Finding regions for which there is higher controversy among different classifiers is insightful with regards to the domain and our models. Such evaluation can falsify assumptions, assert some, or also, bring to the attention unknown phenomena. The present work describes an algorithm, which is based on the Exceptional Model Mining framework, and enables that kind of investigations. We explore several public datasets and show the usefulness of this approach in classification tasks. We show in this paper a few interesting observations about those well explored datasets, some of which are general knowledge, and other that as far as we know, were not reported before.
If one manages to compress the model and the data, for example following the (MDL) framework @cite_2 , then they somehow capture the essence of the model data. One should describe a model and then the exceptions in the data that do not follow the model and to find the point for which the overall description is minimal (the model is described in sufficient detail and the leftover exceptions are few).
@cite_2
2034230784 2106596127 2101460669 2786674049
Summary form only. Inspired by Kolmogorov's structure function for finite sets as models of data in the algorithmic theory of information we adapt the construct to families of probability models to avoid the noncomputability problem. The picture of modeling looks then as follows: The models in the family have a double index, where the first specifies a structure, ranging over a finite or a countable set, and the second consists of parameter values, ranging over a continuum. An optimal structure index can be determined by the MDL (Minimum Description Length) principle in a two-part code, where the sum of the code lengths for the structure and the data is minimized. The latter is obtained from the universal NML (Normalized Maximum Likelihood) model for the subfamily of models having a specified structure. The determination of the optimal model in the optimized structure is more difficult. It requires a partition of the parameter space into equivalence classes, each associated with a model, in such a way that the Kullback-Leibler distance between any two adjacent models is equal and that the models are optimally distinguishable from the given amount of data. This notion of distinguishability is a modification of a related idea of Balasubramanian. The particular model, specified by the observed data, is the simplest one that incorporates all the properties in the data that can be extracted with the model class considered. of the number of bits required to write down the observed data, has been reformulated to extend the classical maximum likelihood principle. The principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models; i.e., of the model structures. The principle rests on a new way to interpret and construct a universal prior distribution for the integers, which makes sense even when the parameter is an individual object. Truncated realvalued parameters are converted to integers by dividing them by their precision, and their prior is determined from the universal prior for the integers by optimizing the precision. 1. Introduction. In this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data, when each observation is given with some precision. Instead of attempting at an absolutely shortest description, which would be futile, we look for the optimum relative to a class of parametrically given distributions. This Minimum Description Length (MDL) principle, which we introduced in a less comprehensive form in [25], turns out to degenerate to the more familiar Maximum Likelihood (ML) principle in case the number of parameters in the models is fixed, so that the description length of the parameters themselves can be ignored. In another extreme case, where the parameters determine the data, it similarly degenerates to Jaynes's principle of maximum entropy, [14]. But the main power of the new criterion is that it permits estimates of the entire model, its parameters, their number, and even the way the parameters appear in the model; i.e., the model structure. Hence, there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or, perhaps, over parameterized. The minimum description length (MDL) principle is a powerful method of inductive inference, the basis of statistical modeling, pattern recognition, and machine learning. It holds that the best explanation, given a limited set of observed data, is the one that permits the greatest compression of the data. MDL methods are particularly well-suited for dealing with model selection, prediction, and estimation problems in situations where the models under consideration can be arbitrarily complex, and overfitting the data is a serious concern. This extensive, step-by-step introduction to the MDL Principle provides a comprehensive reference (with an emphasis on conceptual issues) that is accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection, including biology, econometrics, and experimental psychology. Part I provides a basic introduction to MDL and an overview of the concepts in statistics and information theory needed to understand MDL. Part II treats universal coding, the information-theoretic notion on which MDL is built, and part III gives a formal treatment of MDL theory as a theory of inductive inference based on universal coding. Part IV provides a comprehensive overview of the statistical theory of exponential families with an emphasis on their information-theoretic properties. The text includes a number of summaries, paragraphs offering the reader a "fast track" through the material, and boxes highlighting the most important concepts. In this paper, we present the results of long-term research conducted in order to study the contribution made by software models based on the Unified Modeling Language (UML) to the comprehensibility of Java source-code deprived of comments. We have conducted 12 controlled experiments in different experimental contexts and on different sites with participants with different levels of expertise (i.e., Bachelor’s, Master’s, and PhD students and software practitioners from Italy and Spain). A total of 333 observations were obtained from these experiments. The UML models in our experiments were those produced in the analysis and design phases. The models produced in the analysis phase were created with the objective of abstracting the environment in which the software will work (i.e., the problem domain), while those produced in the design phase were created with the goal of abstracting implementation aspects of the software (i.e., the solution application domain). Source-code comprehensibility was assessed with regard to correctness of understanding, time taken to accomplish the comprehension tasks, and efficiency as regards accomplishing those tasks. In order to study the global effect of UML models on source-code comprehensibility, we aggregated results from the individual experiments using a meta-analysis. We made every effort to account for the heterogeneity of our experiments when aggregating the results obtained from them. The overall results suggest that the use of UML models affects the comprehensibility of source-code, when it is deprived of comments. Indeed, models produced in the analysis phase might reduce source-code comprehensibility, while increasing the time taken to complete comprehension tasks. That is, browsing source code and this kind of models together negatively impacts on the time taken to complete comprehension tasks without having a positive effect on the comprehensibility of source code. One plausible justification for this is that the UML models produced in the analysis phase focus on the problem domain. That is, models produced in the analysis phase say nothing about source code and there should be no expectation that they would, in any way, be beneficial to comprehensibility. On the other hand, UML models produced in the design phase improve source-code comprehensibility. One possible justification for this result is that models produced in the design phase are more focused on implementation details. Therefore, although the participants had more material to read and browse, this additional effort was paid back in the form of an improved comprehension of source code.