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FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting

JOURNAL OF MACHINE LEARNING RESEARCH 2022年第1期23卷 1-82页

作者： Zhao, Boxin Wang, Y. Samuel Kolar, Mladen Univ Chicago Booth Sch Business Chicago IL 60637 USA Cornell Univ Dept Stat & Data Sci Ithaca NY 14853 USA

We consider the problem of estimating the difference between two undirected functional graphical models with shared structures. In many applications, data are naturally regarded as a vector of random functions rather than as a vector of scalars. For example, electroen-cephalography (EEG) data are treated more appropriately as functions of time. In such a problem, not only can the number of functions measured per sample be large, but each function is itself an infinite-dimensional object, making estimation of model parameters challenging. This is further complicated by the fact that curves are usually observed only at discrete time points. We first define a functional differential graph that captures the differences between two functional graphical models and formally characterize when the functional differential graph is well defined. We then propose a method, FuDGE, that directly estimates the functional differential graph without first estimating each individual graph. This is particularly beneficial in settings where the individual graphs are dense but the differential graph is sparse. We show that FuDGE consistently estimates the functional differential graph even in a high-dimensional setting for both fully observed and discretely observed function paths. We illustrate the finite sample properties of our method through simulation studies. We also propose a competing method, the Joint Functional Graphi-cal Lasso, which generalizes the Joint graphical Lasso to the functional setting. Finally, we apply our method to EEG data to uncover differences in functional brain connectivity between a group of individuals with alcohol use disorder and a control group.

关键词： differential graph estimation functional data analysis multivariate functional data probabilistic graphical models structure learning

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BARD: A Structured Technique for Group Elicitation of Bayesian Networks to Support Analytic Reasoning

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RISK ANALYSIS 2022年第6期42卷 1155-1178页

作者： Nyberg, Erik P. Nicholson, Ann E. Korb, Kevin B. Wybrow, Michael Zukerman, Ingrid Mascaro, Steven Thakur, Shreshth Alvandi, Abraham Oshni Riley, Jeff Pearson, Ross Morris, Shane Herrmann, Matthieu Azad, A. K. M. Bolger, Fergus Hahn, Ulrike Lagnado, David Monash Univ Dept Data Sci & AI Clayton Vic 3800 Australia Bayesian Intelligence Pty Ltd Melbourne Vic Australia Automat Studio Pty Ltd Melbourne Vic Australia Univ Strathclyde Strathclyde Business Sch Glasgow Lanark Scotland UCL Dept Expt Psychol London England Birkbeck Univ London Dept Psychol Sci London England

In many complex, real-world situations, problem solving and decision making require effective reasoning about causation and uncertainty. However, human reasoning in these cases is prone to confusion and error. Bayesian networks (BNs) are an artificial intelligence technology that models uncertain situations, supporting better probabilistic and causal reasoning and decision making. However, to date, BN methodologies and software require (but do not include) substantial upfront training, do not provide much guidance on either the model building process or on using the model for reasoning and reporting, and provide no support for building BNs collaboratively. Here, we contribute a detailed description and motivation for our new methodology and application, Bayesian ARgumentation via Delphi (BARD). BARD utilizes BNs and addresses these shortcomings by integrating (1) short, high-quality e-courses, tips, and help on demand;(2) a stepwise, iterative, and incremental BN construction process;(3) report templates and an automated explanation tool;and (4) a multiuser web-based software platform and Delphi-style social processes. The result is an end-to-end online platform, with associated online training, for groups without prior BN expertise to understand and analyze a problem, build a model of its underlying probabilistic causal structure, validate and reason with the causal model, and (optionally) use it to produce a written analytic report. Initial experiments demonstrate that, for suitable problems, BARD aids in reasoning and reporting. Comparing their effect sizes also suggests BARD's BN-building and collaboration combine beneficially and cumulatively.

关键词： Delphi process probabilistic graphical models probabilistic reasoning

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probabilistic joint models incorporating logic and learning via structured variational approximation for information extraction

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KNOWLEDGE AND INFORMATION SYSTEMS 2012年第2期32卷 415-444页

作者： Yu, Xiaofeng Lam, Wai Chinese Univ Hong Kong Informat Syst Lab Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Traditional information extraction systems for compound tasks adopt pipeline architectures, which are highly ineffective and suffer from several problems such as cascading accumulation of errors. In this paper, we propose a joint discriminative probabilistic framework to optimize all relevant subtasks simultaneously. This framework offers a great flexibility to incorporate the advantage of both uncertainty for sequence modeling and first-order logic for domain knowledge. The first-order logic model provides a more expressive formalism tackling the issue of limited expressiveness of traditional attribute-value representation. Our framework defines a joint probability distribution for both segmentations in sequence data and possible worlds of relations between segments in the form of an exponential family. Since exact parameter estimation and inference are prohibitively intractable in this model, a structured variational inference algorithm is developed to perform parameter estimation approximately. For inference, we propose a highly coupled, bi-directional Metropolis-Hastings (MH) algorithm to find the maximum a posteriori (MAP) assignments for both segmentations and relations. Extensive experiments on two real-world information extraction tasks, entity identification and relation extraction from Wikipedia, and citation matching show that (1) the proposed model achieves significant improvement on both tasks compared to state-of-the-art pipeline models and other joint models;(2) the bi-directional MH inference algorithm obtains boosted performance compared to the greedy, N-best list, and uni-directional MH sampling algorithms.

关键词： probabilistic graphical models First-order logic Structured variational approximation Bi-directional Metropolis-Hastings sampling Joint information extraction

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Combining object and feature dynamics in probabilistic tracking

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COMPUTER VISION AND IMAGE UNDERSTANDING 2007年第3期108卷 243-260页

作者： Taycher, Leonid Fisher, John W., III Darrell, Trevor MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

Objects can exhibit different dynamics at different spatio-temporal scales, a property that is often exploited by visual tracking algorithms. A local dynamic model is typically used to extract image features that are then used as inputs to a system for tracking the object using a global dynamic model. Approximate local dynamics may be brittle-point trackers drift due to image noise and adaptive background models adapt to foreground objects that become stationary-and constraints from the global model can make them more robust. We propose a probabilistic framework for incorporating knowledge about global dynamics into the local feature extraction processes. A global tracking algorithm can be formulated as a generative model and used to predict feature values thereby influencing the observation process of the feature extractor, which in turn produces feature values that are used in high-level inference. We combine such models utilizing a multichain graphical model framework. We show the utility of our framework for improving feature tracking as well as shape and motion estimates in a batch factorization algorithm. We also propose an approximate filtering algorithm appropriate for online applications and demonstrate its application to tasks in background subtraction, structure from motion and articulated body tracking. (c) 2007 Elsevier Inc. All rights reserved.

关键词： probabilistic graphical models approximate models articulated body tracking background subtraction shape from motion

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Hinge-Loss Markov Random Fields and probabilistic Soft Logic

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JOURNAL OF MACHINE LEARNING RESEARCH 2017年第1期18卷 3846-3912页

作者： Bach, Stephen H. Broecheler, Matthias Huang, Bert Getoor, Lise Stanford Univ Comp Sci Dept Stanford CA 94305 USA DataStax Santa Clara CA USA Virginia Tech Comp Sci Dept Blacksburg VA 24061 USA Univ Calif Santa Cruz Comp Sci Dept Santa Cruz CA 95064 USA

A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to images, video, and natural language. In this paper, we introduce two new formalisms for modeling structured data, and show that they can both capture rich structure and scale to big data. The first, hinge-loss Markov random fields (HL-MRFs), is a new kind of probabilistic graphical model that generalizes different approaches to convex inference. We unite three approaches from the randomized algorithms, probabilistic graphical models, and fuzzy logic communities, showing that all three lead to the same inference objective. We then define HL-MRFs by generalizing this unified objective. The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic. We introduce an algorithm for inferring most-probable variable assignments (MAP inference) that is much more scalable than general-purpose convex optimization methods, because it uses message passing to take advantage of sparse dependency structures. We then show how to learn the parameters of HL-MRFs. The learned HL-MRFs are as accurate as analogous discrete models, but much more scalable. Together, these algorithms enable HL-MRFs and PSL to model rich, structured data at scales not previously possible.

关键词： probabilistic graphical models statistical relational learning structured prediction

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Bayesian distance metric learning for discriminative fuzzy c-means clustering

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NEUROCOMPUTING 2018年 319卷 21-33页

作者： Heidari, Negar Moslehi, Zahra Mirzaei, Abdolreza Safayani, Mehran Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran

A great number of machine learning algorithms strongly depend on the underlying distance metric for representing the important correlations of input data. Distance metric learning is defined as learning an appropriate similarity or distance metric for all input data pairs. Metric learning algorithms are of supervised and unsupervised categories with different deterministic and probabilistic approaches. One of the objectives of unsupervised metric learning is to project data points into a new space in such a way that high clustering accuracy is provided. This is obtainable by maximizing between-clusters separation. There exist some deterministic metric learning methods to serve this purpose. In this article, a probabilistic method for unsupervised distance metric learning is proposed which aims to maximize the separability among different clusters in the projected space. In this proposed method, distance metric learning and fuzzy c-means clustering are jointly formulated in a sense that FCM provides clusters, and distance metric learning algorithm applies the obtained clusters to materialize the maximum separability among all;moreover, Markov Chain Monte Carlo (MCMC) algorithm is applied to infer the latent variables. This proposed method, not only can obtain a low dimensional projection with specified number of dimensions, but also it can learn the proper number of reduced dimensions for each dataset in an automated sense. The experimental results reveal the out-performance of this method on different real-world datasets against its counterparts. (c) 2018 Elsevier B.V. All rights reserved.

关键词： Distance metric learning Fuzzy clustering Unsupervised learning probabilistic graphical models Bayesian inference Markov chain monte carlo

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Diverse and consistent multi-view networks for semi-supervised regression

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MACHINE LEARNING 2023年第7期112卷 2359-2395页

作者： Nguyen, Cuong Raja, Arun Zhang, Le Xu, Xun Unnikrishnan, Balagopal Ragab, Mohamed Lu, Kangkang Foo, Chuan-Sheng ASTAR Inst Infocomm Res I2R 1 Fusionopolis WayConnexis North Tower 20-10 Singapore 138632 Singapore ASTAR Ctr Frontier AI Res CFAR 1 Fusionopolis WayConnexis North Tower 16-16 Singapore 138632 Singapore Univ Elect Sci & Technol China 4 1st Ring Rd East 2 Sect Chengdu 610056 Sichuan Peoples R China Univ Toronto 27 Kings Coll Cir Toronto ON M5S 1A1 Canada

Label collection is costly in many applications, which poses the need for label-efficient learning. In this work, we present Diverse and Consistent Multi-view Networks (DiCoM)-a novel semi-supervised regression technique based on a multi-view learning framework. DiCoM combines diversity with consistency-two seemingly opposing yet complementary principles of multi-view learning-based on underlying probabilistic graphical assumptions. Given multiple deep views of the same input, DiCoM encourages a negative correlation among the views' predictions on labeled data, while simultaneously enforces their agreement on unlabeled data. DiCoM can utilize either multi-network or multi-branch architectures to make a trade-off between computational cost and modeling performance. Under realistic evaluation setups, DiCoM outperforms competing methods on tabular, time series and image data. Our ablation studies confirm the importance of having both consistency and diversity.

关键词： Semi-supervised regression Multi-view learning Diversity regularization probabilistic graphical models

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An Adaptive Markov Random Field for Structured Compressive Sensing

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2019年第3期28卷 1556-1570页

作者： Suwanwimolkul, Suwichaya Zhang, Lei Gong, Dong Zhang, Zhen Chen, Chao Ranasinghe, Damith C. Shi, Javen Qinfeng Univ Adelaide Sch Comp Sci Adelaide SA 5005 Australia Natl Univ Singapore Dept Comp Sci Singapore 119077 Singapore SUNY Stony Brook Dept Biomed Informat Stony Brook NY 11794 USA

Exploiting intrinsic structures in sparse signals underpin the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (i.e., the ability to fit a wide range of signals with diverse structures) and adaptability (i.e., being adaptive to a specific signal). Most existing approaches, however, often only achieve one of these two properties. In this paper, we propose a novel adaptive Markov random field sparsity prior for CS, which not only is able to capture a broad range of sparsity structures, but also can adapt to each sparse signal through refining the parameters of the sparsity prior with respect to the compressed measurements. To maximize the adaptability, we also propose a new sparse signal estimation, where the sparse signals, support, noise, and signal parameter estimation are unified into a variational optimization problem, which can be effectively solved with an alternative minimization scheme. Extensive experiments on three real-world datasets demonstrate the effectiveness of the proposed method in recovery accuracy, noise tolerance, and runtime.

关键词： Structured compressive sensing probabilistic graphical models sparse representation

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FunCat functional inference with belief propagation and feature integration

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2008年第5期32卷 375-377页

作者： Surmeli, Dimitrij Ratmann, Oliver Mewes, Hans-Werner Tetko, Igor V. Inst Bioinformat & Syst Biol Helmholtz Zentrum Munchen German Res Ctr Environm D-85764 Neuherberg Germany BrainLAB Feldkirchen Germany Univ London Imperial Coll Sci Technol & Med Ctr Biostat London W2 1PG England Tech Univ Munich Life & Food Sci Ctr Weihenstephan D-85354 Freising Weihenstephan Germany

Pairwise comparison of sequence data is intensively used for automated functional protein annotation, while graphical models emerge as promising candidates for an integration of various heterogeneous features. We designed a model, termed hRMN that integrates different genomic features and implemented a variant of belief propagation for functional annotation transfer. hRMN allows the assignment Of multiple functional categories while avoiding common problems in annotation transfer from heterogeneous datasets, such as an independency of the investigated datasets, We benchmarked this system with large-scale annotation transfer (based oil the MIPS FunCat ontology) to proteins of the prokaryotes Bacillus subtilis, Helicobacter pylori, Listeria monocytogenes, and Listeria innocua. hRMN consistently outperformed two competitors in annotation of four bacterial genomes. The developed code is available for download at http://***/proj/bfab/bfab/***. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： Automatic functional annotation Belief propagation Bacterial genomes Heterogeneous data sources probabilistic graphical models

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Saving computational budget in Bayesian network-based evolutionary algorithms

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NATURAL COMPUTING 2021年第4期20卷 775-790页

作者： Scoczynski, Marcella Delgado, Myriam Luders, Ricardo Oliva, Diego Wagner, Markus Sung, Inkyung El Yafrani, Mohamed Fed Univ Technol Parana UTFPR Curitiba Parana Brazil Univ Oberta Catalunya IN3 Comp Sci Dept Barcelona Spain Univ Guadalajara Dept Ciencias Computac CUCEI Guadalajara Jalisco Mexico Univ Adelaide Optimisat & Logist Adelaide SA Australia Aalborg Univ Operat Res Grp Aalborg Denmark

During the evolutionary process, algorithms based on probability distributions for generating new individuals suffer from computational burden due to the intensive computation of probability distribution estimations, particularly when using probabilistic Graph models (PGMs). In the Bayesian Optimisation Algorithm (BOA), for instance, determining the optimal Bayesian network structure by a given solution sample is an NP-hard problem. To overcome this issue, we consider a new BOA-based optimisation approach (FBOA) which explores the fact that patterns of PGM adjustments can be used as a guide to reduce the frequency of PGM updates because significant changes in PGM structure might not occur so frequently, and because they can be particularly sparse at the end of evolution. In the present paper, this new approach is scrutinised in the search space of an NK-landscape optimisation problem for medium and large-size instances. Average gaps and success rates as well as the correlation between the landscape ruggedness of the problem and the expected runtime of FBOA and BOA are presented for medium-size instances. For large-size instances, optimisation results from FBOA and BOA are compared. The experiments show that, despite our FBOA being of almost three times faster than BOA, it still produces competitive optimisation results.

关键词： Estimation of distribution algorithms probabilistic graphical models Bayesian networks

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