Statistical learning theory

Vapnik VN. Statistical learning theory. New York John Wiley Sons, 1998. 

Vapnik, V. The Nature of Statistical Learning Theory. Springer, New York, 1995. 

Vapnik, V.N. Statistical Learning Theory. John Wiley Sons New York, 1998. 

Vapnik, V. N. (1998). Statistical Learning Theory. Wiley-Interscience, New York. 

Vapnik VN. The nature of statistical learning theory. New York Springer, 1995. 

Vol. 1851 O. Catoni, Statistical Learning Theory and Stochastic Optimization (2004)... 

Support vector machine (SVM) is originally a binary supervised classification algorithm, introduced by Vapnik and his co-workers [13, 32], based on statistical learning theory. Instead of traditional empirical risk minimization (ERM), as performed by artificial neural network, SVM algorithm is based on the structural risk minimization (SRM) principle. In its simplest form, linear SVM for a two class problem finds an optimal hyperplane that maximizes the separation between the two classes. The optimal separating hyperplane can be obtained by solving the following quadratic optimization problem ... 

The methods of discrete mathematics, introduced in this chapter, were sufficient for describing chemical compounds as discrete structures. However, once the relationships between properties and structures have to be modelled, non-discrete methods are required. Methods from supervised statistical learning theory and machine learning are particularly useful and thus some of these will be introduced in the next chapter. 

Vapnik VN (1998) Statistical learning theory. Wiley, New York... 

So far, the direct use of continuous molecular fields in their functional form in statistical analysis was not possible because standard data analysis procedures can only work with finite and fixed number of features (molecular descriptors). Only recently, thanks to the development of the statistical learning theory [5] and the methodology of using kernels [6] in machine learning instead of fixed-sized feature vectors, it has become possible to process data of any form and complexity. 

Vamek A, Baskin I (2012) Machine learning methods for property prediction in chemoinformatics quo vadis J Chem Inf Mod 52(6) 1413 1437. doi 10.1021/ci200409x Vapnik V (1998) Statistical learning theory. Wiley-Interscience, New York Scholkopf B, Smola AJ (2002) Learning with kernels support vector machines, regularization, optimization, and beyond. MIT, Cambridge... 

Application of statistical learning theory and QSPR, data mining and combinatorial high-throughput methods, virtual high-throughput screening... 

In this chapter, the basic principles of statistical learning theory will be introduced. And the possibility of application of support vector machine to various fields in chemistry and chemical technology will be discussed. 

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