Empirical Bayesian Inference Research Articles

A Metabolomics Approach to Identify Metabolites Associated With Mortality in Patients Receiving Maintenance Hemodialysis

BackgroundUremic toxins contributing to increased risk of death remain largely unknown. We used untargeted metabolomics to identify plasma metabolites associated with mortality in patients receiving maintenance hemodialysis. MethodsWe measured metabolites in serum samples from 522 Longitudinal US/Canada Incident Dialysis (LUCID) study participants. We assessed the association between metabolites and 1-year mortality, adjusting for age, sex, race, cardiovascular disease, diabetes, body mass index, serum albumin, Kt/Vurea, dialysis duration, and country. We modeled these associations using limma, a metabolite-wise linear model with empirical Bayesian inference, and two machine learning (ML) models: LASSO and random forest (RF). We accounted for multiple testing using a false discovery rate (pFDR) adjustment. We defined significant mortality-metabolite associations as pFDR<0.1 in the limma model and metabolites of at least medium importance in both ML models. ResultsThe mean age of the participants was 64 years, the mean dialysis duration was 35 days, and there were 44 deaths (8.4%) during a 1-year follow-up period. Two metabolites were significantly associated with 1-year mortality. Quinolinate levels (kynurenine pathway metabolite) were 1.72-fold higher in patients who died by year 1 compared to those who did not (pFDR, 0.009), while mesaconate levels (an emerging immunometabolite) were 1.57-fold higher (pFDR, 0.002). An additional 42 metabolites had high importance by LASSO, 46 by RF, and 9 by both ML models but were not significant by limma. ConclusionQuinolinate and mesaconate were significantly associated with a 1-year risk of death in incident patients receiving maintenance hemodialysis. External validation of our findings is needed.

Finite sample inference for empirical Bayesian methods

AbstractIn recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real‐life problems, especially in complex and high‐dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the Universal Inference framework, we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts.

Empirical Bayesian Inference Using a Support Informed Prior

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors of noisy observable data. Specifically, by exploiting the joint sparsity across the multiple measurements in the sparse domain of the underlying signal or image, we construct a new support informed prior. Several applications can be modeled using this framework, including synthetic aperture radar observations using nearby azimuth angles and parallel magnetic resonance imaging. Our numerical experiments suggest that using the support informed prior usually improves accuracy of the recovery in the form of the sampled posterior mean and reduces its uncertainty when compared to posteriors constructed using some more standard priors.

A metabolomics approach identified toxins associated with uremic symptoms in advanced chronic kidney disease

Uremic symptoms are common in patients with advanced chronic kidney disease, but the toxins that cause these symptoms are unknown. To evaluate this, we performed a cross-sectional study of the 12 month post-randomization follow-up visit of Modification of Diet in Renal Disease (MDRD) participants reporting uremic symptoms who also had available stored serum. We quantified 1,163 metabolites by liquid chromatography-tandem mass spectrometry. For each uremic symptom, we calculated a score as the severity multiplied by the number of days the symptom was experienced. We analyzed the associations of the individual symptom scores with metabolites using linear models with empirical Bayesian inference, adjusted for multiple comparisons. Among 695 participants, the mean measured glomerular filtration rate (mGFR) was 28 mL/min/1.73 m2. Uremic symptoms were more common in the subgroup of 214 patients with an mGFR under 20 mL/min/1.73 m2 (mGFR under 20 subgroup) than in the full group. For all metabolites with significant associations, the direction of the association was concordant in the full group and the subgroup. For gastrointestinal symptoms (bad taste, loss of appetite, nausea, and vomiting), eleven metabolites were associated with symptoms. For neurologic symptoms (decreased alertness, falling asleep during the day, forgetfulness, lack of pep and energy, and tiring easily/weakness), seven metabolites were associated with symptoms. Associations were consistent across sensitivity analyses. Thus, our proof-of-principle study demonstrates the potential for metabolomics to understand metabolic pathways associated with uremic symptoms. Larger, prospective studies with external validation are needed.

Comparing Bayesian models for simultaneity judgement with different causal assumptions

In recent years, Bayesian causal inference has emerged as a computational principle for multisensory integration; it considers the causal relationships of multisensory stimuli and combines stimuli only when they are causally related. Many empirical studies have confirmed the predictions of Bayesian causal inference models and have begun to reveal the neural mechanisms of their computations. However, some studies have suggested that Bayesian causal inference does not always hold, and it is still unclear if Bayesian causal inference is a general computational principle or whether it simply represents a limited range of multisensory integration. Most theoretical and empirical Bayesian causal inference studies have focused on the binary judgement of pairs of multisensory stimuli or sequences of stimuli. One empirical study presented a more complex case with one auditory stimulus and two visual stimuli. In this study, I propose three Bayesian causal models with different causal structures regarding the same scenario. The first model assumes that an auditory stimulus is integrated with a visual stimulus only when they share the same source. During model derivation, I present a hierarchical formulation of causal structural priors in complex situations with multiple number of audio-visual stimuli. The second model assumes that an auditory stimulus is forcibly integrated with one of two visual stimuli. The third model assumes that all three stimuli are forcibly integrated. First, with minimum assumptions, I demonstrated that the full causal model explains existing experimental results better than the other two models. Meanwhile, by introducing another modelling parameter for simultaneity judgement criterion in different experimental conditions, the extended versions of the other two models also described the experimental results almost as accurately as the full causal model. It was confirmed that all three models explain the empirical results of simultaneity judgements of audio-visual stimuli, as well as the enhancement of sensitivity, to some degree. Although these models are difficult to distinguish based on existing data, they provide different interpretations of the underlying mechanisms of empirical findings. Additionally, I demonstrated that these models make qualitatively different predictions, and presented experimental manipulations that can distinguish the models based on the underlying causal structures of multiple multisensory stimuli.

Sparse Bayesian Learning for Robust PCA: Algorithms and Analyses

In this paper, we propose a new Bayesian model to solve the Robust PCA problem - recovering the underlying low-rank matrix and sparse matrix from their noisy compositions. We first derive and analyze a new objective function, which is proven to be equivalent to the fundamental objective of minimizing the “rank+sparsity”. To solve this objective, we develop a concise Sparse Bayesian Learning (SBL) method that makes minimal assumptions and effectively deals with the requirements of the problem. The concise modeling allows simple and effective Empirical Bayesian inference via maximum a posteriori expectation-maximization (MAP-EM). We further propose a modified SBL method that additionally utilizes the sparsity pattern information of the outliers in the Robust PCA problem. Simulation studies demonstrate the superiority of the proposed methods over the existing state-of-the-art methods. The efficacy of the proposed methods is further verified through two image processing tasks.

Improved cuckoo search load distribution (ICS‐LD) and attack detection in cloud environment

SummaryFor the purpose of obtaining an answer to a spoofing IP issue and related problems in the cloud computing (CC) environment, a novel path identifier is recommended, in which a new packet approach with a new identifier (ID) is produced to every user or client system. For the purpose of identification of the spoofing attack, any watermark image pattern is introduced. Following this, the hypervisor is employed to ascertain plausible trust relationships among the VMs by considering personal sources that can be trusted along with utilizing empirical Bayesian inference (EBI) for the purpose of combining the VMs. With a restricted budget of resources for the maximized detection of attacks, an optimal detection load distribution strategy by improved cuckoo search (ICS) over VMs can be used, which thus provides the intended solution to the hypervisor. The ICS algorithm directs a hypervisor so as to assert among the VMs the optimal load distribution, taking into consideration real time, which causes maximization of the DDoS attacks and detection of transmission control protocol (TCP) flood attacks. Lastly, a fuzzy extreme learning machine (FELM) classifier is proposed in order to detect the attacks.

Species trees from consensus single nucleotide polymorphism (SNP) data: Testing phylogenetic approaches with simulated and empirical data

Datasets of hundreds or thousands of SNPs (Single Nucleotide Polymorphisms) from multiple individuals per species are increasingly used to study population structure, species delimitation and shallow phylogenetics. The principal software tool to infer species or population trees from SNP data is currently the BEAST template SNAPP which uses a Bayesian coalescent analysis. However, it is computationally extremely demanding and tolerates only small amounts of missing data. We used simulated and empirical SNPs from plants (Australian Craspedia, Asteraceae, and Pelargonium, Geraniaceae) to compare species trees produced (1) by SNAPP, (2) using SVD quartets, and (3) using Bayesian and parsimony analysis with several different approaches to summarising data from multiple samples into one set of traits per species. Our aims were to explore the impact of tree topology and missing data on the results, and to test which data summarising and analyses approaches would best approximate the results obtained from SNAPP for empirical data. SVD quartets retrieved the correct topology from simulated data, as did SNAPP except in the case of a very unbalanced phylogeny. Both methods failed to retrieve the correct topology when large amounts of data were missing. Bayesian analysis of species level summary data scoring the two alleles of each SNP as independent characters and parsimony analysis of data scoring each SNP as one character produced trees with branch length distributions closest to the true trees on which SNPs were simulated. For empirical data, Bayesian inference and Dollo parsimony analysis of data scored allele-wise produced phylogenies most congruent with the results of SNAPP. In the case of study groups divergent enough for missing data to be phylogenetically informative (because of additional mutations preventing amplification of genomic fragments or bioinformatic establishment of homology), scoring of SNP data as a presence/absence matrix irrespective of allele content might be an additional option. As this depends on sampling across species being reasonably even and a random distribution of non-informative instances of missing data, however, further exploration of this approach is needed. Properly chosen data summary approaches to inferring species trees from SNP data may represent a potential alternative to currently available individual-level coalescent analyses especially for quick data exploration and when dealing with computationally demanding or patchy datasets.

Learning Non-Linear Dynamics of Decision Boundaries for Maintaining Classification Performance

We propose a method that involves a probabilistic model for learning future classifiers for tasks in which decision boundaries nonlinearly change over time. In certain applications, such as spam-mail classification, the decision boundary dynamically changes over time. Accordingly, the performance of the classifiers will deteriorate quickly unless the classifiers are updated using additional data. However, collecting such data can be expensive or impossible. The proposed model alleviates this deterioration in performance without additional data by modeling the non-linear dynamics of the decision boundary using Gaussian processes. The method also involves our developed learning algorithm for our model based on empirical variational Bayesian inference by which uncertainty of dynamics can be incorporated for future classification. The effectiveness of the proposed method was demonstrated through experiments using synthetic and real-world data sets.

Simple exponential family PCA.

Principal component analysis (PCA) is a widely used model for dimensionality reduction. In this paper, we address the problem of determining the intrinsic dimensionality of a general type data population by selecting the number of principal components for a generalized PCA model. In particular, we propose a generalized Bayesian PCA model, which deals with general type data by employing exponential family distributions. Model selection is realized by empirical Bayesian inference of the model. We name the model as simple exponential family PCA (SePCA), since it embraces both the principal of using a simple model for data representation and the practice of using a simplified computational procedure for the inference. Our analysis shows that the empirical Bayesian inference in SePCA formally realizes an intuitive criterion for PCA model selection - a preserved principal component must sufficiently correlate to data variance that is uncorrelated to the other principal components. Experiments on synthetic and real data sets demonstrate effectiveness of SePCA and exemplify its characteristics for model selection.

A probabilistic model for predicting the probability of no-show in hospital appointments

The number of no-shows has a significant impact on the revenue, cost and resource utilization for almost all healthcare systems. In this study we develop a hybrid probabilistic model based on logistic regression and empirical Bayesian inference to predict the probability of no-shows in real time using both general patient social and demographic information and individual clinical appointments attendance records. The model also considers the effect of appointment date and clinic type. The effectiveness of the proposed approach is validated based on a patient dataset from a VA medical center. Such an accurate prediction model can be used to enable a precise selective overbooking strategy to reduce the negative effect of no-shows and to fill appointment slots while maintaining short wait times.

ConSurf 2010: calculating evolutionary conservation in sequence and structure of proteins and nucleic acids

It is informative to detect highly conserved positions in proteins and nucleic acid sequence/structure since they are often indicative of structural and/or functional importance. ConSurf (http://consurf.tau.ac.il) and ConSeq (http://conseq.tau.ac.il) are two well-established web servers for calculating the evolutionary conservation of amino acid positions in proteins using an empirical Bayesian inference, starting from protein structure and sequence, respectively. Here, we present the new version of the ConSurf web server that combines the two independent servers, providing an easier and more intuitive step-by-step interface, while offering the user more flexibility during the process. In addition, the new version of ConSurf calculates the evolutionary rates for nucleic acid sequences. The new version is freely available at: http://consurf.tau.ac.il/.

Discrete visual features modeling via leave-one-out likelihood estimation and applications

Discrete data are an important component in many image processing and computer vision applications. In this work we propose an unsupervised statistical approach to learn structures of this kind of data. The central ingredient in our model is the introduction of the generalized Dirichlet distribution as a prior to the multinomial. An estimation algorithm, based on leave-one-out likelihood and empirical Bayesian inference, for the parameters is developed. This estimation algorithm can be viewed as a hybrid expectation–maximization (EM) which alternates EM iterations with Newton–Raphson iterations using the Hessian matrix. We propose then the use of our model as a parametric basis for support vector machines within a hybrid generative/discriminative framework. In a series of experiments involving scene modeling and classification using visual words, and color texture modeling we show the efficiency of the proposed approach.

The ConSurf-DB: pre-calculated evolutionary conservation profiles of protein structures

ConSurf-DB is a repository for evolutionary conservation analysis of the proteins of known structures in the Protein Data Bank (PDB). Sequence homologues of each of the PDB entries were collected and aligned using standard methods. The evolutionary conservation of each amino acid position in the alignment was calculated using the Rate4Site algorithm, implemented in the ConSurf web server. The algorithm takes into account the phylogenetic relations between the aligned proteins and the stochastic nature of the evolutionary process explicitly. Rate4Site assigns a conservation level for each position in the multiple sequence alignment using an empirical Bayesian inference. Visual inspection of the conservation patterns on the 3D structure often enables the identification of key residues that comprise the functionally important regions of the protein. The repository is updated with the latest PDB entries on a monthly basis and will be rebuilt annually. ConSurf-DB is available online at http://consurfdb.tau.ac.il/

The mirror-neuron system: a Bayesian perspective

Is it possible to understand the intentions of other people by simply observing their movements? Many neuroscientists believe that this ability depends on the brain's mirror-neuron system, which provides a direct link between action and observation. Precisely how intentions can be inferred through movement-observation, however, has provoked much debate. One problem in inferring the cause of an observed action, is that the problem is ill-posed because identical movements can be made when performing different actions with different goals. Here we suggest that this problem is solved by the mirror-neuron system using predictive coding on the basis of a statistical approach known as empirical Bayesian inference. This means that the most likely cause of an observed movement can be inferred by minimizing the prediction error at all cortical levels that are engaged during movement observation. This account identifies a precise role for the mirror-neuron system in our ability to infer intentions from observed movement and outlines possible computational mechanisms.

Optimising newspaper sales using neural-Bayesian technology

We describe a software system, called just enough delivery (JED), for optimising single-copy newspaper sales, based on a combination of neural and Bayesian technology. The prediction model is a huge feedforward neural network, in which each output corresponds to the sales prediction for a single outlet. Input-to-hidden weights are shared between outlets. The hidden-to-output weights are specific to each outlet, but linked through the introduction of priors. All weights and hyperparameters can be inferred using (empirical) Bayesian inference. The system has been tested on data for several different newspapers and magazines. Consistent performance improvements of 1 to 3% more sales with the same total amount of deliveries have been obtained.

Adaptive CFAR detection for clutter-edge heterogeneity using Bayesian inference

Radar constant false alarm rate (CFAR) detection is addressed in this correspondence. Motivated by the frequently encountered problem of clutter-edge heterogeneity, we model the secondary data as a probability mixture and impose a hierarchical model for the inference problem. A two-stage CFAR detector structure is proposed. Empirical Bayesian inference is adopted in the first stage for training data selection followed by a CFAR processor using the identified homogeneous training set for target detection. One of the advantages of the proposed algorithm is its inherent adaptivity; i.e., the threshold setting is much less sensitive to the nonstationary environment compared with other standard CFAR procedures.

Spatial and Multivariate Analysis, Random Sampling Error, and Analytical Noise: Empirical Bayesian Methods at Teotihuacan, Mexico

Methods of empirical Bayesian statistical inference can help archaeologists deal with problems inherent in variably-sized and, particularly, small artifact samples. The desirability of systematically controlling random effects of sampling error when mapping estimates of artifact type proportions is emphasized in this paper, and concrete examples are provided using ceramic data from the Central Mexican city of Teotihuacan. A Bayesian approach also may be beneficial for pretreating data destined for other kinds of quantitative analysis, such as exploratory multivariate analysis. Correspondence analysis using observed proportions of different types of pottery in assemblages pertaining to the Xolalpan and Metepec phases produces vague results that suggest little in the way of interpretable structure. However, a parallel analysis using posterior estimates of proportions reveals meaningful associations of ceramic categories that appear to relate to more general dimensions of behavioral variability.

Density estimation by mixture models with smoothing priors

In the statistical approach for self-organizing maps (SOMs), learning is regarded as an estimation algorithm for a gaussian mixture model with a gaussian smoothing prior on the centroid parameters. The values of the hyperparameters and the topological structure are selected on the basis of a statistical principle. However, since the component selection probabilities are fixed to a common value, the centroids concentrate on areas with high data density. This deforms a coordinate system on an extracted manifold and makes smoothness evaluation for the manifold inaccurate. In this article, we study an extended SOM model whose component selection probabilities are variable. To stabilize the estimation, a smoothing prior on the component selection probabilities is introduced. An estimation algorithm for the parameters and the hyperparameters based on empirical Bayesian inference is obtained. The performance of density estimation by the new model and the SOM model is compared via simulation experiments.

Log Gaussian Cox Processes

Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases. The appealing properties of such models are demonstrated theoretically as well as through data examples and simulations. In particular, the first, second and third‐order properties are studied and utilized in the statistical analysis of clustered point patterns. Also empirical Bayesian inference for the underlying intensity surface is considered.