The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian models allows the model to better adapt to the data nature (i.e. heterogeneity, sparsity), obtaining a more representative latent space.
The objective of this article is to propose a general FA framework capable of modelling any problem. To do so, we start from the Bayesian Inter-Battery Factor Analysis (BIBFA) model, enhancing it with new functionalities to be able to work with heterogeneous data, include feature selection, and handle missing values as well as semi-supervised problems.
The performance of the proposed model, Sparse Semi-supervised Heterogeneous Interbattery Bayesian Analysis (SSHIBA) has been tested on 4 different scenarios to evaluate each one of its novelties, showing not only a great versatility and an interpretability gain, but also outperforming most of the state-of-the-art algorithms.
Virginia Polytechnic Institute and State University（弗吉尼亚理工学院暨州立大学）；U.S. Army Research Laboratory（美国陆军研究实验室）
Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior…
University of Michigan（密歇根大学）；Duke University（杜克大学）
Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by applications arising in the transportation domain, in this paper we develop a model for learning heterogeneous and dynamic patterns of velocity field data. We draw from basic nonparameric Bayesian modeling elements such as hierarchical Dirichlet process and infinite hidden Markov model, while the smoothness of each homogeneous velocity field element is captured with…
For assistive robots and virtual agents to achieve ubiquity, machines will need to anticipate the needs of their human counterparts. The field of Learning from Demonstration (LfD) has sought to enable machines to infer predictive models of human behavior for autonomous robot control. However, humans exhibit heterogeneity in decision-making, which traditional LfD approaches fail to capture. To overcome this challenge, we propose a Bayesian LfD framework to infer an integrated representation of all human task demonstrators by inferring human-specific embeddings, thereby distilling their unique c…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of matrix decomposition methods have been extended for such multi-view data integration and pattern discovery. While only few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, we propos…
Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applications
Department of Statistics, University of Chicago（芝加哥大学统计学系）；University of Tübingen（图宾根大学）；Department of Statistics & Data Science Institute, University of Chicago（芝加哥大学统计学与数据科学研究所）；Seminars for Statistics, ETH Zürich（苏黎世联邦理工学院统计系）
We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian ensemble trees (BET) and model them as an infinite mixture Dirichlet process. We show that BET adapts to data heterogeneity and accurately estimates each component. Compared with the bootstrap-aggregating approach, BET shows improved prediction performance with fewer trees. We develop an efficient estimating procedure with improved sampling strategies in both CART and m…
The development of human-robot systems able to leverage the strengths of both humans and their robotic counterparts has been greatly sought after because of the foreseen, broad-ranging impact across industry and research. We believe the true potential of these systems cannot be reached unless the robot is able to act with a high level of autonomy, reducing the burden of manual tasking or teleoperation. To achieve this level of autonomy, robots must be able to work fluidly with its human partners, inferring their needs without explicit commands. This inference requires the robot to be able to d…
Spatially-Heterogeneous Causal Bayesian Networks for Seismic Multi-Hazard Estimation: A Variational Approach with Gaussian Processes and Normalizing Flows
Johns Hopkins University（约翰斯·霍普金斯大学）；Data Science and AI Institute, Johns Hopkins University（约翰斯·霍普金斯大学数据科学与人工智能学院）
Data in the form of ranking lists are frequently encountered, and combining ranking results from different sources can potentially generate a better ranking list and help understand behaviors of the rankers. Of interest here are the rank data under the following settings: (i) covariate information available for the ranked entities; (ii) rankers of varying qualities or having different opinions; and (iii) incomplete ranking lists for non-overlapping subgroups. We review some key ideas built around the Thurstone model family by researchers in the past few decades and provide a unifying approach …
Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains
School of Energy and Power Engineering, Dalian University of Technology（大连理工大学能源与动力工程学院）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）
A major focus of causal inference is the estimation of heterogeneous average treatment effects (HTE) - average treatment effects within strata of another variable of interest such as levels of a biomarker, education, or age strata. Inference involves estimating a stratum-specific regression and integrating it over the distribution of confounders in that stratum - which itself must be estimated. Standard practice involves estimating these stratum-specific confounder distributions independently (e.g. via the empirical distribution or Rubin's Bayesian bootstrap), which becomes problematic for spa…
We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in $\sim$1500 dimensions after discretization. To infer these parameters, we use reported data on t…
There is a widespread need for statistical methods that can analyze high-dimensional datasets with- out imposing restrictive or opaque modeling assumptions. This paper describes a domain-general data analysis method called CrossCat. CrossCat infers multiple non-overlapping views of the data, each consisting of a subset of the variables, and uses a separate nonparametric mixture to model each view. CrossCat is based on approximately Bayesian inference in a hierarchical, nonparamet- ric model for data tables. This model consists of a Dirichlet process mixture over the columns of a data table in …
Bayesian Additive Regression Trees (BART) is a flexible machine learning algorithm capable of capturing nonlinearities between an outcome and covariates and interaction among covariates. We extend BART to a semiparametric regression framework in which the conditional expectation of an outcome is a function of treatment, its effect modifiers, and confounders. The confounders, not of scientific interest, are allowed to have unspecified functional form, while treatment and other covariates that do have scientific importance are given the usual linear form from parametric regression. The result is…
University of Waterloo（滑铁卢大学）；Vector Institute（向量研究所）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Making predictions robust is an important challenge. A separate challenge in federated learning (FL) is to reduce the number of communication rounds, particularly since doing so reduces performance in heterogeneous data settings. To tackle both issues, we take a Bayesian perspective on the problem of learning a global model. We show how the global predictive posterior can be approximated using client predictive posteriors. This is unlike other works which aggregate the local model space posteriors into the global model space posterior, and are susceptible to high approximation errors due to th…
Renmin University of China（中国人民大学）；Tsinghua University（清华大学）；University of Technology Sydney（悉尼科技大学）；Shanghai Jiao Tong University（上海交通大学）；JD.com Inc（京东集团）；JD Explore Academy（京东探索研究院）
University of Cambridge（剑桥大学）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Uber AI Labs（Uber人工智能实验室）
This paper introduces a general Bayesian non- parametric latent feature model suitable to per- form automatic exploratory analysis of heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or mixed variables. The proposed model presents several important properties. First, it accounts for heterogeneous data while can be inferred in linear time with respect to the number of objects and attributes. Second, its Bayesian nonparametric nature allows us to automatically infer the model complexity from the data, i.e., the number of features necessary to…
Columbia University（哥伦比亚大学）；University of Ljubljana（卢布尔雅那大学）；Aalto University（阿尔托大学）
Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can further improve the stacked mixture with a hierarchical model. We generalize stacking to Bayesian hierarchical stacking. The model weights are varying as a function of data, partially-pooled, and inferred using Bayesian inference. We further incorporate discrete and continuous inputs, other structured priors, and time series and longitudinal data. To verify the p…
Genetic association analyses often involve data from multiple potentially-heterogeneous subgroups. The expected amount of heterogeneity can vary from modest (e.g., a typical meta-analysis) to large (e.g., a strong gene--environment interaction). However, existing statistical tools are limited in their ability to address such heterogeneity. Indeed, most genetic association meta-analyses use a "fixed effects" analysis, which assumes no heterogeneity. Here we develop and apply Bayesian association methods to address this problem. These methods are easy to apply (in the simplest case, requiring on…
The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network reconstruction approaches based on Bayesian inference. These approaches, however, rely on assumptions of uniform error rates and on direct estimations of the existence of each edge via repeated measurements, something that is currently unavailable for the majority of network data. Here we develop a Bayesian reconstruction approach that lifts these limitations …
The purpose of this study is to leverage modern technology (such as mobile or web apps in Beckman et al. (2014)) to enrich epidemiology data and infer the transmission of disease. Homogeneity related research on population level has been intensively studied in previous work. In contrast, we develop hierarchical Graph-Coupled Hidden Markov Models (hGCHMMs) to simultaneously track the spread of infection in a small cell phone community and capture person-specific infection parameters by leveraging a link prior that incorporates additional covariates. We also reexamine the model evolution of the …
In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify communities, and graph Laplacian-based methods are routinely used. However, these methods are currently limited to a single network and do not provide measures of uncertainty on the community assignment. In this work, we propose a probabilistic network model called the ``Spiked Laplacian Graph'' that considers each network as an invertible transform of the …
Two key challenges in modern statistical applications are the large amount of information recorded per individual, and that such data are often not collected all at once but in batches. These batch effects can be complex, causing distortions in both mean and variance. We propose a novel sparse latent factor regression model to integrate such heterogeneous data. The model provides a tool for data exploration via dimensionality reduction while correcting for a range of batch effects. We study the use of several sparse priors (local and non-local) to learn the dimension of the latent factors. Our…
Bayesian optimization (BO) is a sample-efficient approach to optimizing costly-to-evaluate black-box functions. Most BO methods ignore how evaluation costs may vary over the optimization domain. However, these costs can be highly heterogeneous and are often unknown in advance. This occurs in many practical settings, such as hyperparameter tuning of machine learning algorithms or physics-based simulation optimization. Moreover, those few existing methods that acknowledge cost heterogeneity do not naturally accommodate a budget constraint on the total evaluation cost. This combination of unknown…
Trajectory-based real-time pedestrian crash prediction at intersections: A novel non-linear link function for block maxima led Bayesian GEV framework addressing heterogeneous traffic condition
Department of Technology, Management and Economics, Danish Technical University（丹麦技术大学技术、管理与经济系）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Percutaneous coronary interventions (PCIs) are nonsurgical procedures to open blocked blood vessels to the heart, frequently using a catheter to place a stent. The catheter can be inserted into the blood vessels using an artery in the groin or an artery in the wrist. Because clinical trials have indicated that access via the wrist may result in fewer post procedure complications, shortening the length of stay, and ultimately cost less than groin access, adoption of access via the wrist has been encouraged. However, patients treated in usual care are likely to differ from those participating in…
Generalizing imaging biomarker repeatability studies using Bayesian inference: Applications in detecting heterogeneous treatment response in whole-body diffusion-weighted MRI of metastatic prostate cancer
提出一种基于 Hamiltonian Monte Carlo 的贝叶斯框架，以量化不同分布假设下影像异质性生物标志物的测量不确定性，并在 mCRPC 的 WBDWI 数据中验证其疗效评估价值。
