Sparse Learning over Infinite Subgraph Features

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.Comment: 42 pages, 24 figures, 4 table

PAC-Bayes Analysis of Multi-view Learning

This paper presents eight PAC-Bayes bounds to analyze the generalization performance of multi-view classifiers. These bounds adopt data dependent Gaussian priors which emphasize classifiers with high view agreements. The center of the prior for the first two bounds is the origin, while the center of the prior for the third and fourth bounds is given by a data dependent vector. An important technique to obtain these bounds is two derived logarithmic determinant inequalities whose difference lies in whether the dimensionality of data is involved. The centers of the fifth and sixth bounds are calculated on a separate subset of the training set. The last two bounds use unlabeled data to represent view agreements and are thus applicable to semi-supervised multi-view learning. We evaluate all the presented multi-view PAC-Bayes bounds on benchmark data and compare them with previous single-view PAC-Bayes bounds. The usefulness and performance of the multi-view bounds are discussed.Comment: 35 page