Group Norm for Learning Latent Structural SVMs

1. Group Norm for Learning Latent Structural SVMs Daozheng Chen (UMD, College Park), Dhruv Batra (TTI-Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.) Overview Induce Group Norm • Our goal • Estimate model parameters • Learn the complexity of latent variable space. • Our approach • norm for regularization to estimate the parameters of a latent-variable model. • Data with complete annotation is rarely ever available. • Latent variable models capture interaction between • observed data (e.g. gradient histogram image features) • latent or hidden variables not observed in the training data (e.g. location of object parts). • Parameter estimation involve a difficult non-convex optimization problem (EM, CCCP, self-paced learning) Key Contribution Inducing Group Norm w partitioned into P groups; each group corresponds to the parameters of a latent variable state Root filters Part filters Part displacement norm for regularization Component #1 Digit Recognition Component #2 Rotation (Latent Var.) Feature Vector Images Felzenszwalb et al. car model on the PASCAL VOC 2007 data. Each row is a component of the model. Latent Structural SVM Label space Latent Space Joint feature vector Prediction Rule: Learning objective: • At group level, the norm behave like norm and induces group sparsity. • Within each group, the norm behave like norm and does not promote sparsity. Alternating Coordinate and Subgradient Descent Experiment • Digit recognition experiment (following the setup of Kumar et al. NIPS ‘10) • MNIST data: binary classification on four difficult digit pairs • (1,7), (2,7), (3,8), (8,9) • Training data 5,851 - 6,742, and testing data 974 - 1,135 • Rotate digit images with angles from -60o to 60o • PCA to form 10 dimensional feature vector Rewrite Learning Objective nonconvex convex convex -48o -36o -24o -12o 0o 12o 24o 36o 48o 60o -60o Minimize Upper bound of convex if {hi} is fixed • l2 norm of the parameter vectors for different angles over the 4 digit pairs. • Select only a few angles, much fewer than 22 angles Angles Not Selected -60o -12o 0o -48o -36o -48o -48o -60o Subgradient • Significantly higher accuracy than random sampling. • 66% faster than full model with no loss in accuracy!