Data Analysis, Mathematical Statistics, Machine Learning, Data…推荐.pdf

Data Analysis, Mathematical Statistics, Machine Learning, Data Mining: Similarities and Differences Boris Mirkin Division of Applied Mathematics and Informatics, National Research University Higher School of Economics, Moscow RF Department of Computer Science, Birkbeck University of London UK Abstract An attempt is made to bring some structure in the meanings of the title subjects based on the perspectives at which they view the data. A rigid framework for Data Analysis is proposed pointing out its role in augmenting the knowledge of a phenomenon the data relate to. In particular, the task of summarization as a general problem is discussed. The ingredients of a data analysis problem are described as a base for positioning of various approaches in data analysis and mathematical statistics. Introduction The similarities between the subjects mentioned in the title relate to two fundamental facts: (i) all of them develop methods and procedures to process data, and (2) any data processing algorithm or procedure may belong to any, or better to say, all of them. The differences are in the different perspectives. The difference in perspectives does not affect the procedures but it does affect the choice of them and, even more so, interpretation of concepts and results. Before I go any further, let me give an example by presenting two concepts that are common at analyzing data: the average and correlation, in the different perspectives. Average : Given observed values y , y , …, y of a variable, compute the average value ȳ  y /N – same 1 2 N i i method in all the perspectives. The meaning:  An unbiased estimate of the central moment of the probability distri