Let D = (X, y) = (x i , y i ) i=1 be a training data set of molecular features x i ∈ R p and properties y i ∈ O. We would like to learn a linear hypothesis h(x; w 0 , w) = w 0 + x, w by minimizing the regularized risk [� � �] to predict the property of a molecule using its features. By calculating molecular descriptors and/or fingerprints, we typically obtain thousands of features of various forms, and if the true h has only a small subset of features with actually nonzero weights, we would want to impose a complexity penalty like Lasso to enforce sparsity. One drawback of Lasso is that for a subset of interrelated features it tends to arbitrarily choose only one feature, ignoring the rest. Reasonably, if there is a group of highly-correlated molecular descriptors, or categories integrating into a single descriptor, our model should either select or remove the entire group depending on its relation to the property. To address this issue, we present three objectives with sparse, grouped feature selection (see Figure � � � � � for penalized least-squares objectives):