results of the evaluation on a gait dataset show that sharing primitives substantially accelerates the evaluation and that our hierarchical probabilistic framework is a robust method for scalable detection of the human body.

Facial Action Unit Recognition by Exploiting Their Dynamic and Semantic Relationships

A system that could automatically analyze the facial actions in real time has applications in a wide range of different fields. However, developing such a system is always challenging due to the richness, ambiguity, and the dynamic nature of facial actions. Although a number of research groups attempt to recognize facial action units (AUs) by either improving facial feature extraction techniques, or the AU classification techniques, these methods often recognize AUs or certain AU combinations individually and statically, ignoring the semantic relationships among AUs and the dynamics of AUs. Hence, these approaches cannot always recognize AUs reliably, robustly, and consistently. In this paper, we propose a novel approach that systematically accounts for the relationships among AUs and their temporal evolutions for AU recognition. Specifically, we use a dynamic Bayesian network (DBN) to model the relationships among different AUs. The DBN provides a coherent and unified hierarchical probabilistic framework to represent probabilistic relationships among various AUs and to account for the temporal changes in facial action development. Within our system, robust computer vision techniques are used to obtain AU measurements. And such AU measurements are then applied as evidence to the DBN for inferring various AUs. The experiments show that the integration of AU relationships and AU dynamics with AU measurements yields significant improvement of AU recognition, especially for spontaneous facial expressions and under more realistic environment including illumination variation, face pose variation, and occlusion.

Active and dynamic information fusion for facial expression understanding from image sequences

This paper explores the use of multisensory information fusion technique with Dynamic Bayesian networks (DBNs) for modeling and understanding the temporal behaviors of facial expressions in image sequences. Our facial feature detection and tracking based on active IR illumination provides reliable visual information under variable lighting and head motion. Our approach to facial expression recognition lies in the proposed dynamic and probabilistic framework based on combining DBNs with Ekman's Facial Action Coding System (FACS) for systematically modeling the dynamic and stochastic behaviors of spontaneous facial expressions. The framework not only provides a coherent and unified hierarchical probabilistic framework to represent spatial and temporal information related to facial expressions, but also allows us to actively select the most informative visual cues from the available information sources to minimize the ambiguity in recognition. The recognition of facial expressions is accomplished by fusing not only from the current visual observations, but also from the previous visual evidences. Consequently, the recognition becomes more robust and accurate through explicitly modeling temporal behavior of facial expression. In this paper, we present the theoretical foundation underlying the proposed probabilistic and dynamic framework for facial expression modeling and understanding. Experimental results demonstrate that our approach can accurately and robustly recognize spontaneous facial expressions from an image sequence under different conditions.