  We present a supervised-learning algorithm from graph data (a set of graphs)
for arbitrary twice-differentiable loss functions and sparse linear models over
all possible subgraph features. To date, it has been shown that under all
possible subgraph features, several types of sparse learning, such as Adaboost,
LPBoost, LARS/LASSO, and sparse PLS regression, can be performed. Particularly
emphasis is placed on simultaneous learning of relevant features from an
infinite set of candidates. We first generalize techniques used in all these
preceding studies to derive an unifying bounding technique for arbitrary
separable functions. We then carefully use this bounding to make block
coordinate gradient descent feasible over infinite subgraph features, resulting
in a fast converging algorithm that can solve a wider class of sparse learning
problems over graph data. We also empirically study the differences from the
existing approaches in convergence property, selected subgraph features, and
search-space sizes. We further discuss several unnoticed issues in sparse
learning over all possible subgraph features.
