Variational Bayesian Optimal Experimental Design

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators by building on ideas from amortized variational inference. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We further demonstrate the practicality of our approach on a number of end-to-end experiments.Comment: Published as a conference paper at the Thirty-third Conference on Neural Information Processing Systems, Vancouver 2019. https://papers.nips.cc/paper/9553-variational-bayesian-optimal-experimental-design.pd

Probabilistic Bayesian optimal experimental design using conditional normalizing flows

Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such problems are computationally challenging because of (1) expensive and repeated evaluation of some optimality criterion that typically involves a double integration with respect to both the system parameters and the experimental data, (2) suffering from the curse-of-dimensionality when the system parameters and design variables are high-dimensional, (3) the optimization is combinatorial and highly non-convex if the design variables are binary, often leading to non-robust designs. To make the solution of the Bayesian OED problem efficient, scalable, and robust for practical applications, we propose a novel joint optimization approach. This approach performs simultaneous (1) training of a scalable conditional normalizing flow (CNF) to efficiently maximize the expected information gain (EIG) of a jointly learned experimental design (2) optimization of a probabilistic formulation of the binary experimental design with a Bernoulli distribution. We demonstrate the performance of our proposed method for a practical MRI data acquisition problem, one of the most challenging Bayesian OED problems that has high-dimensional (320 $\times$ 320) parameters at high image resolution, high-dimensional (640 $\times$ 386) observations, and binary mask designs to select the most informative observations

OpenBox: A Python Toolkit for Generalized Black-box Optimization

Black-box optimization (BBO) has a broad range of applications, including automatic machine learning, experimental design, and database knob tuning. However, users still face challenges when applying BBO methods to their problems at hand with existing software packages in terms of applicability, performance, and efficiency. This paper presents OpenBox, an open-source BBO toolkit with improved usability. It implements user-friendly inferfaces and visualization for users to define and manage their tasks. The modular design behind OpenBox facilitates its flexible deployment in existing systems. Experimental results demonstrate the effectiveness and efficiency of OpenBox over existing systems. The source code of OpenBox is available at https://github.com/PKU-DAIR/open-box

Enhanced Multimodal Representation Learning with Cross-modal KD

This paper explores the tasks of leveraging auxiliary modalities which are only available at training to enhance multimodal representation learning through cross-modal Knowledge Distillation (KD). The widely adopted mutual information maximization-based objective leads to a short-cut solution of the weak teacher, i.e., achieving the maximum mutual information by simply making the teacher model as weak as the student model. To prevent such a weak solution, we introduce an additional objective term, i.e., the mutual information between the teacher and the auxiliary modality model. Besides, to narrow down the information gap between the student and teacher, we further propose to minimize the conditional entropy of the teacher given the student. Novel training schemes based on contrastive learning and adversarial learning are designed to optimize the mutual information and the conditional entropy, respectively. Experimental results on three popular multimodal benchmark datasets have shown that the proposed method outperforms a range of state-of-the-art approaches for video recognition, video retrieval and emotion classification.Comment: Accepted by CVPR202

Stability estimates for the expected utility in Bayesian optimal experimental design

We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special case. To make the problem more concrete we proceed by considering non-linear Bayesian inverse problems with Gaussian likelihood and prove that the assumptions set out for the general case are satisfied and regain the stability of the expected utility with respect to perturbations to the observation map. Theoretical convergence rates are demonstrated numerically in three different examples.Comment: 20 pages; 6 figure

Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities

We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this combinatorial optimization problem is computationally costly, not only due to the complexity of the combinatorial search but also the difficulty of evaluating MI in nonlinear/non-Gaussian settings. We propose greedy approaches based on new computationally inexpensive lower bounds for MI, constructed via log-Sobolev inequalities. We demonstrate that our method outperforms random selection strategies, Gaussian approximations, and nested Monte Carlo (NMC) estimators of MI in various settings, including optimal design for nonlinear models with non-additive noise

Cross-Entropy Estimators for Sequential Experiment Design with Reinforcement Learning

Reinforcement learning can effectively learn amortised design policies for designing sequences of experiments. However, current methods rely on contrastive estimators of expected information gain, which require an exponential number of contrastive samples to achieve an unbiased estimation. We propose an alternative lower bound estimator, based on the cross-entropy of the joint model distribution and a flexible proposal distribution. This proposal distribution approximates the true posterior of the model parameters given the experimental history and the design policy. Our estimator requires no contrastive samples, can achieve more accurate estimates of high information gains, allows learning of superior design policies, and is compatible with implicit probabilistic models. We assess our algorithm's performance in various tasks, including continuous and discrete designs and explicit and implicit likelihoods

The Fundamental Dilemma of Bayesian Active Meta-learning

Many applications involve estimation of parameters that generalize across multiple diverse, but related, data-scarce task environments. Bayesian active meta-learning, a form of sequential optimal experimental design, provides a framework for solving such problems. The active meta-learner's goal is to gain transferable knowledge (estimate the transferable parameters) in the presence of idiosyncratic characteristics of the current task (task-specific parameters). We show that in such a setting, greedy pursuit of this goal can actually hurt estimation of the transferable parameters (induce so-called negative transfer). The learner faces a dilemma akin to but distinct from the exploration--exploitation dilemma: should they spend their acquisition budget pursuing transferable knowledge, or identifying the current task-specific parameters? We show theoretically that some tasks pose an inevitable and arbitrarily large threat of negative transfer, and that task identification is critical to reducing this threat. Our results generalize to analysis of prior misspecification over nuisance parameters. Finally, we empirically illustrate circumstances that lead to negative transfer