In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is typically NP-hard, and thus alternative approximate methods should be considered. In this paper, our choice for alternative method is sparse Bayesian learning, which, as empirical Bayesian approaches, uses a parameterized prior to encourage sparsity in solution, rather than the other methods with fixed priors such as LASSO. Screening test, however, aims at quickly identifying a subset of features whose coefficients are guaranteed to be zero in the optimal solution, and then can be safely removed from the complete dictionary to obtain a smaller, more easily solved problem. Next, we solve the smaller problem, after which the solution of the original problem can be recovered by padding the smaller solution with zeros. The performance of the proposed method will be examined on various data sets and applications.
We present new multi-test Bayesian optimization models and algorithms for use in large scale material screening applications. Our screening problems are designed around two tests, one expensive and one cheap. This paper differs from other recent work on multi-test Bayesian optimization through use of a flexible model that allows for complex, non-linear relationships between the cheap and expensive test scores. This additional modeling flexibility is essential in the material screening applications which we describe. We demonstrate the power of our new algorithms on a family of synthetic toy pr…
Washington University in St. Louis（圣路易斯华盛顿大学）；SigOpt（SigOpt公司）
Classical methods for psychometric function estimation either require excessive measurements or produce only a low-resolution approximation of the target psychometric function. In this paper, we propose a novel solution for rapid screening for a change in the psychometric function estimation of a given patient. We use Bayesian active model selection to perform an automated pure-tone audiogram test with the goal of quickly finding if the current audiogram will be different from a previous audiogram. We validate our approach using audiometric data from the National Institute for Occupational Saf…
University of Chicago（芝加哥大学）；Arizona State University（亚利桑那州立大学）
Bayesian additive regression trees (BART) (Chipman et. al., 2010) is a powerful predictive model that often outperforms alternative models at out-of-sample prediction. BART is especially well-suited to settings with unstructured predictor variables and substantial sources of unmeasured variation as is typical in the social, behavioral and health sciences. This paper develops a modified version of BART that is amenable to fast posterior estimation. We present a stochastic hill climbing algorithm that matches the remarkable predictive accuracy of previous BART implementations, but is many times …
University of Cambridge（剑桥大学）；Google Research（谷歌研究院）
We introduce repriorisation, a data-dependent reparameterisation which transforms a Bayesian neural network (BNN) posterior to a distribution whose KL divergence to the BNN prior vanishes as layer widths grow. The repriorisation map acts directly on parameters, and its analytic simplicity complements the known neural network Gaussian process (NNGP) behaviour of wide BNNs in function space. Exploiting the repriorisation, we develop a Markov chain Monte Carlo (MCMC) posterior sampling algorithm which mixes faster the wider the BNN. This contrasts with the typically poor performance of MCMC in hi…
University of South Carolina（南卡罗来纳大学）；University of North Carolina Charlotte（北卡罗来纳大学夏洛特分校）
Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on Metropolis-Hastings (MH) algorithm for unimodal distributions. Here, an enhanced MH algorithm is proposed that requires less number of expensive function evaluations, has shorter burn-in period, and uses a better proposal distribution. The main innovations include the use of Bayesian optimization to reach the high probability region quickly, emulating the target distribut…
Virtual screening aims to find desirable compounds from chemical library by using computational methods. For this purpose with machine learning, model outputs that can be interpreted as predictive probability will be beneficial, in that a high prediction score corresponds to high probability of correctness. In this work, we present a study on the prediction performance and reliability of graph neural networks trained with the recently proposed Bayesian learning algorithms. Our work shows that Bayesian learning algorithms allow well-calibrated predictions for various GNN architectures and class…
High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross-plate correlation or statistical strength among plates. We present a new statistical framework for high throughput screening of compounds based on Bayesian nonparametric modeling. The proposed approach is able to identify candidate hits from multiple plates simultaneously, shari…
Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where the integration is tractable, we can sample new feature assignments according to a predictive likelihood. We present a novel method to accelerate the mixing of latent variable model inference by proposing feature locations based on the data, as opposed to the prior. First, we introduce an accelerated feature proposal mechanism that we show is a valid MCMC alg…
Deakin University（迪肯大学）；Office of National Statistics（国家统计局）；University of Western Sydney（西悉尼大学）；National University of Singapore（新加坡国立大学）
Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a set of standard covariance functions. From a weight-space view, this models the objective as a linear function in a feature space implied by the given covariance K, with an arbitrary Gaussian weight prior ${\bf w} \sim \mathcal{N} ({\bf 0}, {\bf I})$. In many practical applications there is data available that has a similar (covariance) structure to the objec…
Feature or variable selection is a problem inherent to large data sets. While many methods have been proposed to deal with this problem, some can scale poorly with the number of predictors in a data set. Screening methods scale linearly with the number of predictors by checking each predictor one at a time, and are a tool used to decrease the number of variables to consider before further analysis or variable selection. For classification, there is a variety of techniques. There are parametric based screening tests, such as t-test or SIS based screening, and non-parametric based screening test…
The paper presents a novel approach to direct covariance function learning for Bayesian optimisation, with particular emphasis on experimental design problems where an existing corpus of condensed knowledge is present. The method presented borrows techniques from reproducing kernel Banach space theory (specifically m-kernels) and leverages them to convert (or re-weight) existing covariance functions into new, problem-specific covariance functions. The key advantage of this approach is that rather than relying on the user to manually select (with some hyperparameter tuning and experimentation) …
In this paper, a Bayesian accelerated life testing model is presented. The Weibull distribution is used as the life distribution and the generalised Eyring model as the time transformation function. This is a model that allows for the use of more than one stressor, whereas other commonly used acceleration models, such as the Arrhenius and power law models, allow for only one stressor. The generalised Eyring-Weibull model is used in an application, where MCMC methods are utilised to generate samples for posterior inference.
This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method using kernel mixtures, which improves performance by borrowing information across the different variables and groups through shared kernels and a common probability of group differences. The inclusion of shared kernels in a finite mixture, with Dirichlet priors on the weights, leads to a simple framework for testing that scales well for high-dimensional data. We…
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain well-defined point known as the $prevalence$ $threshold$, below which the reliability of a positive screening test drops precipitously. Herein, we establish a mathematical model to determine whether sequential testing overcomes the aforementioned Bayesian limitations and thus improves the reliability of screening tests. We show that for a desired positive predicti…
There has been much recent interest in screening populations for an infectious disease. Here, we present a stochastic-control model, wherein the optimum screening policy is provably difficult to find, but wherein Thompson sampling has provably optimal performance guarantees in the form of Bayesian regret. Thompson sampling seems applicable especially to diseases, for which we do not understand the dynamics well, such as to the super-spreading COVID-19.
Accelerated life testing (ALT) is typically used to assess the reliability of material's lifetime under desired stress levels. Recent advances in material engineering have made a variety of material alternatives readily available. To identify the most reliable material setting with efficient experimental design, a sequential test planning strategy is preferred. To guarantee a tractable statistical mechanism for information collection and update, we develop explicit model parameter update formulas via approximate Bayesian inference. Theories show that our explicit update formulas give consisten…
Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they should also be reasonably brief; adaptive screening tests are useful for this purpose. Adaptive tests constructed using classification and regression trees are becoming a popular alternative to traditional Item Response Theory (IRT) approaches for adaptive testing. However, tree-based adaptive tests lack a principled criterion for terminating…
In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network (NN) to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. We begin by demonstrating, with a few toy examples, the ab…
Socrates-Mol: Self-Oriented Cognitive Reasoning through Autonomous Trial-and-Error with Empirical-Bayesian Screening for Molecules
State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing), Beijing 102249, China（石油加工国家重点实验室，中国石油大学（北京））；Shanghai AI Laboratory,L1 Building, International Media Port, No. 129 Longwen Road, Xuhui District, Shanghai（上海人工智能实验室）；College of Energy Innovation, China University of Petroleum (Beijing), Beijing 102249, China（能源创新学院，中国石油大学（北京））
The accelerated failure time (AFT) model is a commonly used tool in analyzing survival data. In public health studies, data is often collected from medical service providers in different locations. Survival rates from different locations often present geographically varying patterns. In this paper, we focus on the accelerated failure time model with spatially varying coefficients. We compare three types of the priors for spatially varying coefficients. A model selection criterion, logarithm of the pseudo-marginal likelihood (LPML), is developed to assess the fit of AFT model with different pri…
Chemical space is so large that brute force searches for new interesting molecules are infeasible. High-throughput virtual screening via computer cluster simulations can speed up the discovery process by collecting very large amounts of data in parallel, e.g., up to hundreds or thousands of parallel measurements. Bayesian optimization (BO) can produce additional acceleration by sequentially identifying the most useful simulations or experiments to be performed next. However, current BO methods cannot scale to the large numbers of parallel measurements and the massive libraries of molecules cur…
This paper deals with unobserved heterogeneity in the survival dataset through Accelerated Failure Time (AFT) models under both frameworks--Bayesian and classical. The Bayesian approach of dealing with unobserved heterogeneity has recently been discussed in Vallejos and Steel (2017), where mixture models are used to diminish the effect that anomalous observations or some kinds of covariates which are not included in the survival models. The frailty models also deal with this kind of unobserved variability under classical framework and have been used by practitioners as alternative to Bayesian.…
This paper presents two case studies of data sets where the main inferential goal is to characterize time-varying patterns in model structure. Both of these examples are seen to be general cases of the so-called "partition problem," where auxiliary information (in this case, time) defines a partition over sample space, and where different models hold for each element of the partition. In the first case study, we identify time-varying graphical structure in the covariance matrix of asset returns from major European equity indices from 2006--2010. This structure has important implications for qu…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the usual fixed-in-advanced sampling plan, we establish posterior contraction rates for mode and maximum and show that they coincide with the minimax rates for this problem. To quantify estimation uncertainty, we construct credible sets for these two quantities that have high coverage probabilities with optimal sizes. If one is allowed to collect data sequential…
We explore the theoretical and numerical property of a fully Bayesian model selection method in sparse ultrahigh-dimensional settings, i.e., $p\gg n$, where $p$ is the number of covariates and $n$ is the sample size. Our method consists of (1) a hierarchical Bayesian model with a novel prior placed over the model space which includes a hyperparameter $t_n$ controlling the model size, and (2) an efficient MCMC algorithm for automatic and stochastic search of the models. Our theory shows that, when specifying $t_n$ correctly, the proposed method yields selection consistency, i.e., the posterior …
High-throughput genetic and epigenetic data are often screened for associations with an observed phenotype. For example, one may wish to test hundreds of thousands of genetic variants, or DNA methylation sites, for an association with disease status. These genomic variables can naturally be grouped by the gene they encode, among other criteria. However, standard practice in such applications is independent screening with a universal correction for multiplicity. We propose a Bayesian approach in which the prior probability of an association for a given genomic variable depends on its gene, and …
State-of-the-art spectral energy distribution (SED) analyses use a Bayesian framework to infer the physical properties of galaxies from observed photometry or spectra. They require sampling from a high-dimensional space of SED model parameters and take $>10-100$ CPU hours per galaxy, which renders them practically infeasible for analyzing the $billions$ of galaxies that will be observed by upcoming galaxy surveys ($e.g.$ DESI, PFS, Rubin, Webb, and Roman). In this work, we present an alternative scalable approach to rigorous Bayesian inference using Amortized Neural Posterior Estimation (ANPE)…
We develop a Bayesian variable selection method, called SVEN, based on a hierarchical Gaussian linear model with priors placed on the regression coefficients as well as on the model space. Sparsity is achieved by using degenerate spike priors on inactive variables, whereas Gaussian slab priors are placed on the coefficients for the important predictors making the posterior probability of a model available in explicit form (up to a normalizing constant). The strong model selection consistency is shown to be attained when the number of predictors grows nearly exponentially with the sample size a…
In practice, optimal screening designs for arbitrary run sizes are traditionally generated using the D-criterion with factor settings fixed at +/- 1, even when considering continuous factors with levels in [-1, 1]. This paper identifies cases of undesirable estimation variance properties for such D-optimal designs and argues that generally A-optimal designs tend to push variances closer to their minimum possible value. New insights about the behavior of the criteria are found through a study of their respective coordinate-exchange formulas. The study confirms the existence of D-optimal designs…
ADMIRE-BayesOpt: Accelerated Data MIxture RE-weighting for Language Models with Bayesian Optimization
Thomson Reuters Foundational Research & Imperial College London（汤姆逊·路透基础研究与帝国理工学院伦敦）；University of Virginia（弗吉尼亚大学）；Graphcore；Thomson Reuters Foundational Research（汤姆逊·路透基础研究）
Traditional accelerated life test plans are typically based on optimizing the C-optimality for minimizing the variance of an interested quantile of the lifetime distribution. The traditional methods rely on some specified planning values for the model parameters, which are usually unknown prior to the actual tests. The ambiguity of the specified parameters can lead to suboptimal designs for optimizing the intended reliability performance. In this paper, we propose a sequential design strategy for life test plans based on considering dual objectives. In the early stage of the sequential experim…
The first investigation is made of designs for screening experiments where the response variable is approximated by a generalised linear model. A Bayesian information capacity criterion is defined for the selection of designs that are robust to the form of the linear predictor. For binomial data and logistic regression, the effectiveness of these designs for screening is assessed through simulation studies using all-subsets regression and model selection via maximum penalised likelihood and a generalised information criterion. For Poisson data and log-linear regression, similar assessments are…
Chalmers University of Technology（查尔姆斯理工大学）；AstraZeneca AB（阿斯利康公司）
We study the problem of performing automated experiment design for drug screening through Bayesian inference and optimisation. In particular, we compare and contrast the behaviour of linear-Gaussian models and Gaussian processes, when used in conjunction with upper confidence bound algorithms, Thompson sampling, or bounded horizon tree search. We show that non-myopic sophisticated exploration techniques using sparse tree search have a distinct advantage over methods such as Thompson sampling or upper confidence bounds in this setting. We demonstrate the significant superiority of the approach …
We describe a computational framework for hierarchical Bayesian inference with simple (typically single-plate) parametric graphical models that uses graphics processing units (GPUs) to accelerate computations, enabling deployment on very large datasets. Its C++ implementation, CUDAHM (CUDA for Hierarchical Models) exploits conditional independence between instances of a plate, facilitating massively parallel exploration of the replication parameter space using the single instruction, multiple data architecture of GPUs. It provides support for constructing Metropolis-within-Gibbs samplers that …
Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling
University of Edinburgh（爱丁堡大学）；Heriot-Watt University（赫瑞-瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学科学研究所）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
Optimal Bayesian feature filtering (OBF) is a supervised screening method designed for biomarker discovery. In this article, we prove two major theoretical properties of OBF. First, optimal Bayesian feature selection under a general family of Bayesian models reduces to filtering if and only if the underlying Bayesian model assumes all features are mutually independent. Therefore, OBF is optimal if and only if one assumes all features are mutually independent, and OBF is the only filter method that is optimal under at least one model in the general Bayesian framework. Second, OBF under independ…
Robust Survival Estimation under Interval Censoring: Expectation-Maximization and Bayesian Accelerated Failure Time Assessment via Simulation and Application
In this paper, we focus on identifying differentially activated brain regions using a light sheet fluorescence microscopy - a recently developed technique for whole-brain imaging. Most existing statistical methods solve this problem by partitioning the brain regions into two classes: significantly and non-significantly activated. However, for the brain imaging problem at the center of our study, such binary grouping may provide overly simplistic discoveries by filtering out weak but important signals, that are typically adulterated by the noise present in the data. To overcome this limitation,…
In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide sufficient information to reliably estimate such a large number of parameters. Sparse regression techniques provide potential solutions, one notable approach being the Bayesian methods based on shrinkage priors. In the "large n & large p" setting, however, posterior computation encounters a major bottleneck at repeated sampling from a high-dimensional Gaussian distri…
Bayesian joint modelling using semiparametric accelerated failure time approaches
The University of Queensland’s Clinical Trials Capability (ULTRA)（昆士兰大学临床试验能力中心（ULTRA））；NHMRC Clinical Trial Centre, University of Sydney（悉尼大学国家健康与医学研究委员会临床试验中心）；Australian and New Zealand Urogenital and Prostate (ANZUP) Cancer Trials Group（澳大利亚和新西兰泌尿生殖和前列腺癌症试验组）
