Approximating discrete probability distributions with dependence trees

By C. Chow, Chao-Ming Liu. 1968

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Neural Autoregressive Distribution Estimation (2016, methodology): “There is an O ( D 2 ) ﬁtting algorithm to ﬁnd the maximum likelihood tree and conditional distributions (Chow and Liu, 1968).”
Marginal Release Under Local Differential Privacy (2017, background): “Exact estimation of a joint distribution for d discrete variables could be computationally infeasible for large d ’s. Chow and Liu in [6] proposed an algorithm for approximating a joint distribution of a set of discrete variables using products of distributions involving no more than pairs of…”
Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm (2005, methodology): “For example, the search space may be restricted to trees as in MWST (Maximum Weight Spanning Trees; see [3] and [7]), or a greedy search is employed.”
High-dimensional Ising model selection using ℓ1-regularized logistic regression (2010, methodology): “idate structures in scoring based approaches is thus typically restricted to either directed graphical models [10] or to simple sub-classes of undirected graphical models such as those based on trees [7] and hypertrees [31]. Abbeel, Koller and Ng [1] propose a method for learning factor graphs based”
DAG-GNN: DAG Structure Learning with Graph Neural Networks (2019, methodology): “Hence, for practical problems in a scale beyond small, approximate search often needs to be employed with additional structure assumption (Nie et al., 2014; Chow & Liu, 1968; Scanagatta et al., 2015; Chen et al., 2016).”
Incremental learning of privacy-preserving Bayesian networks (2013, methodology): “[8] C.”
ARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context (2004, background): “However, unlike standard tree reconstruction methods (e.g. Chow and Liu [15]), ARACNE is not limited to trees and can produce complicated structures containing many loops.”
A Continuous Occlusion Model for Road Scene Understanding (2016, methodology): “Our future work will explore speeding up the inference, for example, by approximating the graph with a tree using the Chow-Liu method [3], which will allow belief propagation for fast inference.”
Parameterized quantum circuits as machine learning models (2019, methodology): “For example, Liu and Wang [26] use the Chow-Liu tree graph [27] to setup the entangling layers.”
Modeling Tabular data using Conditional GAN (2019, methodology): “In our benchmarking suite, we have baselines that consist of Bayesian networks (CLBN [7], PrivBN [28]), and implementations of current deep learning approaches for synthetic data generation (MedGAN [6], VeeGAN [21], TableGAN [18]).”
Competition on counter measures to 2-D facial spoofing attacks (2011, methodology): “Among the different algorithms available we have selected the Chow and Liu algorithm [5], that reported the best re-”
Information-Theoretic Inference of Large Transcriptional Regulatory Networks (2007, methodology): “The adoption of mutual information in probabilistic model design can be traced back to Chow-Liu tree algo-rithm [3] and its extensions proposed by [7, 8].”
Pictorial Structures for Object Recognition (2004, methodology): “This can be done in a similar way to the algorithm of Chow and Liu described in [ 11 ], which estimates a tree distribution for discrete random variables.”
Analyzing 3D Objects in Cluttered Images (2012, unknown): “[6, 15].”
Bayesian Network Classifiers (1997, methodology): “The procedure for learning these edges is based on a well-known method reported by Chow and Liu (CL from now on) (1968), for learning tree-like Bayesian networks (see also (Pearl, 1988, pp.”