Sparse Bilinear Logistic Regression

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.Comment: 27 pages, 5 figure

Weakly Supervised Object Localization with Multi-fold Multiple Instance Learning

Object category localization is a challenging problem in computer vision. Standard supervised training requires bounding box annotations of object instances. This time-consuming annotation process is sidestepped in weakly supervised learning. In this case, the supervised information is restricted to binary labels that indicate the absence/presence of object instances in the image, without their locations. We follow a multiple-instance learning approach that iteratively trains the detector and infers the object locations in the positive training images. Our main contribution is a multi-fold multiple instance learning procedure, which prevents training from prematurely locking onto erroneous object locations. This procedure is particularly important when using high-dimensional representations, such as Fisher vectors and convolutional neural network features. We also propose a window refinement method, which improves the localization accuracy by incorporating an objectness prior. We present a detailed experimental evaluation using the PASCAL VOC 2007 dataset, which verifies the effectiveness of our approach.Comment: To appear in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI