The most common approach to implementing data analysis pipelines involves obtaining point estimates from the upstream modules and then treating these as known quantities when working with the downstream ones. This approach is straightforward, but it is likely to underestimate the overall uncertainty associated with any final estimates. An alternative approach involves estimating parameters from the modules jointly using a Bayesian hierarchical model, which has the advantage of propagating upstream uncertainty into the downstream estimates. However, when modules are misspecified, such a joint model can behave in unexpected ways. Furthermore, hierarchical models require the development of ad-hoc computational implementations that can be laborious and computationally expensive. Cut inference modifies the posterior distribution to prevent information flow between certain parameters and provides a third alternative for statistical inference in data analysis pipelines. This paper presents a unified framework that encompasses two-step, cut, and joint inference in the context of data analysis pipelines with two modules and uses two examples to illustrate the tradeoffs associated with these approaches. Our work shows that cut inference provides both some level of robustness and ease of implementation for data analysis pipelines at a lower cost in terms of statistical inference.
We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed as an additive expansion of coarse to fine step functions. Our Modular and Multiscale (M&M) methodology provides multiscale decomposition of high-dimensional data arising from very fine measurements. Unlike more complex methods for functional predictors, our approach provides easy interpretation of the results. Additionally, it provides a quantification of …
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model consists of a number of coupled modules, with only some of the modules being misspecified. Cutting feedback methods represent the full posterior distribution in terms of conditional and sequential components, and then modify some terms in such a representation based on the modular structure for specification or computation of a modified posterior distribution.…
Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real world systems, inputs are passed through a sequence of different operations or modules, making variables in earlier stages of processing more costly to update. Such structure imposes a cost on switching variables in early parts of a data processing pipeline. In this work, we propose a new algorithm for switch cost-aware optimization called Lazy Modular Bayesian Optimization (LaMBO). This method efficiently identifies…
We present an efficient, principled, and interpretable technique for inferring module assignments and for identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how the method overcomes the resolution limit problem, accurately recovering the true number of modules. Our approach is based on Bayesian methods for model selection which have been used with success for almost a century, implemented using a variational technique developed only in the past decade. We…
In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. "Expert opinion" and "user self-evaluation" have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-h…
Machine learning pipeline potentially consists of several stages of operations like data preprocessing, feature engineering and machine learning model training. Each operation has a set of hyper-parameters, which can become irrelevant for the pipeline when the operation is not selected. This gives rise to a hierarchical conditional hyper-parameter space. To optimize this mixed continuous and discrete conditional hierarchical hyper-parameter space, we propose an efficient pipeline search and configuration algorithm which combines the power of Reinforcement Learning and Bayesian Optimization. Em…
A Gaussian process and linear-based framework for computing cut distributions in modular Bayesian calibration of two chained computer models
Université Paris-Saclay（巴黎萨克雷大学）；CEA（法国原子能和替代能源委员会）；Institut de Mathématiques de Toulouse, Université Paul Sabatier（图卢兹数学研究所，保罗·萨巴蒂尔大学）；Université d’Avignon（阿维尼翁大学）
To solve a machine learning problem, one typically needs to perform data preprocessing, modeling, and hyperparameter tuning, which is known as model selection and hyperparameter optimization.The goal of automated machine learning (AutoML) is to design methods that can automatically perform model selection and hyperparameter optimization without human interventions for a given dataset. In this paper, we propose a meta-learning method that can search for a high-performance machine learning pipeline from the predefined set of candidate pipelines for supervised classification datasets in an effici…
Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an improved modular Bayesian approach based on Gaussian Process (GP) for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy is described with a GP emulator. Numerical tests have demonstrated that such treatment of model discrepancy can avoid over-fitting. Furthermo…
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）
Clinical prognostic models derived from largescale healthcare data can inform critical diagnostic and therapeutic decisions. To enable off-theshelf usage of machine learning (ML) in prognostic research, we developed AUTOPROGNOSIS: a system for automating the design of predictive modeling pipelines tailored for clinical prognosis. AUTOPROGNOSIS optimizes ensembles of pipeline configurations efficiently using a novel batched Bayesian optimization (BO) algorithm that learns a low-dimensional decomposition of the pipelines high-dimensional hyperparameter space in concurrence with the BO procedure.…
Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, most Bayesian papers have focused on the retrospective segmentation problem. Here we examine the case where the model parameters before and after the changepoint are independent and we derive an online algorithm for exact inference of the most recent changepoint. We compute the prob…
This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with …
MCMC methods for sampling from the space of DAGs can mix poorly due to the local nature of the proposals that are commonly used. It has been shown that sampling from the space of node orders yields better results [FK03, EW06]. Recently, Koivisto and Sood showed how one can analytically marginalize over orders using dynamic programming (DP) [KS04, Koi06]. Their method computes the exact marginal posterior edge probabilities, thus avoiding the need for MCMC. Unfortunately, there are four drawbacks to the DP technique: it can only use modular priors, it can only compute posteriors over modular fe…
Qing Yuan Research Institute, Shanghai Jiao Tong University（上海交通大学清源研究院）；Tsinghua University（清华大学）
Despite their theoretical appealingness, Bayesian neural networks (BNNs) are left behind in real-world adoption, mainly due to persistent concerns on their scalability, accessibility, and reliability. In this work, we develop the BayesAdapter framework to relieve these concerns. In particular, we propose to adapt pre-trained deterministic NNs to be variational BNNs via cost-effective Bayesian fine-tuning. Technically, we develop a modularized implementation for the learning of variational BNNs, and refurbish the generally applicable exemplar reparameterization trick through exemplar paralleliz…
Data science relies on pipelines that are organized in the form of interdependent computational steps. Each step consists of various candidate algorithms that maybe used for performing a particular function. Each algorithm consists of several hyperparameters. Algorithms and hyperparameters must be optimized as a whole to produce the best performance. Typical machine learning pipelines consist of complex algorithms in each of the steps. Not only is the selection process combinatorial, but it is also important to interpret and understand the pipelines. We propose a method to quantify the importa…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the Bayesian framework. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well-defined, encompassing both non-linear and non-Gaussian models. For general computation, a numerical approximation scheme is proposed and its asymptotic convergence established. The theoretical development is then extended to pipeline…
UltraNest is a general-purpose Bayesian inference package for parameter estimation and model comparison. It allows fitting arbitrary models specified as likelihood functions written in Python, C, C++, Fortran, Julia or R. With a focus on correctness and speed (in that order), UltraNest is especially useful for multi-modal or non-Gaussian parameter spaces, computational expensive models, in robust pipelines. Parallelisation to computing clusters and resuming incomplete runs is available.
The Cut posterior and related Semi-Modular Inference are Generalised Bayes methods for Modular Bayesian evidence combination. Analysis is broken up over modular sub-models of the joint posterior distribution. Model-misspecification in multi-modular models can be hard to fix by model elaboration alone and the Cut posterior and SMI offer a way round this. Information entering the analysis from misspecified modules is controlled by an influence parameter $η$ related to the learning rate. This paper contains two substantial new methods. First, we give variational methods for approximating the Cut …
We introduce a Bayesian defect detector to facilitate the defect detection on the motion blurred images on rough texture surfaces. To enhance the accuracy of Bayesian detection on removing non-defect pixels, we develop a class of reflected non-local prior distributions, which is constructed by using the mode of a distribution to subtract its density. The reflected non-local priors forces the Bayesian detector to approach 0 at the non-defect locations. We conduct experiments studies to demonstrate the superior performance of the Bayesian detector in eliminating the non-defect points. We impleme…
Rapidly assaying the diversity of a bacterial species present in a sample obtained from a hospital patient or an evironmental source has become possible after recent technological advances in DNA sequencing. For several applications it is important to accurately identify the presence and estimate relative abundances of the target organisms from short sequence reads obtained from a sample. This task is particularly challenging when the set of interest includes very closely related organisms, such as different strains of pathogenic bacteria, which can vary considerably in terms of virulence, res…
In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines consisting of data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we tackle this meta-learning task by combining ideas from collaborative filtering and Bayesian …
