Breast cancers with PIK3CA mutations can be treated with PIK3CA inhibitors in hormone receptor-positive HER2 negative subtypes. We applied a supervised elastic net penalized logistic regression model to predict PIK3CA mutations from gene expression data. This regression approach was applied to predict modeling using the TCGA pan-cancer dataset. Approximately 10,000 cases were available for PIK3CA mutation and mRNA expression data. In 10-fold cross-validation, the model with $\lambda$ = 0.01 and $\alpha$ = 1.0 (ridge regression) showed the best performance, in terms of area under the receiver operating characteristic (AUROC). The final model was developed with selected hyper-parameters using the entire training set. The training set AUROC was 0.93, and the test set AUROC was 0.84. The area under the precision-recall (AUPR) of the training set was 0.66, and the test set AUPR was 0.39. Cancer types were the most important predictors. Both insulin like growth factor 1 receptor (IGF1R) and the phosphatase and tensin homolog (PTEN) were the most significant genes in gene expression predictors. Our study suggests that predicting genomic alterations using gene expression data is possible, with good outcomes.