This paper presents an information-theoretic framework for unifying active learning problems: level set estimation (LSE), Bayesian optimization (BO), and their generalized variant. We first introduce a novel active learning criterion that subsumes an existing LSE algorithm and achieves state-of-the-art performance in LSE problems with a continuous input domain. Then, by exploiting the relationship between LSE and BO, we design a competitive information-theoretic acquisition function for BO that has interesting connections to upper confidence bound and max-value entropy search (MES). The latter connection reveals a drawback of MES which has important implications on not only MES but also on other MES-based acquisition functions. Finally, our unifying information-theoretic framework can be applied to solve a generalized problem of LSE and BO involving multiple level sets in a data-efficient manner. We empirically evaluate the performance of our proposed algorithms using synthetic benchmark functions, a real-world dataset, and in hyperparameter tuning of machine learning models.
The Information Bottleneck principle offers both a mechanism to explain how deep neural networks train and generalize, as well as a regularized objective with which to train models. However, multiple competing objectives are proposed in the literature, and the information-theoretic quantities used in these objectives are difficult to compute for large deep neural networks, which in turn limits their use as a training objective. In this work, we review these quantities and compare and unify previously proposed objectives, which allows us to develop surrogate objectives more friendly to optimiza…
Stochastic gradient descent based algorithms are typically used as the general optimization tools for most deep learning models. A Restricted Boltzmann Machine (RBM) is a probabilistic generative model that can be stacked to construct deep architectures. For RBM with Bernoulli inputs, non-Euclidean algorithm such as stochastic spectral descent (SSD) has been specifically designed to speed up the convergence with improved use of the gradient estimation by sampling methods. However, the existing algorithm and corresponding theoretical justification depend on the assumption that the possible conf…
RWTH Aachen University（亚琛工业大学）；Technical University Darmstadt（达姆施塔特工业大学）
Active inference (AI) is a persuasive theoretical framework from computational neuroscience that seeks to describe action and perception as inference-based computation. However, this framework has yet to provide practical sensorimotor control algorithms that are competitive with alternative approaches. In this work, we frame active inference through the lens of control as inference (CaI), a body of work that presents trajectory optimization as inference. From the wider view of `probabilistic numerics', CaI offers principled, numerically robust optimal control solvers that provide uncertainty q…
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset shifts and can be used for prediction in new, unseen environments. However, these methods consider different types of shifts and have been developed under disparate frameworks, making it difficult to theoretically analyze how solutions differ with respect to stability and accuracy. Taking a causal graphical view, we use a flexible graphical representation t…
Sogang University（西江大学）；University of Pennsylvania（宾夕法尼亚大学）；Princeton University（普林斯顿大学）
Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov c…
With the recent demand of deploying neural network models on mobile and edge devices, it is desired to improve the model's generalizability on unseen testing data, as well as enhance the model's robustness under fixed-point quantization for efficient deployment. Minimizing the training loss, however, provides few guarantees on the generalization and quantization performance. In this work, we fulfill the need of improving generalization and quantization performance simultaneously by theoretically unifying them under the framework of improving the model's robustness against bounded weight pertur…
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…
Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a model's training. Are these different approaches connected, and if so, how? We revisit the fundamentals of Bayesian optimal experiment design and show that these recently proposed methods can be understood as approximations to information-theoretic quantities: among them, the mutual information between predictions and model parameters, known as expected informatio…
Ghent University（根特大学）；Poznań University of Technology（波兹南理工大学）；Paderborn University（帕德博恩大学）
Multi-target prediction (MTP) is concerned with the simultaneous prediction of multiple target variables of diverse type. Due to its enormous application potential, it has developed into an active and rapidly expanding research field that combines several subfields of machine learning, including multivariate regression, multi-label classification, multi-task learning, dyadic prediction, zero-shot learning, network inference, and matrix completion. In this paper, we present a unifying view on MTP problems and methods. First, we formally discuss commonalities and differences between existing MTP…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；Facebook AI Research（Facebook人工智能研究院）；Columbia University（哥伦比亚大学）
Distillation (Hinton et al., 2015) and privileged information (Vapnik & Izmailov, 2015) are two techniques that enable machines to learn from other machines. This paper unifies these two techniques into generalized distillation, a framework to learn from multiple machines and data representations. We provide theoretical and causal insight about the inner workings of generalized distillation, extend it to unsupervised, semisupervised and multitask learning scenarios, and illustrate its efficacy on a variety of numerical simulations on both synthetic and real-world data.
Northeastern University（东北大学）；University of Pittsburgh（匹兹堡大学）；Georgetown University（乔治城大学）
Obtaining labels can be costly and time-consuming. Active learning allows a learning algorithm to intelligently query samples to be labeled for efficient learning. Fisher information ratio (FIR) has been used as an objective for selecting queries in active learning. However, little is known about the theory behind the use of FIR for active learning. There is a gap between the underlying theory and the motivation of its usage in practice. In this paper, we attempt to fill this gap and provide a rigorous framework for analyzing existing FIR-based active learning methods. In particular, we show t…
Function Based Isolation Forest (FuBIF): A Unifying Framework for Interpretable Isolation-Based Anomaly Detection
Brain, Mind and Computer Science, University of Padova, Italy（脑科学与计算机科学系，帕多瓦大学，意大利）；Department of Mathematics, Sapienza University of Roma, Italy（数学系，罗马萨皮恩扎大学，意大利）；Department of Information Engineering, University of Padova, Italy（信息工程系，帕多瓦大学，意大利）
Universitat Pompeu Fabra（庞培法布拉大学）；Barcelona Graduate School of Economics（巴塞罗那经济学研究生院）；Imperial College London（帝国理工学院）
The principle of optimism in the face of uncertainty underpins many theoretically successful reinforcement learning algorithms. In this paper we provide a general framework for designing, analyzing and implementing such algorithms in the episodic reinforcement learning problem. This framework is built upon Lagrangian duality, and demonstrates that every model-optimistic algorithm that constructs an optimistic MDP has an equivalent representation as a value-optimistic dynamic programming algorithm. Typically, it was thought that these two classes of algorithms were distinct, with model-optimist…
University of Geneva（日内瓦大学）；Harvard University（哈佛大学）；Imperial College London（帝国理工学院）
Bottleneck problems are an important class of optimization problems that have recently gained increasing attention in the domain of machine learning and information theory. They are widely used in generative models, fair machine learning algorithms, design of privacy-assuring mechanisms, and appear as information-theoretic performance bounds in various multi-user communication problems. In this work, we propose a general family of optimization problems, termed as complexity-leakage-utility bottleneck (CLUB) model, which (i) provides a unified theoretical framework that generalizes most of the …
