**Regularized Discriminant Analysis (RDA)**

The regularized discriminant analysis (RDA) is a generalization of the linear discriminant analysis (LDA) and the quadratic discreminant analysis (QDA). Both algorithms are special cases of this algorithm. If the alpha parameter is set to 1, this operator performs LDA. Similarly if the alpha parameter is set to 0, this operator performs QDA. For more information about LDA and QDA please study the documentation of the corresponding operators.

Discriminant analysis is used to determine which variables discriminate between two or more naturally occurring groups. For example, an educational researcher may want to investigate which variables discriminate between high school graduates who decide (1) to go to college, (2) NOT to go to college. For that purpose the researcher could collect data on numerous variables prior to students’ graduation. After graduation, most students will naturally fall into one of the two categories. Discriminant Analysis could then be used to determine which variable(s) are the best predictors of students’ subsequent educational choice. Computationally, discriminant function analysis is very similar to analysis of variance (ANOVA). For example, suppose the same student graduation scenario. We could have measured students’ stated intention to continue on to college one year prior to graduation. If the means for the two groups (those who actually went to college and those who did not) are different, then we can say that intention to attend college as stated one year prior to graduation allows us to discriminate between those who are and are not college bound (and this information may be used by career counselors to provide the appropriate guidance to the respective students). The basic idea underlying discriminant analysis is to determine whether groups differ with regard to the mean of a variable, and then to use that variable to predict group membership (e.g., of new cases).

Discriminant Analysis may be used for two objectives: either we want to assess the adequacy of classification, given the group memberships of the objects under study; or we wish to assign objects to one of a number of (known) groups of objects. Discriminant Analysis may thus have a descriptive or a predictive objective. In both cases, some group assignments must be known before carrying out the Discriminant Analysis. Such group assignments, or labeling, may be arrived at in any way. Hence Discriminant Analysis can be employed as a useful complement to Cluster Analysis (in order to judge the results of the latter) or Principal Components Analysis.

http://…/ESLII_print10.pdf

http://…/slac-pub-4389.pdf

http://…/citation.cfm?id=1658388 … **Ellipsoid Method for Linear Programming**

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good knowledge of linear algebra. … **Freedman’s Paradox**

In statistical analysis, Freedman’s paradox, named after David Freedman, describes a problem in model selection whereby predictor variables with no explanatory power can appear artificially important. Freedman demonstrated (through simulation and asymptotic calculation) that this is a common occurrence when the number of variables is similar to the number of data points. Recently, new information-theoretic estimators have been developed in an attempt to reduce this problem, in addition to the accompanying issue of model selection bias, whereby estimators of predictor variables that have a weak relationship with the response variable are biased.

Freedman’s Paradox …

# If you did not already know

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