Active learning frameworks offer efficient data annotation without remarkable accuracy degradation. In other words, active learning starts training the model with a small size of labeled data while exploring the space of unlabeled data in order to select most informative samples to be labeled. Generally speaking, representing the uncertainty is crucial in any active learning framework, however, deep learning methods are not capable of either representing or manipulating model uncertainty. On the other hand, from the real world application perspective, uncertainty representation is getting more and more attention in the machine learning community. Deep Bayesian active learning frameworks and generally any Bayesian active learning settings, provide practical consideration in the model which allows training with small data while representing the model uncertainty for further efficient training. In this paper, we briefly survey recent advances in Bayesian active learning and in particular deep Bayesian active learning frameworks.
University of Surrey（萨里大学）；Bielefeld University（比勒费尔德大学）；Honda Research Institute Europe GmbH（本田欧洲研究所有限公司）
Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their applications. Hence, this paper attempts to provide a comprehensive and updated survey of recent advances in Bayesian optimization and identify interesting open problems. We categorize the existing work on Bayesian optimization into nine main groups according to the motivations and focus of the proposed algorithms. For each category, we present the main advan…
UNSW Sydney（悉尼新南威尔士大学）；Manipal Institute of Technology（马尼帕尔理工学院）
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be represented via graphs. These types of data are often found in health and medicine, social networks, and research data repositories. Graph convolutional neural networks have recently gained attention in the field of deep learning that takes advantage of graph-based data representation with automatic feature extraction via convolutions. Given the popularity of the…
We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n (n - 1) potential edges can be computed in O(n 2^n) total time. This result is achieved by a forward-backward technique and fast Moebius transform algorithms, which are of independent interest.…
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…
The work focuses on the modelling and imputation of oil and gas reservoirs parameters, specifically, the problem of predicting the oil recovery factor (RF) using Bayesian networks (BNs). Recovery forecasting is critical for the oil and gas industry as it directly affects a company's profit. However, current approaches to forecasting the RF are complex and computationally expensive. In addition, they require vast amount of data and are difficult to constrain in the early stages of reservoir development. To address this problem, we propose a BN approach and describe ways to improve parameter pre…
Universidade de São Paulo（圣保罗大学）；Dalle Molle Institute for Artificial Intelligence（达莱莫莱人工智能研究所）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to eac…
Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches
Center for Applied Statistics and School of Statistics, Renmin University of China（应用统计中心和中国人民大学统计学院）；Independent Researcher（独立研究者）；School of Computer Science, Guangdong University of Technology（广东工业大学计算机学院）；School of Statistics and Data Science, Southeast University（东南大学统计与数据科学学院）
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent variables are called nonidentifiable, because the map from a parameter to a statistical model is not one-to-one. In nonidentifiable models, both the likelihood function and the posterior distribution have singularities in general, hence it was difficult to analyze their statistical properties. However, from the end of the 20th century, new theory and methodology…
Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider a…
In this report, we present qualitative analysis of Monte Carlo (MC) dropout method for measuring model uncertainty in neural network (NN) models. We first consider the sources of uncertainty in NNs, and briefly review Bayesian Neural Networks (BNN), the group of Bayesian approaches to tackle uncertainties in NNs. After presenting mathematical formulation of MC dropout, we proceed to suggesting potential benefits and associated costs for using MC dropout in typical NN models, with the results from our experiments.
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；Aalto University School of Science（阿尔托大学理工学院）
Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is focused on the computational efficiency issue. However, it is still not feasible to combine many kernels using existing Bayesian approaches due to their high time complexity. We propose a fully conjugate Bayesian formulation and derive a deterministic variational approximation, which allows us to combine hundreds or thousands of kernels very efficiently. We …
Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference offers the tools to tackle this challenge in a scalable way and with some degree of flexibility on the approximation, but for over-parameterized models this is challenging due to the over-regularization property of the variational objective. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random …
Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide robust uncertainty quantification remains a challenge. This has been addressed with variational autoencoders so far. Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling has faced several limitations for large models; however, recent advances in parallel computing and advanced proposal schemes have opened routes less traveled. This paper presents B…
Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）
Continual Learning is a learning paradigm where learning systems are trained with sequential or streaming tasks. Two notable directions among the recent advances in continual learning with neural networks are ($i$) variational Bayes based regularization by learning priors from previous tasks, and, ($ii$) learning the structure of deep networks to adapt to new tasks. So far, these two approaches have been orthogonal. We present a novel Bayesian approach to continual learning based on learning the structure of deep neural networks, addressing the shortcomings of both these approaches. The propos…
Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process predictors across output channels. We leverage this observation to study representation learning in these networks, allowing us to connect limiting results obtained in previous studies within a unified framework. In total, these results advance o…
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…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999). In this paper, we propose a kind of Bayesian networks in which low-dimensional mixtures of Gaussians over different subsets of the domain's variables are combined into a coherent joint probability model over the entire domain. The network is also capable of modeling complex dependencie…
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learning, with substantial recent developments on adaptive, flexible and scalable Bayesian learning. This article provides a survey of the recent advances in Big learning with Bayesian methods, termed Big Bayesian Learning, including nonparametric Bayesian methods for adaptively inferr…
The medical field stands to see significant benefits from the recent advances in deep learning. Knowing the uncertainty in the decision made by any machine learning algorithm is of utmost importance for medical practitioners. This study demonstrates the utility of using Bayesian LSTMs for classification of medical time series. Four medical time series datasets are used to show the accuracy improvement Bayesian LSTMs provide over standard LSTMs. Moreover, we show cherry-picked examples of confident and uncertain classifications of the medical time series. With simple modifications of the common…
EDML is a recently proposed algorithm for learning MAP parameters in Bayesian networks. In this paper, we present a number of new advances and insights on the EDML algorithm. First, we provide the multivalued extension of EDML, originally proposed for Bayesian networks over binary variables. Next, we identify a simplified characterization of EDML that further implies a simple fixed-point algorithm for the convex optimization problem that underlies it. This characterization further reveals a connection between EDML and EM: a fixed point of EDML is a fixed point of EM, and vice versa. We thus id…
Cornell University（康奈尔大学）；UNSW Australia（澳大利亚新南威尔士大学）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predictive accuracy. In this paper, we address two critical gaps concerning the usage and understanding of VB for MMNL. First, extant VB methods are limited to utility specifications involving only individual-specific taste parameters. Second, the finite-sample properties of VB estimato…
Department of Computer Science, University of Pisa（比萨大学计算机科学系）
The study of deep recurrent neural networks (RNNs) and, in particular, of deep Reservoir Computing (RC) is gaining an increasing research attention in the neural networks community. The recently introduced Deep Echo State Network (DeepESN) model opened the way to an extremely efficient approach for designing deep neural networks for temporal data. At the same time, the study of DeepESNs allowed to shed light on the intrinsic properties of state dynamics developed by hierarchical compositions of recurrent layers, i.e. on the bias of depth in RNNs architectural design. In this paper, we summariz…
