Nonparametric Bayesian Method Research Articles

Application of non parametric Bayesian methods in high dimensional data

With the development of technology and the widespread collection of data, high-dimensional data analysis has become a research hotspot in many fields. Traditional parameter methods often face problems such as dimensional disasters in high-dimensional data analysis. Non parametric methods have broad application prospects in high-dimensional data because they do not rely on specific parameter distribution assumptions. The Bayesian rule is more suitable for dealing with noise and outliers in high-dimensional data because it takes uncertainty into account. Therefore, it is of great significance to combine non parametric methods with Bayesian methods for application research in high-dimensional data analysis. In this paper, the nonparametric Bayesian method was applied to the analysis of high-dimensional data, and the Dirichlet process Mixture model was used to cluster high-dimensional data. The regression analysis of high-dimensional data was carried out through the prediction model of nonparametric Bayesian regression. In this paper, the nonparametric Bayesian method based on Bayesian sparse linear model was used for feature selection of high-dimensional data. In order to determine the superiority of nonparametric Bayesian methods in high-dimensional data analysis, this paper conducted experiments on nonparametric Bayesian methods and traditional parametric methods in high-dimensional data analysis from five aspects of cluster analysis, classification analysis, regression analysis, feature selection and anomaly detection, and evaluated them through multiple indicators. This article explored the application of non parametric Bayesian methods in high-dimensional data analysis from these aspects through simulation experiments. The experimental results show that the clustering accuracy of the non parametric Bayesian clustering algorithm was 0.93, and the accuracy of the non parametric Bayesian classification algorithm was between 0.93 and 0.99; the coefficient of determination of nonparametric Bayesian regression algorithm was 0.98; the F1 values of non parametric Bayesian methods in anomaly detection ranged from 0.86 to 0.91, which was superior to traditional methods. Non parametric Bayesian methods have broad application prospects in high-dimensional data analysis, and can be applied in multiple fields such as clustering, classification, regression, etc.

Driving patterns in connected environments: A case study of intersection-approaching behavior of professional and non-professional drivers

The in-vehicle communication provides promising opportunities to improve the road safety and traffic efficiency. Previous studies demonstrated that the professional drivers have better driving skills than the non-professional drivers who allocate more attention to secondary tasks. However, they may not be sensitive to the new in-vehicle technology. In addition, these qualitative studies failed to elaborate on the visual and response behavior differences among different driver groups (professional drivers such as taxi, bus, motorcoach, and non-professional drivers), and lacked the quantitative analysis of driving patterns in a new environment. This paper explores the differences in visual interaction, response characteristics, driving performance, and behavior patterns between the professional and non-professional drivers in the connected environment through a case study of intersection-approaching behavior using a driving simulator. More precisely, two driving scenarios (baseline and human–machine interface (HMI)) were designed in the driving simulator, and 65 participants, including 34 professional drivers and 31 non-professional drivers, completed the experiment. In the HMI scenario, the driver was provided with the signal light phase and phase transition remaining time of the current intersection. This paper also proposes a driving pattern extraction model based on the Bayesian non-parametric method combined with a text clustering algorithm to perform a quantitative description of the driving patterns. The results show that the professional drivers tend to interact less with the HMI compared with the non-professional drivers. Moreover, the professional drivers’ first gaze at the HMI occurs and responds earlier. The proposed driving model can effectively describe 7 patterns of intersection-approaching behavior. The connected information can significantly improve the efficiency of the intersection traffic and the driving behavior. However, the professional drivers are more responsive and behave more consistently. This study can provide insights into the development of personalized assisted driving systems, as the two driving populations differ in their interactions, responses, and behavioral patterns.

A dynamic driving-style analysis method based on drivers’ interaction with surrounding vehicles

The ability to recognize different driving styles of surrounding vehicles is crucial to determine the safest and most efficient driving decisions, prevent accidents, and analyze the causes of traffic accidents. Understanding if the surrounding vehicle is aggressive or cautious can greatly assist in the decision making of vehicles in terms of whether and when it is appropriate to make particular maneuvers. A driver’s driving style usually changes with the environment, which brings great challenges to the current research. To this end, a dynamic driving-style analysis framework, in which drivers’ interactions with other vehicles are considered, is proposed in this article. First, by analyzing common traffic scenarios, five surrounding vehicles are selected as the environmental vehicles to be considered. Time headway (THW) and time to collision (TTC) that can consider the relative speed and position with the ego vehicle are selected as the clustering indicators. Then, a Bayesian nonparametric learning method based on a hierarchical Dirichlet-process hidden semi-Markov model (HDP-HSMM) is introduced to extract primitive driving patterns from time-series driving data without prior knowledge of the number of these patterns. Then the driving pattern is scored according to the risk degree. A driver’s aggressiveness is scored and drivers are divided into different styles based on the frequency distribution of driving patterns. The effectiveness of the proposed method is demonstrated on a real-world vehicle trajectory data set where results show that driving pattern switches and more complex driving behaviors can be better captured and understood semantically.

Bayesian spatial cluster signal learning with application to adverse event (AE)

ABSTRACT There is growing interest in understanding geographic patterns of medical device-related adverse events (AEs). A spatial scan method combined with the likelihood ratio test (LRT) for spatial-cluster signal detection over the geographical region is universally used. The spatial scan method used a moving window to scan the entire study region and collected some candidate sub-regions from which the spatial-cluster signal(s) will be found. However, it has some challenges, especially in computation. First, the computational cost increased when the number of sub-regions increased. Second, the computational cost may increase if a large spatial-cluster pattern is present and a flexible-shaped window is used. To reduce the computational cost, we propose a Bayesian nonparametric method that combines the ideas of Markov random field (MRF) to leverage geographical information to find potential signal clusters. Then, the LRT is applied for the detection of spatial cluster signals. The proposed method provides an ability to capture both locally spatially contiguous clusters and globally discontiguous clusters, and is manifested to be effective and tractable using hypothetical Left Ventricular Assist Device (LVAD) data as an illustration.

A Bayesian nonparametric approach for multiple mediators with applications in mental health studies.

Mediation analysis with contemporaneously observed multiple mediators is a significant area of causal inference. Recent approaches for multiple mediators are often based on parametric models and thus may suffer from model misspecification. Also, much of the existing literature either only allow estimation of the joint mediation effect or estimate the joint mediation effect just as the sum of individual mediator effects, ignoring the interaction among the mediators. In this article, we propose a novel Bayesian nonparametric method that overcomes the two aforementioned drawbacks. We model the joint distribution of the observed data (outcome, mediators, treatment, and confounders) flexibly using an enriched Dirichlet process mixture with three levels. We use standardization (g-computation) to compute all possible mediation effects, including pairwise and all other possible interaction among the mediators. We thoroughly explore our method via simulations and apply our method to a mental health data from Wisconsin Longitudinal Study, where we estimate how the effect of births from unintended pregnancies on later life mental depression (CES-D) among the mothers is mediated through lack of self-acceptance and autonomy, employment instability, lack of social participation, and increased family stress. Our method identified significant individual mediators, along with some significant pairwise effects.

Comparative Analysis of Improved Dirichlet Process Mixture Model

Due to the development of information technology, large amounts of data are generated every day in various industries such as engineering, healthcare, finance, anomaly detection, image recognition, and artificial intelligence. This massive data poses the challenge of analyzing accurately and appropriate classifications. The traditional clustering methods require specifying the number of clusters and are mostly based on distance, which cannot effectively consider the correlations between different indicators of high-dimensional and multi-source data. Moreover, the number of clusters cannot automatically adjust when new data is generated. In order to improve the clustering analysis of high-dimensional and multi-source data in a big data environment, this study utilizes non-parametric mixture models based on distribution clustering, which does not require specifying the number of clusters and can auto update with the data. By combining Principal Component Analysis (PCA), t-Distributed Stochastic Neighbour Embedding (t-SNE), and the non-parametric Bayesian method called Dirichlet Process Mixture Model (DPMM), the Bayesian non-parametric PCA model (PCA-DPMM) and Bayesian non-parametric t-SNE model (TSNE-DPMM) are proposed. The Chinese restaurant process of DPMM is used for sampling by introducing a finite normal mixture distribution. The clustering results on the iris dataset are compared and analyzed. The accuracy of DPMM and TSNE-DPMM reaches 0.97, while PCA-DPMM achieves a maximum accuracy of only 0.94. When different numbers of iterations are set, TSNE-DPMM maintains an accuracy ranging from 0.92 to 0.97, DPMM ranges from 0.66 to 0.97, and PCA-DPMM ranges from 0.73 to 0.94. Therefore, the proposed TSNE-DPMM ensures accuracy and exhibits better model stability in clustering results. Future research can explore the improvement of the model by incorporating deep learning algorithms, among others, to further enhance its performance. Additionally, applying the TSNE-DPMM model to data analysis in other fields is also a future research direction. Through these efforts, we can better tackle the challenges of analyzing high-dimensional and multi-source data in a big data environment and extract valuable information from it.

Bayesian nonparametric method for genetic dissection of brain activation region.

Biological evidence indicewates that the brain atrophy can be involved at the onset of neuropathological pathways of Alzheimer's disease. However, there is lack of formal statistical methods to perform genetic dissection of brain activation phenotypes such as shape and intensity. To this end, we propose a Bayesian hierarchical model which consists of two levels of hierarchy. At level 1, we develop a Bayesian nonparametric level set (BNLS) model for studying the brain activation region shape. At level 2, we construct a regression model to select genetic variants that are strongly associated with the brain activation intensity, where a spike-and-slab prior and a Gaussian prior are chosen for feature selection. We develop efficient posterior computation algorithms based on the Markov chain Monte Carlo (MCMC) method. We demonstrate the advantages of the proposed method via extensive simulation studies and analyses of imaging genetics data in the Alzheimer's disease neuroimaging initiative (ADNI) study.

A Bayesian Nonparametric Modeling Approach to Settlement Patterns of Pastoralists Population in Kenya

Pastoralists' settlement patterns in Kenya have been studied for decades using various statistical and mathematical models. However, traditional models have often relied on restrictive assumptions, such as the normality of the data or the linearity of relationships. In this paper, we apply a Bayesian nonparametric approach to model the settlement patterns of pastoralists in Kenya, allowing for more flexible and realistic representations of the data. We first collected settlement data for pastoralists in Kenya and compiled a database of environmental covariates, such as distance to water sources, vegetation cover, and road networks. We then applied a Bayesian nonparametric clustering method to identify distinct settlement patterns and tested the performance of the model against other commonly used clustering techniques. Our results indicate that the Bayesian nonparametric approach outperforms other clustering techniques in terms of model fit and accuracy in identifying distinct settlement patterns. Additionally, we conducted a spatial regression analysis to investigate the relationship between settlement patterns and environmental covariates, revealing that distance to water sources and road networks are significant predictors of settlement patterns. Overall, our study highlights the usefulness of Bayesian nonparametric methods in modelling settlement patterns of pastoralists in Kenya and provides valuable insights into the relationship between environmental factors and settlement patterns.

Bayesian non-parametric method for decision support: Forecasting online product sales

Forecasting online product sales is essential for retailers and e-commerce platforms, but it can be challenging owing to the complex dynamics and mixed trends in sales data. Popular end-to-end approaches tend to capture spurious correlations in historical data, whereas two-stage approaches that decompose time series and make separate predictions often result in error accumulation. To address these issues, we propose PoissonGP, a novel Bayesian model that employs a non-homogeneous Poisson process with a Gaussian process prior for sales prediction. PoissonGP can capture complex patterns in data with multiple trends and manage distribution shifts caused by changes in long-run sales. Additionally, it incorporates forecast uncertainty and provides interpretability for building efficient and visual decision support systems. Experimental results on several synthetic and empirical datasets suggest that PoissonGP outperforms existing approaches, making it a promising tool for e-commerce platforms.

Bayesian approaches to include real-world data in clinical studies.

Randomized clinical trials have been the mainstay of clinical research, but are prohibitively expensive and subject to increasingly difficult patient recruitment. Recently, there is a movement to use real-world data (RWD) from electronic health records, patient registries, claims data and other sources in lieu of or supplementing controlled clinical trials. This process of combining information from diverse sources calls for inference under a Bayesian paradigm. We review some of the currently used methods and a novel non-parametric Bayesian (BNP) method. Carrying out the desired adjustment for differences in patient populations is naturally done with BNP priors that facilitate understanding of and adjustment for population heterogeneities across different data sources. We discuss the particular problem of using RWD to create a synthetic control arm to supplement single-arm treatment only studies. At the core of the proposed approach is the model-based adjustment to achieve equivalent patient populations in the current study and the (adjusted) RWD. This is implemented using common atoms mixture models. The structure of such models greatly simplifies inference. The adjustment for differences in the populations can be reduced to ratios of weights in such mixtures. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Modeling the generative mechanism of personalized preferences from latent groups: A hierarchical nonparametric Bayesian method

Personalization is among the most prominent marketing strategies for facing online and offline retailers. The basis for personalization is learning the customer’s personalized preferences, but the sparsity of customer behavioral data makes it difficult to calculate personalized preferences and predict behaviors. Assuming that customer preferences are influenced by the latent group, we propose a Hierarchical Nonparametric Bayesian method (HNB) to model the generative mechanism of personalized preferences from latent groups. The proposed HNB employs a hierarchical and nonparametric structure based on the Dirichlet process, and constructs a combined model to analyze personalized preferences and latent groups. In the context of online shopping, HNB not only mitigates data sparsity with information from the latent groups, but also identifies the meaning of preference in customer purchase history and discovers latent groups accurately. Our experiments also show the number of preferences and latent groups is calculated automatically from the data, understand the generative mechanism of personalized preference from latent groups, and predict personalized purchases based on preferences.

Resolving Molecular Heterogeneity with Single-Molecule Centrifugation.

For many classes of biomolecules, population-level heterogeneity is an essential aspect of biological function─from antibodies produced by the immune system to post-translationally modified proteins that regulate cellular processes. However, heterogeneity is difficult to fully characterize for multiple reasons: (i) single-molecule approaches are needed to avoid information lost by ensemble-level averaging, (ii) sufficient statistics must be gathered on both a per-molecule and per-population level, and (iii) a suitable analysis framework is required to make sense of a potentially limited number of intrinsically noisy measurements. Here, we introduce an approach that overcomes these difficulties by combining three techniques: a DNA nanoswitch construct to repeatedly interrogate the same molecule, a benchtop centrifuge force microscope (CFM) to obtain thousands of statistics in a highly parallel manner, and a Bayesian nonparametric (BNP) inference method to resolve separate subpopulations with distinct kinetics. We apply this approach to characterize commercially available antibodies and find that polyclonal antibody from rabbit serum is well-modeled by a mixture of three subpopulations. Our results show how combining a spatially and temporally multiplexed nanoswitch-CFM assay with BNP analysis can help resolve complex biomolecular interactions in heterogeneous samples.

Global gold prices forecasting using Bayesian nonparametric quantile generalized additive model

Gold is one of the most attractive commodities and popular investments. Investment experts often recommend investing in gold because gold is one of the safest investments. It is a stable classic hedge, although the conditions of currency volatility or global markets are depreciated. However, the gold price fluctuations can be influenced by some other factors, such as the USD Index, which reflect and measure the strength of the US Dollar currency, and the Index of Dow Jones Industrial Average (DJIA) or a reflection of the political and economic conditions of the stock market. In this study, we conduct a global gold price forecast (USD) based on the USD Index, the DJIA Index, and the influence of time trends. Based on the data's characteristics, we face the fact that the data is nonlinear, contains outliers, and its pattern is not easy to specify parametrically. Due to the complexity of the model, we then propose a more flexible, robust modeling technique called the Bayesian Nonparametric Quantile Generalized Additive Model method. According to the results for the median case, the proposed method shows an accurate forecasting category due to the value of the Mean Absolute Percentage Error, MAPE less than 10 percent.

Clustering of Linear Time-Invariant Systems: A Bayesian Nonparametric Method

In this paper, we consider the clustering of linear time-invariant (LTI) systems according to the similarity of dynamics. There are two main difficulties for clustering of LTI systems: one is to determine the labels of LTI systems and the number of clusters, and another one is to build models of LTI systems. To address these two difficulties simultaneously, a Bayesian nonparametric method based on Dirichlet process mixture models (DPMM) and kernel-based regularization method is proposed. To be specific, the Dirichlet process mixtures of Bayesian linear regression models (DPM-BLRM) is proposed to determine the label of each LTI system according to the probability that the system belongs to each cluster, and adapt the number of clusters to the complexity of data. In addition, DPM-BLRM incorporates the prior knowledge of LTI systems to deal with the possible large variance of model parameters estimation when the collected data is short or has low signal-to-noise ratio, where the carrier of prior knowledge is kernel matrix. Then Markov chain Monte Carlo (MCMC) method is used for Bayesian inference for the DPM-BLRM. The simulation results illustrate the efficiency of the proposed method.

Learning personalized preference: A segmentation strategy under consumer sparse data

Personalization is crucial to consumer satisfaction and repeat purchases. Learning personalized preferences from consumer data is often challenged by data sparsity because each consumer’s history only accounts for a small part of the total data. Since consumer segmentation and personalized preference are often highly correlated and can be mutually reinforcing, the segmentation strategy to alleviate the data sparsity problem is proposed. The proposed strategy utilizes a Nonparametric Hierarchal Bayesian method to integrate Preference learning and consumer Segmentation into a unified model, named as NHBPS, that estimates the number of segmentations and preferences in a data-adaptive way. The NHBPS model is applied to a real-world dataset containing consumer behavior history and demographics. The analysis results show the following: (1) at least 17.50% improvement in consumer segmentation compared to benchmark methods. (2) personalized preference distributions and insightful interpretations are learned successfully. (3) the NHBPS model outperforms benchmarks in predicting consumer behaviors and demographics.

A Bayesian nonparametric method for detecting rapid changes in disease transmission

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number, Rt. Real-time or retrospective identification of changes in Rt following the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts in Rt within a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman–Yor process. We assume that Rt is piecewise-constant, and the incidence data and priors determine when or whether Rt should change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty in Rt and its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where the Rt profile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Adversarial Evaluation of Autonomous Vehicles in Lane-Change Scenarios

Autonomous vehicles must be comprehensively evaluated before deployed in cities and highways. However, most existing evaluation approaches for autonomous vehicles are static and lack adaptability, so they are usually inefficient in generating challenging scenarios for tested vehicles. In this paper, we propose an adaptive evaluation framework to efficiently evaluate autonomous vehicles in adversarial environments generated by deep reinforcement learning. Considering the multimodal nature of dangerous scenarios, we use ensemble models to represent different local optimums for diversity. We then utilize a nonparametric Bayesian method to cluster the adversarial policies. The proposed method is validated in a typical lane-change scenario that involves frequent interactions between the ego vehicle and the surrounding vehicles. Results show that the adversarial scenarios generated by our method significantly degrade the performance of the tested vehicles. We also illustrate different patterns of generated adversarial environments, which can be used to infer the weaknesses of the tested vehicles.

A Unified Bayesian Framework for Bi-overlapping-Clustering Multi-omics Data via Sparse Matrix Factorization.

The advances of modern sequencing techniques have generated an unprecedented amount of multi-omics data which provide great opportunities to quantitatively explore functional genomes from different but complementary perspectives. However, distinct modalities/sequencing technologies generate diverse types of data which greatly complicate statistical modeling because uniquely optimized methods are required for handling each type of data. In this paper, we propose a unified framework for Bayesian nonparametric matrix factorization that infers overlapping bi-clusters for multi-omics data. The proposed method adaptively discretizes different types of observations into common latent states on which cluster structures are built hierarchically. The proposed Bayesian nonparametric method is able to automatically determine the number of clusters. We demonstrate the utility of the proposed method using simulation studies and applications to a single-cell RNA-sequencing dataset, a combination of single-cell RNA-sequencing and single-cell ATAC-sequencing dataset, a bulk RNA-sequencing dataset, and a DNA methylation dataset which reveal several interesting findings that are consistent with biological literature.

Use of a Non-parametric Bayesian Method to Model Health State Preferences: An Application to Polish and Irish EQ-5D-5L Valuations.

Valuations of preference-based measures for health are conducted in different countries. There is scope to use results from existing countries' valuations to generate better valuation estimates than analyzing the data from each country separately. We analyse data from two smaller design EQ-5D-5L valuation studies where a sample of 119 Polish migrants and 123 native Irish valued 30 common health states using similar composite time trade-off protocols. We apply a non-parametric Bayesian method to provide better predictions of the Polish (Irish) population utility function when the existing Irish (Polish) results were used as informative priors. The resultant new estimates were then compared to those obtained by analyzing the data from each country by itself via different prediction criterions. The results suggest that existing countries' valuations could be used as potential informative priors to produce better valuation estimates under all prediction criterions used. The implications of these results will be hugely important in countries where valuation studies are expensive and hard to conduct. Future application to other countries and to other preference-based health measures are encouraged.

Abstract 1224: UMIBB: A novel nonparametric Bayesian method improves robustness and sensitivity of analysis in pooled CRISPR-Cas9 screens leveraging unique molecular identifiers

Abstract CRISPR-based functional genomics screens are a powerful tool for identifying synthetically lethal cancer drug targets. Current strategies for analyzing pooled CRISPR screens usually rely on signals from single guide RNAs (sgRNA) with differential relative abundance between two experimental conditions. However, conventional approaches are susceptible to false positives and false negatives driven by outlier cell clones, since the sgRNA abundance does not account for the heterogeneous phenotypes resulting from different editing outcomes of the same sgRNA. To overcome this, we added DNA barcodes to each sgRNA to create unique molecular identifiers (UMIs) for CRISPR libraries and developed a companion analytical platform that enables robust, industry-scale CRISPR screens. Here, we present UMIBB, a novel nonparametric Bayesian approach for analyzing UMI-CRISPR data. The number of UMIs with normalized count depletion or enrichment compared to the control experimental condition for each sgRNA is modeled by a beta-binomial distribution. The gene level statistics are derived by combining z-scores of the sgRNAs level posterior probabilities weighted by the number of UMIs in each sgRNA. This approach minimizes the impact of outlier cell clones on statistics and prioritizes genes with consistent count differentials across multiple UMIs in each gene. To assess the power of UMIBB, we benchmarked it on a low coverage (200X) genome-scale negative-selection screen, comparing with results from a high coverage (1000X) screen. These screens were conducted on KRAS mutant cancer celllines (A549) treated with trametinib or vehicle control. Despite the high noise level usually observed in lower coverage screens, our method was able to uncover most of the validated sensitizer genes for trametinib and achieved the highest sensitivity compared to conventional methods. Furthermore, we applied UMIBB on a genome-scale positive-selection screen and successfully identified novel genes (RAD18 and UBE2K) as key mediators of USP1 dependency in BRCA1 mutant cell lines. Our studies demonstrate that UMIBB is highly robust against false positives due to clonal heterogeneity and is more likely to identify true genetic interactions. Citation Format: Ashley Choi, Samuel Meier, Silvia Fenoglio, Tianshu Feng, Justin Engel, Binzhang Shen, Shangtao Liu, Teng Teng, Tenzing Khendu, Alan Huang, Jannik Andersen, Xuewen Pan, Yi Yu. UMIBB: A novel nonparametric Bayesian method improves robustness and sensitivity of analysis in pooled CRISPR-Cas9 screens leveraging unique molecular identifiers [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 1224.