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Simultaneous Inference for Pairwise graphical models with Generalized Score Matching

JOURNAL OF MACHINE LEARNING RESEARCH 2020年第1期21卷 1-51页

作者： Yu, Ming Gupta, Varun Kolar, Mladen Univ Chicago Booth Sch Business Chicago IL 60637 USA

probabilistic graphical models provide a flexible yet parsimonious framework for modeling dependencies among nodes in networks. There is a vast literature on parameter estimation and consistent model selection for graphical models. However, in many of the applications, scientists are also interested in quantifying the uncertainty associated with the estimated parameters and selected models, which current literature has not addressed thoroughly. In this paper, we propose a novel estimator for statistical inference on edge parameters in pairwise graphical models based on generalized Hyvarinen scoring rule. Hyvarinen scoring rule is especially useful in cases where the normalizing constant cannot be obtained efficiently in a closed form, which is a common problem for graphical models, including Ising models and truncated Gaussian graphical models. Our estimator allows us to perform statistical inference for general graphical models whereas the existing works mostly focus on statistical inference for Gaussian graphical models where finding normalizing constant is computationally tractable. Under mild conditions that are typically assumed in the literature for consistent estimation, we prove that our proposed estimator is root n-consistent and asymptotically normal, which allows us to construct confidence intervals and build hypothesis tests for edge parameters. Moreover, we show how our proposed method can be applied to test hypotheses that involve a large number of model parameters simultaneously. We illustrate validity of our estimator through extensive simulation studies on a diverse collection of data-generating processes.

关键词： generalized score matching high-dimensional inference probabilistic graphical models simultaneous inference

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Latent classification models

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MACHINE LEARNING 2005年第3期59卷 237-265页

作者： Langseth, H Nielsen, TD Norwegian Univ Sci & Technol Dept Math Sci N-7491 Trondheim Norway Aalborg Univ Dept Comp Sci DK-9220 Aalborg Denmark

One of the simplest, and yet most consistently well-performing set of classifiers is the Naive Bayes models. These models rely on two assumptions: (i) All the attributes used to describe an instance are conditionally independent given the class of that instance, and (ii) all attributes follow a specific parametric family of distributions. In this paper we propose a new set of models for classification in continuous domains, termed latent classification models. The latent classification model can roughly be seen as combining the Naive Bayes model with a mixture of factor analyzers, thereby relaxing the assumptions of the Naive Bayes classifier. In the proposed model the continuous attributes are described by a mixture of multivariate Gaussians, where the conditional dependencies among the attributes are encoded using latent variables. We present algorithms for learning both the parameters and the structure of a latent classification model, and we demonstrate empirically that the accuracy of the proposed model is significantly higher than the accuracy of other probabilistic classifiers.

关键词： classification probabilistic graphical models naive Bayes correlation

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ROAM: A Rich Object Appearance Model with Application to Rotoscoping

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2020年第8期42卷 1996-2010页

作者： Perez-Rua, Juan-Manuel Miksik, Ondrej Crivelli, Tomas Bouthemy, Patrick Torr, Philip H. S. Perez, Patrick Technicolor F-35576 Cesson Sevigne Bretagne France Univ Oxford Dept Engn Sci Oxford OX1 2JD England Technicolor Rennes Res & Innovat F-35576 Cesson Sevigne Bretagne France IRISA INRIA F-35000 Rennes France Valeo Ai F-75017 Paris France

Rotoscoping, the detailed delineation of scene elements through a video shot, is a painstaking task of tremendous importance in professional post-production pipelines. While pixel-wise segmentation techniques can help for this task, professional rotoscoping tools rely on parametric curves that offer the artists a much better interactive control on the definition, editing and manipulation of the segments of interest. Sticking to this prevalent rotoscoping paradigm, we propose a novel framework to capture and track the visual aspect of an arbitrary object in a scene, given an initial closed outline of this object. This model combines a collection of local foreground/background appearance models spread along the outline, a global appearance model of the enclosed object and a set of distinctive foreground landmarks. The structure of this rich appearance model allows simple initialization, efficient iterative optimization with exact minimization at each step, and on-line adaptation in videos. We further extend this model by so-called trimaps which serve as an input to alpha-matting algorithms to allow truly seamless compositing. To this end, we leverage local classifiers attached to the roto-curves to define a confidence measure that is well-suited to define trimaps with adaptive band-widths. The resulting trimaps are parametric, temporally consistent and remain fully editable by the artist. We demonstrate qualitatively and quantitatively the merit of this framework through comparisons with tools based on either dynamic segmentation with a closed curve or pixel-wise binary labelling.

关键词： Adaptation models Tools Shape Task analysis Pipelines Labeling Deformable models Rotoscoping trimaps video segmentation video alpha-matting probabilistic graphical models dynamic programming

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Tractable inference in credal sentential decision diagrams

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2020年 125卷 26-48页

作者： Mattei, Lilith Antonucci, Alessandro Maua, Denis Deratani Facchini, Alessandro Llerena, Julissa Villanueva Ist Dalle Molle Intelligenza Artificiale Manno Lugano Switzerland Univ Sao Paulo Inst Math & Stat Sao Paulo Brazil

probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually "learned" from a set of observations. This leads to overconfident and prior-dependent inferences when data are scarce, unreliable or conflicting. In this work, we develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with (so-called credal) sets of mass functions. These models induce a joint credal set over the set of Boolean variables, that sharply assigns probability zero to states inconsistent with the logical constraints. Three inference algorithms are derived for these models. These allow to compute: (i) the lower and upper probabilities of an observation for an arbitrary number of variables;(ii) the lower and upper conditional probabilities for the state of a single variable given an observation;(iii) whether or not all the probabilistic sentential decision diagrams compatible with the credal specification have the same most probable explanation of a given set of variables given an observation of the other variables. These inferences are tractable, as all the three algorithms, based on bottom-up traversal with local linear programming tasks on the disjunctive gates, can be solved in polynomial time with respect to the circuit size. The first algorithm is always exact, while the remaining two might induce a conservative (outer) approximation in the case of multiply connected circuits. A semantics for this approximation together with an auxiliary algorithm able to decide whether or not the result is exact is also provided together with a brute-force characterization of the exact inference in these

关键词： probabilistic graphical models Imprecise probability Credal sets probabilistic circuits Sentential decision diagrams Sum-product networks

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Modeling challenges with influence diagrams: Constructing probability and utility models

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DECISION SUPPORT SYSTEMS 2010年第4期49卷 354-364页

作者： Bielza, C. Gomez, M. Shenoy, P. P. Univ Granada Dept Comp Sci & Artificial intelligence E-18071 Granada Spain Univ Politecn Madrid Dept Inteligencia Artificial Sch Comp Sci E-28660 Madrid Spain Univ Kansas Sch Business Lawrence KS 66045 USA

Influence diagrams have become a popular tool for representing and solving complex decision-making problems under uncertainty. In this paper, we focus on the task of building probability models from expert knowledge, and also on the challenging and less known task of constructing utility models in influence diagrams. Our goal is to review the state of the art and list some challenges. Similarly to probability models, which are embedded in influence diagrams as a Bayesian network, preferential/utility independence conditions can be used to factor the joint utility function into small factors and reduce the number of parameters needed to fully define the joint function. A number of graphical models have been recently proposed to factor the joint utility function, including the generalized additive independence networks, ceteris paribus networks, utility ceteris paribus networks, expected utility networks, and utility diagrams. Similarly to probability models, utility models can also be engineered from a domain expert or induced from data. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Decision-making under uncertainty Influence diagrams Bayesian networks probabilistic graphical models Generalized additive independence networks Ceteris paribus networks Utility ceteris paribus networks Expected utility networks Utility diagrams

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Assessing transcriptomic heterogeneity of single-cell RNASeq data by bulk-level gene expression data

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BMC BIOINFORMATICS 2024年第1期25卷 1页

作者： Tiong, Khong-Loon Luzhbin, Dmytro Yeang, Chen-Hsiang Acad Sinica Inst Stat Sci Taipei Taiwan

Background Single-cell RNA sequencing (sc-RNASeq) data illuminate transcriptomic heterogeneity but also possess a high level of noise, abundant missing entries and sometimes inadequate or no cell type annotations at all. Bulk-level gene expression data lack direct information of cell population composition but are more robust and complete and often better annotated. We propose a modeling framework to integrate bulk-level and single-cell RNASeq data to address the deficiencies and leverage the mutual strengths of each type of data and enable a more comprehensive inference of their transcriptomic heterogeneity. Contrary to the standard approaches of factorizing the bulk-level data with one algorithm and (for some methods) treating single-cell RNASeq data as references to decompose bulk-level data, we employed multiple deconvolution algorithms to factorize the bulk-level data, constructed the probabilistic graphical models of cell-level gene expressions from the decomposition outcomes, and compared the log-likelihood scores of these models in single-cell data. We term this framework backward deconvolution as inference operates from coarse-grained bulk-level data to fine-grained single-cell data. As the abundant missing entries in sc-RNASeq data have a significant effect on log-likelihood scores, we also developed a criterion for inclusion or exclusion of zero entries in log-likelihood score *** We selected nine deconvolution algorithms and validated backward deconvolution in five datasets. In the in-silico mixtures of mouse sc-RNASeq data, the log-likelihood scores of the deconvolution algorithms were strongly anticorrelated with their errors of mixture coefficients and cell type specific gene expression signatures. In the true bulk-level mouse data, the sample mixture coefficients were unknown but the log-likelihood scores were strongly correlated with accuracy rates of inferred cell types. In the data of autism spectrum disorder (ASD) and normal contr

关键词： Single-cell RNASeq data Deconvolution probabilistic graphical models Heterogeneity

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Concurrent filtering and smoothing: A parallel architecture for real-time navigation and full smoothing

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2014年第12期33卷 1544-1568页

作者： Williams, Stephen Indelman, Vadim Kaess, Michael Roberts, Richard Leonard, John J. Dellaert, Frank Georgia Inst Technol Inst Robot & Intelligent Machines Atlanta GA 30332 USA Carnegie Mellon Univ Sch Comp Sci Field Robot Ctr Inst Robot Pittsburgh PA 15213 USA MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

We present a parallelized navigation architecture that is capable of running in real-time and incorporating long-term loop closure constraints while producing the optimal Bayesian solution. This architecture splits the inference problem into a low-latency update that incorporates new measurements using just the most recent states (filter), and a high-latency update that is capable of closing long loops and smooths using all past states (smoother). This architecture employs the probabilistic graphical models of factor graphs, which allows the low-latency inference and high-latency inference to be viewed as sub-operations of a single optimization performed within a single graphical model. A specific factorization of the full joint density is employed that allows the different inference operations to be performed asynchronously while still recovering the optimal solution produced by a full batch optimization. Due to the real-time, asynchronous nature of this algorithm, updates to the state estimates from the high-latency smoother will naturally be delayed until the smoother calculations have completed. This architecture has been tested within a simulated aerial environment and on real data collected from an autonomous ground vehicle. In all cases, the concurrent architecture is shown to recover the full batch solution, even while updated state estimates are produced in real-time.

关键词： Information fusion smoothing filtering real time navigation SLAM probabilistic graphical models

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probabilistic Reasoning for Assembly-Based 3D Modeling

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ACM TRANSACTIONS ON GRAPHICS 2011年第4期30卷 1-10页

作者： Chaudhuri, Siddhartha Kalogerakis, Evangelos Guibas, Leonidas Koltun, Vladlen Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9781450309431

Assembly-based modeling is a promising approach to broadening the accessibility of 3D modeling. In assembly-based modeling, new models are assembled from shape components extracted from a database. A key challenge in assembly-based modeling is the identification of relevant components to be presented to the user. In this paper, we introduce a probabilistic reasoning approach to this problem. Given a repository of shapes, our approach learns a probabilistic graphical model that encodes semantic and geometric relationships among shape components. The probabilistic model is used to present components that are semantically and stylistically compatible with the 3D model that is being assembled. Our experiments indicate that the probabilistic model increases the relevance of presented components.

关键词： data-driven 3D modeling probabilistic reasoning probabilistic graphical models

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Decision analysis networks

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2018年 96卷 1-17页

作者： Javier Diez, Francisco Luque, Manuel Bermejo, Inigo UNED Dept Artificial Intelligence Juan Rosal 16 Madrid 28040 Spain

This paper presents decision analysis networks (DANs) as a new type of probabilistic graphical model. Like influence diagrams (IDs), DANs are much more compact and easier to build than decision trees and can represent conditional independencies. In fact, for every ID there is an equivalent symmetric DAN, but DANs can also represent asymmetric problems involving partial orderings of the decisions (order asymmetry), restrictions between the values of the variables (domain asymmetry), and conditional observability (information asymmetry). Symmetric DANs can be evaluated with the same algorithms as IDs. Every asymmetric DAN can be evaluated by converting it into an equivalent decision tree or, much more efficiently, by decomposing it into a tree of symmetric DANs. Given that DANs can solve symmetric problems as easily and as efficiently as IDs, and are more appropriate for asymmetric problems which include virtually all real-world problems DANs might replace IDs as the standard type of probabilistic graphical model for decision support and decision analysis. We also argue that DANs compare favorably with other formalisms proposed for asymmetric decision problems. In practice, DANs can be built and evaluated with OpenMarkov, a Java open-source package for probabilistic graphical models. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Decision analysis Decision trees Influence diagrams probabilistic graphical models Asymmetric decision problems

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Managing uncertainty in group recommending processes

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USER MODELING AND USER-ADAPTED INTERACTION 2009年第3期19卷 207-242页

作者： de Campos, Luis M. Fernandez-Luna, Juan M. Huete, Juan F. Rueda-Morales, Miguel A. Univ Granada Dept Comp Sci & Artificial Intelligence E-18071 Granada Spain

While the problem of building recommender systems has attracted considerable attention in recent years, most recommender systems are designed for recommending items to individuals. The aim of this paper is to automatically recommend a ranked list of new items to a group of users. We will investigate the value of using Bayesian networks to represent the different uncertainties involved in a group recommending process, i.e. those uncertainties related to mechanisms that govern the interactions between group members and the processes leading to the final choice or recommendation. We will also show how the most common aggregation strategies might be encoded using a Bayesian network formalism. The proposed model can be considered as a collaborative Bayesian network-based group recommender system, where group ratings are computed from the past voting patterns of other users with similar tastes.

关键词： Group recommending Management of uncertainty probabilistic graphical models

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