DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Sung-Ho | - |
dc.contributor.advisor | 김성호 | - |
dc.contributor.author | Kim, Gang-Hoo | - |
dc.contributor.author | 김강후 | - |
dc.date.accessioned | 2015-04-29 | - |
dc.date.available | 2015-04-29 | - |
dc.date.issued | 2014 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=592345&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/198139 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2014.8, [ v, 49 p. ] | - |
dc.description.abstract | The operations, marginalization and conditionalization, on a probability model affect the probability model in a variety of ways. If we denote the probability model before one of the operations by M and by M`` that after the operation, M and M`` may belong to the same family of probability models or not. For example, marginalization on a Gaussian model (or a multinomial model) yields another Gaussian model (or a multinomial model) while it may not be the case for some other models such as a mixture of Gaussian models. If we interpret the model structure of a probability model as a graphical representation of the Markov properties which are latent in the probability model, then different probability models may share a model structure. In this thesis we will investigate, in the context of model structure, the relationship between the models before and after each of the two operations. Consider a set of random variables, $X_1, … , X_n$ where $X_i$ (i=2, … , n) has a set of possibly explanatory variables, $X_1, … , X_{i-1}$ in the form of a linear regression model. Such cause-effect relationships among the X variables can be represented in a directed acyclic graph (DAG) and can also be represented in a linear triangular system. Let G be a DAG of the n random variables. Then G can be represented in an adjacency matrix, which we will denote by A(G). The (i,j)-entry of the matrix equals 1 if there is an arrow from node i to node j, or i → j, in G. We will propose a method of finding the new model structure of a DAG, G, by using matrix operations, which is created by applying each of marginalization and conditionalization on the model of G. We will also explore properties of the matrix operations. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Adjacency matrix | - |
dc.subject | Directed acyclic graph | - |
dc.subject | 그래프 모형 | - |
dc.subject | 인접행렬 | - |
dc.subject | Graphical model | - |
dc.subject | 유향 비순환 그래프 | - |
dc.title | An application of the colored adjacency matrix for understanding the graphical model structures | - |
dc.title.alternative | 그래프 모형 구조 이해를 위한 Colored Adjacency Matrix의 활용 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 592345/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020124347 | - |
dc.contributor.localauthor | Kim, Sung-Ho | - |
dc.contributor.localauthor | 김성호 | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.