Review of the scientific supervisor of​ bachelor’s thesis of
Kulikov Daniil
"Dimension reduction of categorical data based on Fisher’s
exact test"

Work of Daniil Kulikov consists of two parts: one part is dedicated to Fisher's exact test (FET), the second part is dedicated to the problem of the dimension reduction of categorical data.
Particular attention is paid to FET due to the fact that in common Statistica version of the package, this criterion is considered to be only for the contingency tables with dimension two by two, and its generalization criterion Freeman-Halton is unavailable. In the work was painted in detail its calculation algorithm, considered special cases, specified ways to address the numerous sorting tables with the same marginal frequencies and some solutions used in SPSS packages, R.
Dimension reduction of the categorical data is using in a quasi-regression model, that is, to finding a set of linear combinations of binary signs over a field of characteristic 2 (syndromes), the greatest way for Fisher's exact test associated with a binary final characteristic. Fast Grassmannian enumeration algorithm (FGEA) with using of degradation to cellular matrices was taken as a basis in  a selection of informative syndromes. Was proved consistency with the flag (nested sequence of finite subspaces) for the N-ary Gray code of order k and inconsistency with the flag of a recurrent sequence. Algorithm FGEA was improved by comparing the Young diagrams and Schubert cells, resulting in reducing calculation time for a quarter part.
Notes: 1) The inaccuracy (p.39) in the expression "product of the matrix A by the corresponding vector design"; 2) was not explained why there was an element resulting in inconsistencies with the flag. 3) small errors.
The mark - "good".

Scientific supervisor
Associate Professor of Department of Statistical Modelling                       N.P. Alexeyeva