Martin Holena

Formal logics of discovery and hypothesis formation by machine

The following are the aims of the paper: (1) To call the attention of the community of Discovery Science (DS) to certain existing formal systems for DS developed in Prague in the 1960s through the 1980s suitable for DS and unfortunately largely unknown. (2) To illustrate the use of the calculi in question by the example of the GUHA method of hypothesis generation by computer, subjecting this method to a critical evaluation in the context of contemporary data mining. (3) To stress the importance of fuzzy logic for DS and to present the state of mathematical foundations of fuzzy logic. (4) Finally, to present a running research program of developing calculi of symbolic fuzzy logic for DS and for a fuzzy GUHA method.

Formal Logics of Discovery and Hypothesis Formation by Machine

The following are the aims of the paper: (1) To call the attention of the community of Discovery Science to certain existing formal systems for DS developed in Prague in 60s till 80s suitable for DS and unfortunately largely unknown. (2) To illustrate the use of the calculi in question on the example of the GUHA method of hypothesis generation by computer, subjecting this method to a criticale valuation in the context of contemporary data mining. (3) To stress the importance of Fuzzy Logic for DS and inform on the present state of mathematical foundations of Fuzzy Logic. (4) Finally, to present a running research program of developing calculi of symbolic fuzzy logic for DS and for a fuzzy GUHA method.

An approach to structure determination and estimation of hierarchical Archimedean Copulas and its application to Bayesian classification

Copulas are distribution functions with standard uniform univariate marginals. Copulas are widely used for studying dependence among continuously distributed random variables, with applications in finance and quantitative risk management; see, e.g., the pricing of collateralized debt obligations (Hofert and Scherer, Quantitative Finance, 11(5), 775–787, 2011). The ability to model complex dependence structures among variables has recently become increasingly popular in the realm of statistics, one example being data mining (e.g., cluster analysis, evolutionary algorithms or classification). The present work considers an estimator for both the structure and the parameters of hierarchical Archimedean copulas. Such copulas have recently become popular alternatives to the widely used Gaussian copulas. The proposed estimator is based on a pairwise inversion of Kendall’s tau estimator recently considered in the literature but can be based on other estimators as well, such as likelihood-based. A simple algorithm implementing the proposed estimator is provided. Its performance is investigated in several experiments including a comparison to other available estimators. The results show that the proposed estimator can be a suitable alternative in the terms of goodness-of-fit and computational efficiency. Additionally, an application of the estimator to copula-based Bayesian classification is presented. A set of new Archimedean and hierarchical Archimedean copula-based Bayesian classifiers is compared with other commonly known classifiers in terms of accuracy on several well-known datasets. The results show that the hierarchical Archimedean copula-based Bayesian classifiers are, despite their limited applicability for high-dimensional data due to expensive time consumption, similar to highly-accurate classifiers like support vector machines or ensemble methods on low-dimensional data in terms of accuracy while keeping the produced models rather comprehensible.

Structure determination and estimation of hierarchical archimedean copulas based on kendall correlation matrix

An estimation method for the copula of a continuous multivariate distribution is proposed. A popular class of copulas, namely the class of hierarchical Archimedean copulas, is considered. The proposed method is based on the close relationship of the copula structure and the values of Kendalls tau computed on all its bivariate margins. A generalized measure based on Kendalls tau adapted for purposes of the estimation is introduced. A simple algorithm implementing the method is provided and its effectiveness is shown in several experiments including its comparison to other available methods. The results show that the proposed method can be regarded as a suitable alternative to existing methods in the terms of goodness of fit and computational efficiency.

The GUHA method and foundations of (relational) data mining

The GUHA method of automatic generation of hypotheses and its underlying logical and statistical theory is surveyed. Links to the theory of information relations and to relational data mining are discussed. Logical foundations present an original approach to finite model theory with generalized quantifiers.

Observational Logic Integrates Data Mining Based on Statistics and Neural Networks

In data mining, artificial neural networks have become one of important competitors of traditional statistical methods. They increase the potential of discovering useful knowledge in data, but only if the differences between both kinds of methods are well understood. Therefore, integrative frameworks are urgently needed. In this paper, a framework based on the calculus of observational logic is presented. Basic concepts of that framework are outlined, and it is explained how generalized quantifiers can be defined in an observational calculus to capture data mining with statistical and ANN-based methods.

Using Copulas in Data Mining Based on the Observational Calculus

The objective of the paper is a contribution to data mining within the framework of the observational calculus, through introducing generalized quantifiers related to copulas. Fitting copulas to multidimensional data is an increasingly important method for analyzing dependencies, and the proposed quantifiers of observational calculus assess the results of estimating the structure of joint distributions of continuous variables by means of hierarchical Archimedean copulas. To this end, the existing theory of hierarchical Archimedean copulas has been slightly extended in the paper: It has been proven that sufficient conditions for the function defining a hierarchical Archimedean copula to be indeed a copula, which have so far been rigorously established only for the special case of fully nested Archimedean copulas, hold in general. These conditions allow us to define three new generalized quantifiers, which are then thoroughly validated on four benchmark data sets and one data set from a real-world application. The paper concludes by comparing the proposed quantifiers to a more traditional approach-maximum weight spanning trees.

Dynamic classifier aggregation using fuzzy integral with interaction-sensitive fuzzy measure

In classifier combining, predictions of several classifiers are aggregated into a single prediction in order to improve the classification quality. Among others, fuzzy integrals are commonly used as aggregation operators. Usually, Sugeno lambda-measure is used as the fuzzy measure of the integral. However, interaction between the classifiers in the team (diversity), an important property in classifier combining, cannot be modeled by such fuzzy measure. In this paper, we present an interaction-sensitive fuzzy measure (ISFM), which can incorporate the diversity of the team into the aggregation process. Experimental results on 27 datasets show that the Choquet integral w.r.t. the ISFM outperforms the Choquet integral w.r.t. the Sugeno-lambda measure.

Towards real-time motion estimation in high-definition video based on points of interest

Currently used motion estimation is usually based on a computation of optical flow from individual images or short sequences. As these methods do not require an extraction of the visual description in points of interest, correspondence can be deduced only by the position of such points. In this paper, we propose an alternative motion estimation method solely using a binary visual descriptor. By tuning the internal parameters, we achieve either a detection of longer time series or a higher number of shorter series in a shorter time. As our method uses the visual descriptors, their values can be directly used in more complex visual detection tasks.

Evolutionary Dynamic Optimization of Control Trajectories for the Catalytic Transformation of the Bioethanol-To-Olefins Process using Neural Networks

This paper presents a study on dynamic optimization of the catalytic transformation of Bioethanol-To-Olefins process. The main objective is to maximize the total production of Olefins by calculating simultaneously the optimal control trajectories for the main operating variables of the process. Using Neural Networks trained with two different types of Evolutionary Algorithms, the optimal trajectories have been automatically achieved, defining both an adequate shape and their corresponding parameters. The results suggest that, comparing with constant setpoints, the maximum production is increased up to 37.31% when using Neural Networks. The optimization procedure has become totally automatic and therefore very useful for real implementation.