Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling resources. In this article, we propose a decision-theoretic selection strategy that (1) directly optimizes the gain in misclassification error, and (2) uses a Bayesian approach by introducing a conjugate prior distribution to determine the class posterior to deal with uncertainties. By reformulating existing selection strategies within our proposed model, we can explain which aspects are not covered in current state-of-the-art and why this leads to the superior performance of our approach. Extensive experiments on a large variety of datasets and different kernels validate our claims.
In Bayesian classification, it is important to establish a probabilistic model for each class for likelihood estimation. Most of the previous methods modeled the probability distribution in the whole sample space. However, real-world problems are usually too complex to model in the whole sample space; some fundamental assumptions are required to simplify the global model, for example, the class conditional independence assumption for naive Bayesian classification. In this paper, with the insight that the distribution in a local sample space should be simpler than that in the whole sample space…
Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In particular, hybrid Bayesian neural networks utilize standard deterministic layers together with few probabilistic layers judicially positioned in the networks for uncertainty estimation. A major aspect and benefit of Bayesian inference is that priors, in principle, provide the means to encode prior knowledge for use in inference and prediction. However, it is…
We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit pr…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead. We…
Probabilistic vehicle trajectory prediction is essential for robust safety of autonomous driving. Current methods for long-term trajectory prediction cannot guarantee the physical feasibility of predicted distribution. Moreover, their models cannot adapt to the driving policy of the predicted target human driver. In this work, we propose to overcome these two shortcomings by a Bayesian recurrent neural network model consisting of Bayesian-neural-network-based policy model and known physical model of the scenario. Bayesian neural network can ensemble complicated output distribution, enabling ri…
Universitat Politècnica de València（瓦伦西亚理工大学）；Universidad Autónoma de Madrid（马德里自治大学）
Deep Neural Networks (DNNs) have achieved state-of-the-art accuracy performance in many tasks. However, recent works have pointed out that the outputs provided by these models are not well-calibrated, seriously limiting their use in critical decision scenarios. In this work, we propose to use a decoupled Bayesian stage, implemented with a Bayesian Neural Network (BNN), to map the uncalibrated probabilities provided by a DNN to calibrated ones, consistently improving calibration. Our results evidence that incorporating uncertainty provides more reliable probabilistic models, a critical conditio…
On Cold Posteriors of Probabilistic Neural Networks: Understanding the Cold Posterior Effect and A New Way to Learn Cold Posteriors with Tight Generalization Guarantees
The Alan Turing Institute（艾伦·图灵研究所）；University of Warwick（华威大学）
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state observation data. Inverse problems for chaotic systems are numerically challenging as small perturbations in model parameters can cause very large changes in estimated forward trajectories. Bayesian Artificial Neural Networks can be used to simultaneously fit a model and estimate model parameter uncertainty. Knowledge of model parameter uncertainty can then be i…
Industrial applications frequently pose a notorious challenge for state-of-the-art methods in the contexts of optimization, designing experiments and modeling unknown physical response. This problem is aggravated by limited availability of clean data, uncertainty in available physics-based models and additional logistic and computational expense associated with experiments. In such a scenario, Bayesian methods have played an impactful role in alleviating the aforementioned obstacles by quantifying uncertainty of different types under limited resources. These methods, usually deployed as a fram…
Eindhoven University of Technology（埃因霍温理工大学）；KU Leuven（鲁汶大学）；Graz University of Technology（格拉茨理工大学）
Probabilistic circuits (PCs) are a prominent representation of probability distributions with tractable inference. While parameter learning in PCs is rigorously studied, structure learning is often more based on heuristics than on principled objectives. In this paper, we develop Bayesian structure scores for deterministic PCs, i.e., the structure likelihood with parameters marginalized out, which are well known as rigorous objectives for structure learning in probabilistic graphical models. When used within a greedy cutset algorithm, our scores effectively protect against overfitting and yield…
A Data-Driven Probabilistic Framework for Cascading Urban Risk Analysis Using Bayesian Networks
Department of Computer Science and Engineering, School of Computing, Coimbatore, Amrita Vishwa Vidyapeetham, Tamil Nadu, India（计算机科学与工程系，计算学院，科瓦尔，阿米塔大学文理学院，泰米尔纳德邦，印度）
I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation Propagation approach (VEP) for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors and zeta. Using a factorized posterior approximation I derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse logistic models. The approach can be…
Active learning is able to reduce the amount of labelling effort by using a machine learning model to query the user for specific inputs. While there are many papers on new active learning techniques, these techniques rarely satisfy the constraints of a real-world project. In this paper, we analyse the main drawbacks of current active learning techniques and we present approaches to alleviate them. We do a systematic study on the effects of the most common issues of real-world datasets on the deep active learning process: model convergence, annotation error, and dataset imbalance. We derive tw…
Optimizing an expensive-to-query function is a common task in science and engineering, where it is beneficial to keep the number of queries to a minimum. A popular strategy is Bayesian optimization (BO), which leverages probabilistic models for this task. Most BO today uses Gaussian processes (GPs), or a few other surrogate models. However, there is a broad set of Bayesian modeling techniques that could be used to capture complex systems and reduce the number of queries in BO. Probabilistic programming languages (PPLs) are modern tools that allow for flexible model definition, prior specificat…
Large multilayer neural networks trained with backpropagation have recently achieved state-of-the-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a large number of hyperparameters to the data, lack of calibrated probabilistic predictions, and a tendency to overfit the training data. In principle, the Bayesian approach to learning neural networks does not have these problems. However, existing Bayesian techniques lack scalability to large dataset and network sizes. In this work we present a novel scalabl…
We design a new myopic strategy for a wide class of sequential design of experiment (DOE) problems, where the goal is to collect data in order to to fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling (MPS), is inspired by the classical posterior (Thompson) sampling algorithm for multi-armed bandits and leverages the flexibility of probabilistic programming and approximate Bayesian inference to address a broad set of problems. Empirically, this general-purpose strategy is competitive with more specialised methods in a wide array of DOE tasks, and more importantly, e…
We present a probabilistic programmed deep kernel learning approach to personalized, predictive modeling of neurodegenerative diseases. Our analysis considers a spectrum of neural and symbolic machine learning approaches, which we assess for predictive performance and important medical AI properties such as interpretability, uncertainty reasoning, data-efficiency, and leveraging domain knowledge. Our Bayesian approach combines the flexibility of Gaussian processes with the structural power of neural networks to model biomarker progressions, without needing clinical labels for training. We run …
There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. An important challenge is to reconcile these probabilistic integrators with rigorous convergence guarantees. In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence …
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's assumptions and reality. We propose a way to systematically detect and mitigate mismatch of a large class of probabilistic models. The idea is to raise the likelihood of each observation to a weight and then to infer both the latent variables and the weights from data. Inferring the weights allows a model to identify observations that match its assumptions and d…
Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of kernel Bayesian inference have been developed by combining kernelized basic probabilistic operations such as the kernel sum rule and kernel Bayes' rule. However, the current framework is fully nonparametric, and it does not allow a user to flexibly combine nonparametric and model-based inferences. This is inefficient when there are good probabilistic models (or …
One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic networks. Our work explores whether fully Bayesian networks are needed to successfully capture model uncertainty. We vary the number and position of Bayesian layers in a network and compare their performance on active learning with the MNIST dataset. We found that we can fully capture the model uncertainty by using only a few Bayesian…
Data cleaning is naturally framed as probabilistic inference in a generative model of ground-truth data and likely errors, but the diversity of real-world error patterns and the hardness of inference make Bayesian approaches difficult to automate. We present PClean, a probabilistic programming language (PPL) for leveraging dataset-specific knowledge to automate Bayesian cleaning. Compared to general-purpose PPLs, PClean tackles a restricted problem domain, enabling three modeling and inference innovations: (1) a non-parametric model of relational database instances, which users' programs custo…
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…
Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information on either users or items, and assumes a common variance for all users. We extend the work of constrained probabilistic matrix factorization by deriving the Gibbs updates for the side feature vectors for items (Salakhutdinov and Minh, 2008). We show that this Bayesian treatment to the constrained PMF model outperforms simple MAP estimation. We also consider e…
Tsinghua University（清华大学）；University of Toronto（多伦多大学）
In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate th…
University of Oxford（牛津大学）；Northeastern University（东北大学）
We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering sig…
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple probabilistic graphics programs that define flexible generative models and to automatically invert them to interpret real-world images. Generative probabilistic graphics programs consist of a stochastic scene generator, a renderer based on graphics software, a stochastic likeliho…
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a non-linear Bayesian filtering problem and all widely-used approximations to the Bayesian f…
Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and improved methods for approximate inference in probabilistic models. In this contribution a probabilistic model for an idealized dark matter localization problem is described. We first derive the probabilistic model for the inference of dark matter locations and masses, and then show how this model can be implemented using BUGS and Infer.NET, two software systems …
Imperial College London（帝国理工学院）；Brown University（布朗大学）；University of Oxford（牛津大学）；University College London（伦敦大学学院）
Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian numerical integration algorithm based on Bayesian Additive Regression Trees (BART) prior…
Center for Perceptual Systems（感知系统中心）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
The ultimate goal of optimization is to find the minimizer of a target function.However, typical criteria for active optimization often ignore the uncertainty about the minimizer. We propose a novel criterion for global optimization and an associated sequential active learning strategy using Gaussian processes.Our criterion is the reduction of uncertainty in the posterior distribution of the function minimizer. It can also flexibly incorporate multiple global minimizers. We implement a tractable approximation of the criterion and demonstrate that it obtains the global minimizer accurately comp…
Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Queensland University of Technology（昆士兰科技大学）
We investigate different strategies for active learning with Bayesian deep neural networks. We focus our analysis on scenarios where new, unlabeled data is obtained episodically, such as commonly encountered in mobile robotics applications. An evaluation of different strategies for acquisition, updating, and final training on the CIFAR-10 dataset shows that incremental network updates with final training on the accumulated acquisition set are essential for best performance, while limiting the amount of required human labeling labor.
Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically principled, BNNs require approximations to be applied to large-scale problems, where both performance and uncertainty estimation are crucial. In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep BNN. We conduct a series of large-scale visual active learning experiments t…
We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties of a broad class of data generating processes, using Bayesian inference to synthesize probabilistic programs in these modeling languages given observed data. We provide a precise formulation of Bayesian synthesis for automatic data modeling that identifies sufficient conditions for the resulting synthesis procedure to be sound. We also derive a general class…
University of Oxford（牛津大学）；Royal Holloway University of London（伦敦大学皇家霍洛威学院）
We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experi…
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）
Even though active learning forms an important pillar of machine learning, deep learning tools are not prevalent within it. Deep learning poses several difficulties when used in an active learning setting. First, active learning (AL) methods generally rely on being able to learn and update models from small amounts of data. Recent advances in deep learning, on the other hand, are notorious for their dependence on large amounts of data. Second, many AL acquisition functions rely on model uncertainty, yet deep learning methods rarely represent such model uncertainty. In this paper we combine rec…
The output of solar power generation is significantly dependent on the available solar radiation. Thus, with the proliferation of PV generation in the modern power grid, forecasting of solar irradiance is vital for proper operation of the grid. To achieve an improved accuracy in prediction performance, this paper discusses a Bayesian treatment of probabilistic forecasting. The approach is demonstrated using publicly available data obtained from the Florida Automated Weather Network (FAWN). The algorithm is developed in Python and the results are compared with point forecasts, other probabilist…
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem w…
Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we connect network metrics to modern probabilistic machine learning. We focus on the centrality metric, which is used a wide variety of applications from web search to gene-analysis. First, we formulate an eigenvector-based Bayesian centrality model for determining node importance. Compared to existing methods, our probabilistic model allows for the assimilation…
In this paper we develop a functorial language of probabilistic morphisms and apply it to some basic problems in Bayesian nonparametrics. First we extend and unify the Kleisli category of probabilistic morphisms proposed by Lawvere and Giry with the category of statistical models proposed by Chentsov and Morse-Sacksteder. Then we introduce the notion of a Bayesian statistical model that formalizes the notion of a parameter space with a given prior distribution in Bayesian statistics. {We revisit the existence of a posterior distribution, using probabilistic morphisms}. In particular, we give a…
Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze streams of data. It approximates a new type of distribution, the population posterior, which combines the notion of a population distribution of the data with Bayesian inference in a probabilistic model. We study our method with latent Dirichlet allocation and Dirichlet process mixtur…
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally line…
It is known that describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, Bayesian tensor network (BTN) is proposed to efficiently capture the conditional probabilities of multiple sets of events with polynomial complexity. BTN is a directed acyclic graphical model that forms a subset of TN. To testify its validity for exponentially many events, BTN is implemented to the image recognition, where the classification is mapped to capturing the conditional probabilities in an exponentially large sample space. Competitive performance is ac…
Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models
School of Information, Computer；Communication Technology Sirindhorn International Institute of Technology, Thammasat University Pathumthani, Thailand 0009-0006-4313-7359；epartment of Architecture, Faculty of Architecture Khon Kaen University Khon Kaen, Thailand
Optimizing expensive-to-evaluate black-box functions of discrete (and potentially continuous) design parameters is a ubiquitous problem in scientific and engineering applications. Bayesian optimization (BO) is a popular, sample-efficient method that leverages a probabilistic surrogate model and an acquisition function (AF) to select promising designs to evaluate. However, maximizing the AF over mixed or high-cardinality discrete search spaces is challenging standard gradient-based methods cannot be used directly or evaluating the AF at every point in the search space would be computationally p…
Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to explain relationships present in the observed data. Bayesian models are useful when an experiment has only a small number of observations and in applications where transparency of data driven decisions is important. Traditionally, parameter inference in Bayesian statistics has involved constructing bespoke MCMC (Markov chain Monte Carlo) schemes for each newly pro…
Wellcome Centre for Human Neuroimaging, University College London（伦敦大学学院威康人类神经影像中心）；Department of Mathematics, Imperial College London（伦敦帝国理工学院数学系）
Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference combines Bayesian decision theory and optimal Bayesian design principles under a single imperative to minimize expected free energy. It is this aspect of active inference that allows for the natural emergence of information-seeking behavior. When removing prior outcomes preferences from expected free energy, active inference reduces to optimal Bayesian design, …
