The HPGENSELECT Procedure

This example shows how you can use PROC HPGENSELECT to perform model selection among Poisson regression models by using the LASSO method in single-machine and distributed modes. For more information about the execution modes of SAS High-Performance Statistics procedures, see the section Processing Modes. The focus of this example is to show how you use the LASSO method and how you can switch the modes of execution of PROC HPGENSELECT. The following DATA step generates the data for this example. There are 1,000,000 observations in the data set, and the response yPoisson is a Poisson variable with a mean that depends on 20 of the 100 regressors.

%let nObs      = 1000000;
%let nContIn   = 20;
%let nContOut  = 80;
%let Seed      = 12345;

data ex4Data;
array xIn{&nContIn};
array xOut{&nContOut};

drop i j sign xBeta expXbeta;

seed = &Seed;
do i=1 to &nObs;
   sign  = -1;
       xBeta = 0;
       do j=1 to dim(xIn);
           call ranuni(seed,xIn[j]);
           xBeta  = xBeta + j*sign*xIn{j};
           sign   = -sign;
       end;

       do j=1 to dim(xOut);
          call ranuni(seed,xOut[j]);
       end;

       call ranuni(seed,xSubtle);
       call ranuni(seed,xTiny);

       xBeta = xBeta + 0.1*xSubtle + 0.05*xTiny;
       expXbeta = exp(xBeta/20);
       call ranpoi(seed,expXbeta,yPoisson);
       output;
end;
run;

The following statements use PROC HPGENSELECT to select a model by using the LASSO method and only the first 10,000 observations:

proc hpgenselect data=ex4Data(Obs=10000);
   model yPoisson = x: / dist=Poisson;
   selection method=Lasso(choose=SBC) details=all;
   performance details;
run;

Output 8.4.1 shows the "Performance Information" table. This shows that the HPGENSELECT procedure executed in single-machine mode on four threads because the client machine has four CPUs. You can select a certain number of threads on any machine involved in the computations by using the NTHREADS= option in the PERFORMANCE statement.

Output 8.4.2 shows the models fit by maximizing the penalized log likelihoods for a sequence of regularization parameters. For each step in the sequence, Output 8.4.2 shows you the effects that are added or removed and the fit statistics AIC, AICC, and BIC (SBC) for each model. Unlike other methods, such as forward selection, LASSO selection includes zero or more effects in each step.

The model in step 14 had the smallest Schwarz Bayesian criterion (BIC in Output 8.4.2), and it was chosen as the final model because the CHOOSE=SBC option was specified in the SELECTION statement. Output 8.4.3 shows the parameter estimates for the selected model. You can see that the LASSO selection in which the final model was chosen based on the SBC criterion retains all 20 of the true effects but also keeps several extraneous effects.

Output 8.4.4 shows timing information for the PROC HPGENSELECT run. This table is produced when you specify the DETAILS option in the PERFORMANCE statement. You can see that, in this case, the majority of time is spent in performing model selection.

You can switch to running PROC HPGENSELECT in distributed mode by specifying valid values for the NODES=, INSTALL=, and HOST= options in the PERFORMANCE statement. An alternative to specifying the INSTALL= and HOST= options in the PERFORMANCE statement is to set appropriate values for the GRIDHOST and GRIDINSTALLLOC environment variables by using OPTIONS SET commands. For more information about setting these options or environment variables, see the section Processing Modes.

The following statements provide an example. All 1,000,000 observations are used in this example of running PROC HPGENSELECT in distributed mode. To run these statements successfully, you need to set the macro variables GRIDHOST and GRIDINSTALLLOC to resolve to appropriate values, or you can replace the references to macro variables with appropriate values.

proc hpgenselect data=ex4Data;
   model yPoisson = x: / dist=Poisson;
   selection method=Lasso(choose=SBC) details=all;
   performance details nodes = 10
               host="&GRIDHOST" install="&GRIDINSTALLLOC";
run;

The Execution Mode row in the "Performance Information" table shown in Output 8.4.5 indicates that the calculations were performed in a distributed environment that used 10 nodes, each of which used 32 threads.

Another indication of distributed execution is the following message in the SAS log, which is issued by all high-performance statistical procedures:

NOTE: The HPGENSELECT procedure is executing in the distributed
      computing environment with 10 worker nodes.

Output 8.4.6 shows timing information for this distributed run of PROC HPGENSELECT. As in the case of the single-machine mode, the majority of time in distributed mode is spent in performing the model selection.

Output 8.4.7 shows the models that were fit by maximizing the penalized log likelihoods for a sequence of regularization parameters. In this case, the model in the last step had the smallest SBC statistic and was the selected model.

Output 8.4.8 shows the parameter estimates for the selected model. Selecting the final model based on the SBC criterion retains all 20 of the true effects and none of the extraneous effects.