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Plenary talk (45 min). In a number of stochastic models a random response variable Y depends on some (in general random) factors X_1,...,X_n. The identification of significant factors when Y takes values in a finite subset of R is the goal of this talk. There are complementary approaches to the problem mentioned above. Among diverse statistical methods employed here we discuss the principle component analysis, logic and logistic regressions, LASSO and various machine learning techniques. We concentrate on the new MDR (multifactor dimensionality reduction) method developed in our recent papers.