A logic-based analysis of Dempster-Shafer theory

AbstractDempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (Σ, ϱ), where Σ is a set of propositional clauses and ϱ is an assignment of mass to each clause Σi ϵ Σ. It is shown that the disjunction of minimal support clauses for a clause Σi with respect to a set Σ of propositional clauses, ξ(Σi, Σ), when represented in terms of symbols for the ϱi 's, corresponds to a symbolic representation of the Dempster-Shafer belief function for δi. The combination of Belief functions using Dempster's rule of combination corresponds to a combination of the corresponding support clauses. The disjointness of the Boolean formulas representing DS Belief functions is shown to be necessary. Methods of computing disjoint formulas using network reliability techniques are discussed.In addition, the computational complexity of deriving DS Belief functions, including that of the logic-based methods which are the focus of this paper, is explored. Because of intractability even for moderately sized problem instances, efficient approximation methods are proposed for such computations. Finally, implementations of DS theory based on domain restrictions of DS theory, hypertree embeddings, and the ATMS, are examined

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde

Fusion of Information and Analytics: A Discussion on Potential Methods to Cope with Uncertainty in Complex Environments (Big Data and IoT)

International audienceInformation overload and complexity are core problems to most organizations of today. The advances in networking capabilities have created the conditions of complexity by enabling richer, real-time interactions between and among individuals, objects, systems and organizations. Fusion of Information and Analytics Technologies (FIAT) are key enablers for the design of current and future decision support systems to support prognosis, diagnosis, and prescriptive tasks in such complex environments. Hundreds of methods and technologies exist, and several books have been dedicated to either analytics or information fusion so far. However, very few have discussed the methodological aspects and the need of integrating frameworks for these techniques coming from multiple disciplines. This paper presents a discussion of potential integrating frameworks as well as the development of a computational model to evolve FIAT-based systems capable of meeting the challenges of complex environments such as in Big Data and Internet of Things (IoT)

Evidential Evolving Gustafson-Kessel Algorithm For Online Data Streams Partitioning Using Belief Function Theory.

International audienceA new online clustering method called E2GK (Evidential Evolving Gustafson-Kessel) is introduced. This partitional clustering algorithm is based on the concept of credal partition defined in the theoretical framework of belief functions. A credal partition is derived online by applying an algorithm resulting from the adaptation of the Evolving Gustafson-Kessel (EGK) algorithm. Online partitioning of data streams is then possible with a meaningful interpretation of the data structure. A comparative study with the original online procedure shows that E2GK outperforms EGK on different entry data sets. To show the performance of E2GK, several experiments have been conducted on synthetic data sets as well as on data collected from a real application problem. A study of parameters' sensitivity is also carried out and solutions are proposed to limit complexity issues