A dynamic Bayesian network (DBN) is a Bayesian network (BN) which relates variables to each other over adjacent time steps.
A dynamic Bayesian network (DBN) is a Bayesian network (BN) which relates variables to each other over adjacent time steps.
A dynamic Bayesian network (DBN) is often called a "two-timeslice" BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by Paul Dagum in the early 1990s at Stanford University's Section on Medical Informatics. [1] [2] Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden Markov models into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains. [3] [4]
Today, DBNs are common in robotics, and have shown potential for a wide range of data mining applications. For example, they have been used in speech recognition, digital forensics, protein sequencing, and bioinformatics. DBN is a generalization of hidden Markov models and Kalman filters. [5]
DBNs are conceptually related to probabilistic Boolean networks [6] and can, similarly, be used to model dynamical systems at steady-state.
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobservable ("hidden") states. As part of the definition, HMM requires that there be an observable process whose outcomes are "influenced" by the outcomes of in a known way. Since cannot be observed directly, the goal is to learn about by observing HMM has an additional requirement that the outcome of at time must be "influenced" exclusively by the outcome of at and that the outcomes of and at must be conditionally independent of at given at time
A Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.
In mathematics, a time series is a series of data points indexed in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
Econometric models involving data sampled at different frequencies are of general interest. Mixed-data sampling (MIDAS) is an econometric regression developed by Eric Ghysels with several co-authors. There is now a substantial literature on MIDAS regressions and their applications, including Ghysels, Santa-Clara and Valkanov (2006), Ghysels, Sinko and Valkanov, Andreou, Ghysels and Kourtellos (2010) and Andreou, Ghysels and Kourtellos (2013).
In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process model. The process relies heavily upon mathematical concepts and models that are theorized within a study of prior and posterior probabilities known as Bayesian statistics.
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Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty and complex, relational structure. Note that SRL is sometimes called Relational Machine Learning (RML) in the literature. Typically, the knowledge representation formalisms developed in SRL use first-order logic to describe relational properties of a domain in a general manner and draw upon probabilistic graphical models to model the uncertainty; some also build upon the methods of inductive logic programming. Significant contributions to the field have been made since the late 1990s.
Structured prediction or structured (output) learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than scalar discrete or real values.
Stuart Alan Geman is an American mathematician, known for influential contributions to computer vision, statistics, probability theory, machine learning, and the neurosciences. He and his brother, Donald Geman, are well known for proposing the Gibbs sampler, and for the first proof of convergence of the simulated annealing algorithm.
Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available.
Stan is a probabilistic programming language for statistical inference written in C++. The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function.
The switching Kalman filtering (SKF) method is a variant of the Kalman filter. In its generalised form, it is often attributed to Kevin P. Murphy, but related switching state-space models have been in use.
The following outline is provided as an overview of and topical guide to machine learning:
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In network theory, collective classification is the simultaneous prediction of the labels for multiple objects, where each label is predicted using information about the object's observed features, the observed features and labels of its neighbors, and the unobserved labels of its neighbors. Collective classification problems are defined in terms of networks of random variables, where the network structure determines the relationship between the random variables. Inference is performed on multiple random variables simultaneously, typically by propagating information between nodes in the network to perform approximate inference. Approaches that use collective classification can make use of relational information when performing inference. Examples of collective classification include predicting attributes of individuals in a social network, classifying webpages in the World Wide Web, and inferring the research area of a paper in a scientific publication dataset.
dynamic Bayesian networks (which include hidden Markov models and Kalman filters as special cases)
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