Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.Comment: 43 page

Infinite Probabilistic Databases

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries

Using Visualization to Support Data Mining of Large Existing Databases

In this paper. we present ideas how visualization technology can be used to improve the difficult process of querying very large databases. With our VisDB system, we try to provide visual support not only for the query specification process. but also for evaluating query results and. thereafter, refining the query accordingly. The main idea of our system is to represent as many data items as possible by the pixels of the display device. By arranging and coloring the pixels according to the relevance for the query, the user gets a visual impression of the resulting data set and of its relevance for the query. Using an interactive query interface, the user may change the query dynamically and receives immediate feedback by the visual representation of the resulting data set. By using multiple windows for different parts of the query, the user gets visual feedback for each part of the query and, therefore, may easier understand the overall result. To support complex queries, we introduce the notion of approximate joins which allow the user to find data items that only approximately fulfill join conditions. We also present ideas how our technique may be extended to support the interoperation of heterogeneous databases. Finally, we discuss the performance problems that are caused by interfacing to existing database systems and present ideas to solve these problems by using data structures supporting a multidimensional search of the database

Intuitive querying of e-Health data repositories

At the centre of the Clinical e-Science Framework (CLEF) project is a repository of well organised, detailed clinical histories, encoded as data that will be available for use in clinical care and in-silico medical experiments. An integral part of the CLEF workbench is a tool to allow biomedical researchers and clinicians to query – in an intuitive way – the repository of patient data. This paper describes the CLEF query editing interface, which makes use of natural language generation techniques in order to alleviate some of the problems generally faced by natural language and graphical query interfaces. The query interface also incorporates an answer renderer that dynamically generates responses in both natural language text and graphics