Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational complexity of large-scale architectures and datasets. Node-based BNNs have recently been introduced as scalable alternatives, which induce epistemic uncertainty by multiplying each hidden node with latent random variables, while learning a point-estimate of the weights. In this paper, we interpret these latent noise variables as implicit representations of simple and domain-agnostic data perturbations during training, producing BNNs that perform well under covariate shift due to input corruptions. We observe that the diversity of the implicit corruptions depends on the entropy of the latent variables, and propose a straightforward approach to increase the entropy of these variables during training. We evaluate the method on out-of-distribution image classification benchmarks, and show improved uncertainty estimation of node-based BNNs under covariate shift due to input perturbations. As a side effect, the method also provides robustness against noisy training labels.
Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity approximate inference via full-batch Hamiltonian Monte Carlo achieve poor generalization under covariate shift, even underperforming classical estimation. We explain this surprising result, showing how a Bayesian model average can in fact be problematic under covariate shift, particularly in cases where linear dependencies in the input features cause a lack of posteri…
University of Cambridge（剑桥大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Alan Turing Institute（艾伦图灵研究所）
Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is crucial in high-stakes applications that involve critical decision-making. Bayesian neural networks (BNNs) aim at solving this problem by placing a prior distribution over the network's parameters, thereby inducing a posterior distribution that encapsulates predictive uncertainty. While existing variants of BNNs based on Monte Carlo dropout produce reliable …
Human Technology Institute, The University of Technology Sydney（悉尼科技大学人类技术研究所）；School of Mathematics and Statistics, The University of Sydney（悉尼大学数学与统计学院）；Brain and Mind Centre, The University of Sydney（悉尼大学大脑与心智中心）
Perceptive Automata, Inc.（感知自动机公司）；University of Notre Dame（圣母大学）；Harvard University（哈佛大学）
Computer Vision practitioners must thoroughly understand their model's performance, but conditional evaluation is complex and error-prone. In biometric verification, model performance over continuous covariates---real-number attributes of images that affect performance---is particularly challenging to study. We develop a generative model of the match and non-match score distributions over continuous covariates and perform inference with modern Bayesian methods. We use mixture models to capture arbitrary distributions and local basis functions to capture non-linear, multivariate trends. Three e…
Historical data about disease outcomes can be integrated into the analysis of clinical trials in many ways. We build on existing literature that uses prognostic scores from a predictive model to increase the efficiency of treatment effect estimates via covariate adjustment. Here we go further, utilizing a Bayesian framework that combines prognostic covariate adjustment with an empirical prior distribution learned from the predictive performances of the prognostic model on past trials. The Bayesian approach interpolates between prognostic covariate adjustment with strict type I error control wh…
Accounting for shared covariates in semi-parametric Bayesian additive regression trees
School of Mathematical Sciences, Lancaster University, United Kingdom.；Hamilton Institute, Maynooth University, Co. Kildare, Ireland.；Department of Mathematics \& Statistics, Maynooth University, Co. Kildare, Ireland.；Insight Centre for Data Analytics, Maynooth University, Co. Kildare, Ireland.；Department of Mathematics \& Statistics, Lancaster University, United Kingdom.
Meta-learning has proven to be successful for few-shot learning across the regression, classification, and reinforcement learning paradigms. Recent approaches have adopted Bayesian interpretations to improve gradient-based meta-learners by quantifying the uncertainty of the post-adaptation estimates. Most of these works almost completely ignore the latent relationship between the covariate distribution $(p(x))$ of a task and the corresponding conditional distribution $p(y|x)$. In this paper, we identify the need to explicitly model the meta-distribution over the task covariates in a hierarchic…
This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Mark…
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is worst-case robust under a specified distributional shift of an uncontrolled covariate. In this paper, we study such a problem when the distributional shift is measured via the maximum mean discrepancy (MMD). For the setting of zeroth-order, noisy optimization, we present a novel distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm provabl…
Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern [1], there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models ex…
Bayesian uncertainty-aware deep learning with noisy labels: Tackling annotation ambiguity in EEG seizure detection
Department of Electrical and Computer Engineering, Johns Hopkins University（约翰霍普金斯大学电气与计算机工程系）；Department of Electrical and Computer Engineering, Boston University（波士顿大学电气与计算机工程系）
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of simulations. Our approach is based on Bayesian inference with kernel mean embedding of distributions, and on the use of an importance-weighted reproducing kernel for covariate shift adaptation. We provide a theoretical analysis for the proposed method, including a novel theoretical result for conditional mean embedding, as well as empirical investigations sugg…
Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov Chain Monte Carlo (MCMC) algorithm that updates all the censored covariate values jointly in a random scan Gibbs sampler. We show that the joint updating of missing covariate values can be at least two orders of magnitude more efficient than univariate updating. This increased efficiency is shown to be crucial for quickly learning the missing covariate values…
Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration (RC), arguably the most commonly adopted approach. We then argue why the Bayesian …
In an empirical Bayesian setting, we provide a new multiple testing method, useful when an additional covariate is available, that influences the probability of each null hypothesis being true. We measure the posterior significance of each test conditionally on the covariate and the data, leading to greater power. Using covariate-based prior information in an unsupervised fashion, we produce a list of significant hypotheses which differs in length and order from the list obtained by methods not taking covariate-information into account. Covariate-modulated posterior probabilities of each null …
In regional economics research, a problem of interest is to detect similarities between regions, and estimate their shared coefficients in economics models. In this article, we propose a mixture of finite mixtures (MFM) clustered regression model with auxiliary covariates that account for similarities in demographic or economic characteristics over a spatial domain. Our Bayesian construction provides both inference for number of clusters and clustering configurations, and estimation for parameters for each cluster. Empirical performance of the proposed model is illustrated through simulation e…
University of California, Berkeley（加州大学伯克利分校）；Department of Electrical Engineering and Computer Sciences（电气工程与计算机科学系）
When faced with distribution shift at test time, deep neural networks often make inaccurate predictions with unreliable uncertainty estimates. While improving the robustness of neural networks is one promising approach to mitigate this issue, an appealing alternate to robustifying networks against all possible test-time shifts is to instead directly adapt them to unlabeled inputs from the particular distribution shift we encounter at test time. However, this poses a challenging question: in the standard Bayesian model for supervised learning, unlabeled inputs are conditionally independent of m…
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 …
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian inverse regression problemsunder appropriate priors in a leave-one-out cross-validation setup. We relate this to posterior consistency of inverse reference distributions (Bhattacharya (2013)) for assessing model adequacy. We illustrate our theory and methods with various examples of Bayesian inverse regression, along with adequate simulation experiments.
With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate time series and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this paper, we propose a group-based method to cluster a collection of multivariate time series via a Bayesian mixture of smoothing splines. Our method assumes each multivariate time series is a mixture o…
To model categorical response variables given their covariates, we propose a permuted and augmented stick-breaking (paSB) construction that one-to-one maps the observed categories to randomly permuted latent sticks. This new construction transforms multinomial regression into regression analysis of stick-specific binary random variables that are mutually independent given their covariate-dependent stick success probabilities, which are parameterized by the regression coefficients of their corresponding categories. The paSB construction allows transforming an arbitrary cross-entropy-loss binary…
Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification
School of Intelligent Systems Engineering, Sun Yat-sen University（智能系统工程学院，中山大学）；Guangdong Provincial Key Laboratory of Intelligent Transportation System（广东省智能交通系统重点实验室）；Guangdong Provincial Engineering Research Center for Traffic Environmental Monitoring and Control（广东省交通环境监测与控制工程研究中心）
In many applications, survey data are collected from different survey centers in different regions. It happens that in some circumstances, response variables are completely observed while the covariates have missing values. In this paper, we propose a joint spatial regression model for the response variable and missing covariates via a sequence of one-dimensional conditional spatial regression models. We further construct a joint spatial model for missing covariate data mechanisms. The properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm is used to s…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a fixed design for covariates. The only random design result we are aware of (van der Vaart & van Zanten, 2011) assumes the assigned Gaussian process to be supported on the smoothness class specified by the true function with probability one. This is a fairly restrictive assumption as it essentially rules out the Gaussian process prior with a squared exponent…
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to p. Treating the covariates as random and adopting an asymptotic scenario in which p increases with n, we show that Bayesian model selection using certain priors on the set of models is asymptotically equivalent to selecting a model using an extended Bayesian information criterion. Moreover, we prove that the smallest true model is selected by either of these…
The functional generalized additive model (FGAM) was recently proposed in McLean et al. (2013) as a more flexible alternative to the common functional linear model (FLM) for regressing a scalar on functional covariates. In this paper, we develop a Bayesian version of FGAM for the case of Gaussian errors with identity link function. Our approach allows the functional covariates to be sparsely observed and measured with error, whereas the estimation procedure of McLean et al. (2013) required that they be noiselessly observed on a regular grid. We consider both Monte Carlo and variational Bayes m…
Accurate diagnosis of disease is of fundamental importance in clinical practice and medical research. Before a medical diagnostic test is routinely used in practice, its ability to distinguish between diseased and nondiseased states must be rigorously assessed through statistical analysis. The receiver operating characteristic (ROC) curve is the most popular used tool for evaluating the discriminatory ability of continuous-outcome diagnostic tests. It has been acknowledged that several factors (e.g., subject-specific characteristics, such as age and/or gender) can affect the test's accuracy be…
Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows different subjects to have different graphical structures depending on extraneous covariates. The pseudo-likelihood approach replaces the joint distribution by a product of the conditional distributions of each variable. We cast the conditional distribution as a heteroscedastic regression problem, with covariate-dependent variance terms, to enable information borr…
In climate change study, the infrared spectral signatures of climate change have recently been conceptually adopted, and widely applied to identifying and attributing atmospheric composition change. We propose a Bayesian hierarchical model for spatial clustering of the high-dimensional functional data based on the effects of functional covariates and local features. We couple the functional mixed-effects model with a generalized spatial partitioning method for: (1) producing spatially contiguous clusters for the high-dimensional spatio-functional data; (2) improving the computational efficienc…
Bayesian Varying-Effects Vector Autoregressive Models for Inference of Brain Connectivity Networks and Covariate Effects in Pediatric Traumatic Brain Injury
