Undirected Graphical Models
نویسنده
چکیده
Read: Chapters 5 and 6 of [CGH]. The first model for a joint probability distribution that we will consider is the undirected graph. We will undirected graphs using two different methods. First, we will show the relationship between undirected graphs and joint probability distributions. Second, we will show the relationship between undirected graphs, and an abstract independence model (called an input list). Let denote probabilistic independence: is independent of given in the joint probability distribution. If and , then. In order to make this definition work for all values of , we will rewrite this condition as The relationship has four properties that hold for any distribution. P1. Symmetry: , where is understood to mean " iff " in this context. (and this also implies) I A B C , () A B C I A B C , () f C c = () 0 > f A a = B b = C c = , () f A a = C c = () f B b = C c = () = C f A a = B b = C c = , , () f C c = () f A a = C c = , () f B b = C c = , () = I I A B C , () I B A C , () ⇔ ⇔
منابع مشابه
MATHEMATICAL ENGINEERING TECHNICAL REPORTS Standard Imsets for Undirected and Chain Graphical Models
We derive standard imsets for undirected graphical models and chain graphical models. Standard imsets for undirected graphical models are described in terms of minimal triangulations for maximal prime subgraphs of the undirected graphs. For describing standard imsets for chain graphical models, we first define a triangulation of a chain graph. We then use the triangulation to generalize our res...
متن کاملNeural Variational Inference and Learning in Undirected Graphical Models
Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the logpartition function parametrized by a function q that we express as a flexible ...
متن کاملVariations on undirected graphical models and their relationships
We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, descr...
متن کاملA conditional independence algorithm for learning undirected graphical models
When it comes to learning graphical models from data, approaches based on conditional independence tests are among the most popular methods. Since Bayesian networks dominate research in this field, these methods usually refer to directed graphs, and thus have to determine not only the set of edges, but also their direction. At least for a certain kind of possibilistic graphical models, however,...
متن کاملCovariance decomposition in undirected Gaussian graphical models
The covariance between two variables in a multivariate Gaussian distribution is decomposed into a sum of path weights for all paths connecting the two variables in an undirected independence graph. These weights are useful in determining which variables are important in mediating correlation between the two path endpoints. The decomposition arises in undirected Gaussian graphical models and doe...
متن کاملA Note on Assessing Multivariate Balance Conditional on the Propensity Score using Undirected Graphical Models
This note proposes a novel approach for assessing the balancing hypothesis that underlies propensity score matching methods based on using an information-theoretic approach to fit undirected graphical models. Graphical models are parametric statistical models for multivariate random variables whose conditional independence structure can be displayed in a mathematical graph. Specialized software...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999