The arboretum procedure
§ PROC DMNEURL: Approximation to PROC NEURAL
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- Bu səhifədəki naviqasiya:
- WEIGHT or WEIGHTS Statement WEIGHT
- Scoring the Model Using the OUTEST= Data set
- SQUARE
- GAUSS
- IDENT
- The DMREG Procedure Overview Procedure Syntax
- Details Examples
32 § PROC DMNEURL: Approximation to PROC NEURAL WEIGHT or WEIGHTS Statement WEIGHT onevar ; WEIGHTS onevar ; One numeric (interval scaled) variable may be specified as a WEIGHT variable. It is recommended to specify the WEIGHT variable already in the PROC DMDB invoca- tion. Then the information is saved in the catalog and that variable is used automati- cally as a FREQ variable in PROC DMNEURL.
The score value Ý is computed for each observation ½ Æ Ó × with nonmissing value of the target (response) variable Ý of the input data set. All information needed for scoring an observation of the DMDB data set is contained in the output of the OUTEST= data set. First an observation from the input data set is mapped into a vector Ú
Ò new values in which 1. CLASS predictor variables with à categories are replaced by à · ½ or à dummy (binary) variables, depending on the fact whether the variable has miss- ing values or not. 2. Missing values in interval predictor variables are replaced by the mean value of this variable in the DMDB data set. This mean value is taken from the catalog of the DMDB data set. 3. The values of a WEIGHT or FREQ variable are multiplied into the observation. 4. For an interval target variable Ý its value is transformed into the interval [0,1] by the relationship Ý Ò Û Ý
Ý Ñ Ò Ý Ñ Ü Ý Ñ Ò 5. All predictor variables are transformed into values with zero mean and unit standard deviation by Ü Ò Û Ü
Å Ò´Ü
µ Ë Ø Ú ´Ü µ The values for Å Ò´Ü µ and
Ë Ø Ú ´Ü µ are listed in the OUTEST= data set. This means, that in the presence of CLASS variables the n-vector Ú has more entries than the observation in the data set. The scoring is additive across the stages. The following information is available for scoring each stage ¯ components (eigenvectors) Þ Ð each of dimension Ò ¯ the best activation function and a specified link function ¯ the Ô ¾ · ½ optimal parameter estimates Purpose of PROC DMNEURL § 33 For each component Þ Ð we compute the component score Ù Ð , Ù Ð Ò ½ Þ Ð Ú similar to principal component analysis. With those values Ù Ð the model can be ex- pressed as Ý Ò×Ø ×Ø ½ ´ ´Ù µµ where is the best activation function and is the specified link function. In other words, this means, that given the Ù Ð the value Û is computed from Û ¼ · Ð ´Ù Ð Ð Ð µ where Ð and Ð are two of the Ô ¾
· ½ optimal parameters and is defined as SQUARE Û ´ · £ Ùµ £ Ù
Û £
Ò ´ £ Ùµ ARCTAN Û £ Ø Ò´ £ Ùµ LOGIST Û ÜÔ´ £ Ùµ ´½ · ÜÔ´
£ Ùµµ
GAUSS Û £ ÜÔ´ ´ £ Ùµ ¾ µ
Û £
Ò´ £ Ùµ COS Û £ Ó×´ £ Ùµ EXP Û £ ÜÔ´ £ Ùµ For the first component ½ ½ and ½ ¾ , for the second component ¾ ¿ and ¾ , and for the last component Ô ½ and
Ô are used. The link function is applied on Û and yields to IDENT Û
ÜÔ´Û µ
· ÜÔ´Û
µ RECIPR ½ Û Across all stages the values of are added to the predicted value (posterior) Ý .
The DMREG Procedure The DMREG Procedure Overview Procedure Syntax PROC DMREG Statement CLASS Statement CODE Statement DECISION Statement FREQ Statement MODEL Statement NLOPTIONS Statement REMOTE Statement SCORE Statement Details Examples Example 1: Linear and Quadratic Logistic Regression with an Ordinal Target (Rings Data) Example 2: Performing a Stepwise OLS Regression (DMREG Baseball Data) Example 3: Comparison of the DMREG and LOGISTIC Procedures when Using a Categorical Input Variable
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