Probabilistic advisory systems for data‐intensive applications

Abstract

Real-world, multidimensional, dynamic, non-linear processes typically exhibit many distinct modes of operation. Mixtures of dynamic models improve greatly on traditional one-component linear models in this context. Improved prediction then points the way to effective adaptive control design. This paper presents the experience gained under the EU Project, ProDaCTool, in designing and implementing advisory systems, based on dynamic mixtures, in diverse domains: urban traffic regulation, therapy recommendations in nuclear medicine, and operator support for metal-strip rolling mills. Efficient, recursive estimation of the dynamic mixtures from archive data is accomplished using the quasi-Bayes (QB) algorithm, implemented with dedicated software developed within ProDaCTool. The advisory systems are designed using the probabilistic control design technique presented in the previous paper. Highly encouraging prediction and performance enhancements are reported for the applications considered.

Mixture-based extension of the AR model and its recursive Bayesian identification

“…The Bayesian posterior moments (11)-(13) correspond to point estimates employed in the signal processing literature. (11), (12) are algorithmically identical to the results of the covariance method [14], and are valid ∀n > p, as derived. The Bayesian identification framework above yields the following extensions.…”

“…G 2 is parameterized by unknown h, each setting of which defines a distinct candidate transformation. Note thatȳ n in (72) depends onâ n−1 (11). Parameter updates are therefore correlated with previous estimates,â n−1 .…”

“…From (68) and (70) however, both q n andẑ n are functions of A (a) (64). In order to obtain a valid EAR model, we replace A (a) in (70), (71) by its expected value, n−1 = A (â n−1 ), using (11). Then, (67) is a valid EAR model defined by the set of transformations…”

“…Recursive algorithms are important in on-line control applications [9], and for adaptive filtering [10]. In off-line cases, the emphasis on computational issues and recursive methods can also pay off, for example in the off-line processing of massive datasets [11].…”

Cooperation via sharing of probabilistic information

“…There is a number of sophisticated and well-elaborated approaches and techniques developed for DM, (DeGroot, 1970;Bell et al, 1988) proven to be successful in many applications (see e.g., Dyer et al, 1992;Quinn et al, 2003). However none of the approaches can serve as a universal one to be applied to the above-mentioned diversity of problems.…”