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, i.e., information gain maximization. Conversely, active inference reduces to Bayesian decision theory in the absence of ambiguity and relative risk, i.e., expected utility maximization. Using these limiting cases, we illustrate how behaviors differ when agents select actions that optimize expected utility, expected information gain, and expected free energy. Our T-maze simulations show optimizing expected free energy produces goal-directed information-seeking behavior while optimizing expected utility induces purely exploitive behavior and maximizing information gain engenders intrinsically motivated behavior.
Technical University of Denmark (DTU)（丹麦技术大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Specifying utility functions is a key step towards applying the discrete choice framework for understanding the behaviour processes that govern user choices. However, identifying the utility function specifications that best model and explain the observed choices can be a very challenging and time-consuming task. This paper seeks to help modellers by leveraging the Bayesian framework and the concept of automatic relevance determination (ARD), in order to automatically determine an optimal utility function specification from an exponentially large set of possible specifications in a purely data…
Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrate…
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…
The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that co…
In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to exist for this problem, so far none of them were particularly tight. In this paper, we show how to efficiently calculate a lower bound, which corresponds to the utility of a near-optimal memoryless policy for the decision problem, which is generally different from both the Bayes-optimal policy and the policy which is optimal for the expected MDP under the c…
Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application, and therefore cannot guarantee optimal predictions for a given task. To make more suitable task-specific approximations, we introduce a new loss-calibrated evidence lower bound for Bayesian neural networks in the context of supervised learning, informed by Bayesian decision theory. By introducing a lower bound that depends on a utility function, we ensure t…
Northeastern University（东北大学）；University of Pittsburgh（匹兹堡大学）
Recursive Bayesian inference (RBI) provides optimal Bayesian latent variable estimates in real-time settings with streaming noisy observations. Active RBI attempts to effectively select queries that lead to more informative observations to rapidly reduce uncertainty until a confident decision is made. However, typically the optimality objectives of inference and query mechanisms are not jointly selected. Furthermore, conventional active querying methods stagger due to misleading prior information. Motivated by information theoretic approaches, we propose an active RBI framework with unified in…
Data-efficient learning algorithms are essential in many practical applications for which data collection is expensive, e.g., for the optimal deployment of wireless systems in unknown propagation scenarios. Meta-learning can address this problem by leveraging data from a set of related learning tasks, e.g., from similar deployment settings. In practice, one may have available only unlabeled data sets from the related tasks, requiring a costly labeling procedure to be carried out before use in meta-learning. For instance, one may know the possible positions of base stations in a given area, but…
A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models. Although straightforward in principle, there are several challenges to finding Bayesian designs in practice. Firstly, the utility and expected utility are rarely available in closed form and require approximation. Secondly, the design space can be of high-dimensionality. In the case of intractable likelihood models, these problems are compounded by the fact t…
We consider black-box global optimization of time-consuming-to-evaluate functions on behalf of a decision-maker (DM) whose preferences must be learned. Each feasible design is associated with a time-consuming-to-evaluate vector of attributes and each vector of attributes is assigned a utility by the DM's utility function, which may be learned approximately using preferences expressed over pairs of attribute vectors. Past work has used a point estimate of this utility function as if it were error-free within single-objective optimization. However, utility estimation errors may yield a poor sugg…
Aalto University（阿尔托大学）；University of Manchester（曼彻斯特大学）
Active learning is usually applied to acquire labels of informative data points in supervised learning, to maximize accuracy in a sample-efficient way. However, maximizing the accuracy is not the end goal when the results are used for decision-making, for example in personalized medicine or economics. We argue that when acquiring samples sequentially, separating learning and decision-making is sub-optimal, and we introduce an active learning strategy which takes the down-the-line decision problem into account. Specifically, we introduce a novel active learning criterion which maximizes the exp…
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…
We consider Bayesian optimization of expensive-to-evaluate experiments that generate vector-valued outcomes over which a decision-maker (DM) has preferences. These preferences are encoded by a utility function that is not known in closed form but can be estimated by asking the DM to express preferences over pairs of outcome vectors. To address this problem, we develop Bayesian optimization with preference exploration, a novel framework that alternates between interactive real-time preference learning with the DM via pairwise comparisons between outcomes, and Bayesian optimization with a learne…
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.
In this paper, we propose an active learning algorithm and models which can gradually learn individual's preference through pairwise comparisons. The active learning scheme aims at finding individual's most preferred choice with minimized number of pairwise comparisons. The pairwise comparisons are encoded into probabilistic models based on assumptions of choice models and deep Gaussian processes. The next-to-compare decision is determined by a novel acquisition function. We benchmark the proposed algorithm and models using functions with multiple local optima and one public airline itinerary …
Recent advances in machine learning have led to increased deployment of black-box classifiers across a wide variety of applications. In many such situations there is a critical need to both reliably assess the performance of these pre-trained models and to perform this assessment in a label-efficient manner (given that labels may be scarce and costly to collect). In this paper, we introduce an active Bayesian approach for assessment of classifier performance to satisfy the desiderata of both reliability and label-efficiency. We begin by developing inference strategies to quantify uncertainty f…
Principled Bayesian deep learning (BDL) does not live up to its potential when we only focus on marginal predictive distributions (marginal predictives). Recent works have highlighted the importance of joint predictives for (Bayesian) sequential decision making from a theoretical and synthetic perspective. We provide additional practical arguments grounded in real-world applications for focusing on joint predictives: we discuss online Bayesian inference, which would allow us to make predictions while taking into account additional data without retraining, and we propose new challenging evaluat…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；IBM Research（IBM研究院）
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are approximated with, potentially crude, surrogates. This difficulty has engendered loss-calibrated techniques that aim to learn posterior approximations that favor high-utility decisions. In this paper, focusing on Bayesian neural networks, we develop methods for correcting approximate posterior predictive distributions encouraging them to prefer high-utility decisions…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；University of Helsinki（赫尔辛基大学）
Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate inference strategies. In such cases, taking the eventual decision-making task into account while performing the inference allows for calibrating the posterior approximation to maximize the utility. We present an automatic pipeline that co-opts continuous utilities into variational inference algorithms to account for decision-making. We provide practical str…
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…
Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior …
The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional design spaces. We provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm. This methodology uses a Gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps. It has flexibility to address problems for any …
Gaussian processes (GPs) are the main surrogate functions used for sequential modelling such as Bayesian Optimization and Active Learning. Their drawbacks are poor scaling with data and the need to run an optimization loop when using a non-Gaussian likelihood. In this paper, we focus on `fantasizing' batch acquisition functions that need the ability to condition on new fantasized data computationally efficiently. By using a sparse Dual GP parameterization, we gain linear scaling with batch size as well as one-step updates for non-Gaussian likelihoods, thus extending sparse models to greedy bat…
Predicting bioactivity and physical properties of small molecules is a central challenge in drug discovery. Deep learning is becoming the method of choice but studies to date focus on mean accuracy as the main metric. However, to replace costly and mission-critical experiments by models, a high mean accuracy is not enough: Outliers can derail a discovery campaign, thus models need reliably predict when it will fail, even when the training data is biased; experiments are expensive, thus models need to be data-efficient and suggest informative training sets using active learning. We show that un…
Bayesian adaptive inference is widely used in psychophysics to estimate psychometric parameters. Most applications used myopic one-step ahead strategy which only optimizes the immediate utility. The widely held expectation is that global optimization strategies that explicitly optimize over some horizon can largely improve the performance of the myopic strategy. With limited studies that compared myopic and global strategies, the expectation was not challenged and researchers are still investing heavily to achieve global optimization. Is that really worthwhile? This paper provides a discouragi…
We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical model-based concerns such as generalization error are only of secondary importance. We approach these problems via Bayesian decision theory; after choosing natural utility functions, we derive the optim…
We describe the R package acebayes and demonstrate its use to find Bayesian optimal experimental designs. A decision-theoretic approach is adopted, with the optimal design maximising an expected utility. Finding Bayesian optimal designs for realistic problems is challenging, as the expected utility is typically intractable and the design space may be high-dimensional. The package implements the approximate coordinate exchange algorithm to optimise (an approximation to) the expected utility via a sequence of conditional one-dimensional optimisation steps. At each step, a Gaussian process regres…
We develop BatchBALD, a tractable approximation to the mutual information between a batch of points and model parameters, which we use as an acquisition function to select multiple informative points jointly for the task of deep Bayesian active learning. BatchBALD is a greedy linear-time $1 - \frac{1}{e}$-approximate algorithm amenable to dynamic programming and efficient caching. We compare BatchBALD to the commonly used approach for batch data acquisition and find that the current approach acquires similar and redundant points, sometimes performing worse than randomly acquiring data. We fini…
National University of Singapore（新加坡国立大学）；Massachusetts Institute of Technology（麻省理工学院）
This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountabl…
Enforcing safety is a key aspect of many problems pertaining to sequential decision making under uncertainty, which require the decisions made at every step to be both informative of the optimal decision and also safe. For example, we value both efficacy and comfort in medical therapy, and efficiency and safety in robotic control. We consider this problem of optimizing an unknown utility function with absolute feedback or preference feedback subject to unknown safety constraints. We develop an efficient safe Bayesian optimization algorithm, StageOpt, that separates safe region expansion and ut…
Bayesian Active Learning in the Presence of Nuisance Parameters
Department of Computer Science University of Manchester（计算机科学系曼彻斯特大学）；Department of Computer Science Aalto University（计算机科学系阿尔托大学）；Inserm Bordeaux Population Health, Vaccine Research Institute Université de Bordeaux Inria Bordeaux Sud-ouest（Inserm波尔多流行病与疫苗研究研究所波尔多大学Inria波尔多南西部）
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and parameters). For most common utility functions, the expected utility is rarely available in closed form and requires a computationally expensive approximation which then needs to be maximised over the space of all possible designs. This hinders practical use of the Bayesian approach to find experimental designs. However, recently, a new utility called Fisher …
We study pool-based active learning with abstention feedbacks, where a labeler can abstain from labeling a queried example with some unknown abstention rate. This is an important problem with many useful applications. We take a Bayesian approach to the problem and develop two new greedy algorithms that learn both the classification problem and the unknown abstention rate at the same time. These are achieved by simply incorporating the estimated abstention rate into the greedy criteria. We prove that both of our algorithms have near-optimality guarantees: they respectively achieve a ${(1-\frac{…
Michigan State University（密歇根州立大学）；Carnegie Mellon University（卡内基梅隆大学）；Intel Research Pittsburgh（英特尔匹兹堡研究院）
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two major problems. First, most algorithms only offer point estimation of the distance metric and can therefore be unreliable when the number of training examples is small. Second, since these algorithms generally select their training examples at random, they can be inefficient if labeling effort is limited. This paper presents a Bayesian framework for distance …
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；Aalto University（阿尔托大学）；Curious AI（Curious AI 公司）；University of Manchester（曼彻斯特大学）
A salient approach to interpretable machine learning is to restrict modeling to simple models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally, however, interpretability is about users' preferences, not the data generation mechanism; it is more natural to formulate interpretability as a utility function. In this work, we propose an interpretability utility, which explicates the trade-off between explanation fidelity and interpretability in the Bayesian framework. The method consists of two steps. First, a …
Much of the micro data used for epidemiological studies contain sensitive measurements on real individuals. As a result, such micro data cannot be published out of privacy concerns, rendering any published statistical analyses on them nearly impossible to reproduce. To promote the dissemination of key datasets for analysis without jeopardizing the privacy of individuals, we introduce a cohesive Bayesian framework for the generation of fully synthetic, high dimensional micro datasets of mixed categorical, binary, count, and continuous variables. This process centers around a joint Bayesian mode…
Several recent papers investigate Active Learning (AL) for mitigating the data dependence of deep learning for natural language processing. However, the applicability of AL to real-world problems remains an open question. While in supervised learning, practitioners can try many different methods, evaluating each against a validation set before selecting a model, AL affords no such luxury. Over the course of one AL run, an agent annotates its dataset exhausting its labeling budget. Thus, given a new task, an active learner has no opportunity to compare models and acquisition functions. This pap…
University of Kassel（卡塞尔大学）；Utrecht University（乌得勒支大学）
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…
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…
National University of Singapore（新加坡国立大学）；Queensland University of Technology（昆士兰科技大学）
We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all $α$-approximate algorithms are robust (i.e., near $α$-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lipschitz. This suggests we should use a Lipschitz utility for AL if robustness is required. For the minimum cost set…
University of Adelaide（阿德莱德大学）；University of Liverpool（利物浦大学）
Deep learning models have demonstrated outstanding performance in several problems, but their training process tends to require immense amounts of computational and human resources for training and labeling, constraining the types of problems that can be tackled. Therefore, the design of effective training methods that require small labeled training sets is an important research direction that will allow a more effective use of resources.Among current approaches designed to address this issue, two are particularly interesting: data augmentation and active learning. Data augmentation achieves t…
Active Preference Learning over Latent Preference Archetypes for Many-Objective Bayesian Optimization
University of Manchester（曼彻斯特大学）；University of Edinburgh（爱丁堡大学）；Aalto University（阿尔托大学）；University of Amsterdam（阿姆斯特丹大学）；ELLIS Institute Finland（芬兰ELLIS研究所）
The paper presents a critical introduction to the complex statistical models used in ${}^{14}$C dating. The emphasis is on the estimation of the transit time between a sequence of archeological layers. Although a frequentist estimation of the parameters is relatively simple, confidence intervals constructions are not standard as the models are not regular. I argue that that the Bayesian paradigm is a natural approach to these models. It is simple, and gives immediate solutions to credible sets, with natural interpretation and simple construction. Indeed it is the standard tool of ${}^{14}$C an…
We introduce the concepts of Bayesian lens, characterizing the bidirectional structure of exact Bayesian inference, and statistical game, formalizing the optimization objectives of approximate inference problems. We prove that Bayesian inversions compose according to the compositional lens pattern, and exemplify statistical games with a number of classic statistical concepts, from maximum likelihood estimation to generalized variational Bayesian methods. This paper is the first in a series laying the foundations for a compositional account of the theory of active inference, and we therefore pa…
We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint distribution of the network variables, and the algorithm iteratively selects which variables to observe in the next sample. We propose a new active learning algorithm for this setting, that finds with a high probability a structure with a score that is $ε$-close to the optimal score. We show that for a class of distributions that we term stable, a sample co…
