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Neighborhood Selection Methods
Published in Marloes Maathuis, Mathias Drton, Steffen Lauritzen, Martin Wainwright, Handbook of Graphical Models, 2018
The chapter is organized as follows: We first establish some notation on graphical models to be used throughout the chapter. We then present algorithms for edge estimation for multivariate Gaussian and Ising models, focusing first on population-level results and then discussing statistical theory. The algorithms we cover generally fall into one of two categories, either involving estimating the adjacency matrix of the graph based on the support of an appropriate matrix, or estimating individual node neighborhoods via penalized regression. We then discuss generalizations of these methods to other classes of distributions, as well as adaptations for contaminated or incomplete data. We close by highlighting a few interesting methods for edge recovery based on conditional independence testing. All mentions of “graphical models” in this chapter refer specifically to undirected graphical models which are also known as Markov networks; recall the terminology introduced in Chapter .
Bayesian-Network-Based AGC Approach
Published in Hassan Bevrani, Takashi Hiyama, Intellyigent Automatic Generation Control, 2017
Hassan Bevrani, Takashi Hiyama
Graphical models are generated by probability and graph theories to introduce a natural tool for dealing with two problems that occur throughout applied mathematics and engineering. In particular, they play a significant role in the synthesis and analysis of machine learning algorithms. Building a complex system by combining simpler parts is the fundamental idea of a graphical model. The probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data. The graph theoretic side of graphical models provides both an intuitively appealing interface by which humans can model highly interacting sets of variables, and a data structure that lends itself naturally to the design of efficient general purpose algorithms.21
Graphical Models
Published in Stephen Marsland, Machine Learning, 2014
The graphs used in graphical models are the exact ones that are taught in basic algorithms classes: a set of nodes, together with links between them, which can be either directed (i.e., have arrows on them so that you can only go one way along them) or not. There are two basic types of graphical models, depending upon whether or not the edges are directed. We will focus primarily on directed graphs, but the undirected kind (known as Markov Random Fields) are described in Section 16.2. For such a simple data structure, graphs have turned out to be incredibly powerful in many different parts of computer science, from constructing compilers to managing computer networks. For this reason, there are lots of readily available algorithms for finding shortest paths (Floyd’s and Djiksta’s algorithms, which we’ve already discussed briefly in Section 6.6), determining cycles, etc. Any good book on algorithms will give details of these and many other graph algorithms.
Crowd evacuation simulation model with soft computing optimization techniques: a systematic literature review
Published in Journal of Management Analytics, 2021
Hamizan Sharbini, Roselina Sallehuddin, Habibollah Haron
The probabilistic graphical models are referring to a structure of likelihood decisions and subjective convictions regarding the probabilities of consequences, similar like a statistical tool that can estimate the likelihood of an event happening in the future based on previous information. There are two types of methods under probabilistic graphical models, namely Bayesian Network and Markov Random Models. Peng and Zhang (2013) in their work have been applying the Bayesian Network model in their crowd simulation for dynamic decision making for dam breaks emergency management. The purpose is to minimize the total loss of evacuees. Li, Lee, and Liu (2013) further their works using the Markov model to also minimize the total loss of evacuees by estimating the health effects during emergency evacuation. Both works produced a positive effect for reducing health factors during evacuation process, but they might not be able to minimize the evacuation time and increase the flow rate of evacuees.
Analysing the past to prepare for the future: Writing a literature review a roadmap for release 2.0
Published in Journal of Decision Systems, 2020
Richard T. Watson, Jane Webster
We contend that a literature review also requires a higher-level synthesis. It typically needs to integrate concepts across domains into a holistic treatment of a subject. The author has to identify what ideas matter and then find a way to coherently link them into a stream that has a clear and relevant expository flow for the intended reader. Because of advances in graphical models, the associations represented by conceptual relationships can be transformed into a mathematical model with well-defined semantics and logic expressed as graphs (Pearl, 2009). In this article, we begin to develop a roadmap for learning how to manage the macro level of discourse synthesis through the application of graph theory,2 which is concerned with the mathematical study of structures modelling dyadic relationships between objects. Graph theory has been applied in many fields, such as computer science networks and social network analysis (Burt, 1982), and is particularly appropriate for modelling conceptual relationships.
Discriminant subgraph learning from functional brain sensory data
Published in IISE Transactions, 2022
Lujia Wang, Todd J. Schwedt, Catherine D. Chong, Teresa Wu, Jing Li
A graphical model includes nodes to represent variables or features and edges to characterize relationships between the variables. The edges can be undirected or directed. One of the most popular types of undirected graphical models is called the Gaussian Graphical Model (GGM), in which the nodes are assumed to follow a multivariate Gaussian distribution. Directed graphical models are also known as Bayesian networks (Jordan and Weiss, 2002). In this article, our methodological development is based upon GGM. Thus, we focus on reviewing the existing research in GGM in this section.