Experimental Design Problem
Experimental design is a classical problem in statistics and has also found new applications in machine learning. In the experimental design problem, the aim is to estimate an unknown vector x in m-dimensions from linear measurements where a Gaussian noise is introduced in each measurement. The goal is to pick k out of the given n experiments so as to make the most accurate estimate of the unknown parameter x. Given a set S of chosen experiments, the most likelihood estimate x’ can be obtained by a least squares computation.
➚ “Design of Experiments” …
Theory of Evidence
The theory of belief functions, also referred to as evidence theory or Dempster-Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty-a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence. In a narrow sense, the term Dempster-Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better. The early contributions have also been the starting points of many important developments, including the transferable belief model and the theory of hints. …
Bayesian Ying-Yang Learning Algorithm (BYY)
Ying-Yang learning considers a learning system featured with two pathways between the external observation domain X and its inner representation domain R. The domain R and the pathway R→X is modeled by one subsystem system, while the domain X and the pathway X→R is modeled by another subsystem. From the view of the ancient Ying-Yang philosophy, the former is called Ying and the latter is called Yang, and the two coordinately form a Ying-Yang system, with the structure of Ying subject to a principle of compactness (least complexity) and the structure of Yang subject to a principle of proper vitality (matched dynamic range) with respect to the Ying. Moreover, all the rest unknowns in the Ying-Yang system are learned under the guidance of a Ying-Yang best harmony principle.
Experimental Design Problem