1. Group Norm for Learning Latent Structural SVMs Overview Daozheng Chen (UMD, College Park), Dhruv Batra (TTI Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.) Data with complete annotation is rarely ever available. Latent variable models capture interaction between observed data and latent variables Parameter estimation involve a difficult non-convex optimization problem 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. Fully trained person models using the PASCAL VOC 2007 data. Each row is a component of the model. Felzenszwalb et al. [8] Root filtersPart filtersPart displacement

2. Latent Structural SVM Prediction Rule: Group Norm for Learning Latent Structural SVMs Daozheng Chen (UMD, College Park), Dhruv Batra (TTI Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.) Learning objective: FeaturesLabelsLatent variables Joint feature vector

3. Induce Group Norm Group Norm for Learning Latent Structural SVMs Digit Recognition Key Contribution Images Rotation (Latent Var.) Feature Vector 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. Daozheng Chen (UMD, College Park), Dhruv Batra (TTI Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.)

4. Alternate coordinate and subgradient descent Group Norm for Learning Latent Structural SVMs Daozheng Chen (UMD, College Park), Dhruv Batra (TTI Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.) Minimize Upper bound of learning objective Alternate coordinate and subgradient descent Fixed and minized w.r.t. Subgradient method Only perform one subgradient step Convex if is fixed Fixed and minized w.r.t.

5. Experiment Group Norm for Learning Latent Structural SVMs Digit recognition experiment: MNIST data (following the setups of Kumar et al. [10] closely) Binary classification on four difficult digit pairs: (1,7), (2,7), (3,8), (8,9) Rotate digit images with angles uniformly distributed from -60 o to 60 o PCA to form 10 dimensional feature vector -60 o -48 o -36 o -24 o -12 o 0o0o 12 o 24 o 36 o 48 o 60 o Daozheng Chen (UMD, College Park), Dhruv Batra (TTI Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.)

6. Experiment Group Norm for Learning Latent Structural SVMs -60 o -48 o Angles with the highest magnitude Select only a few angles Random sampling needs higher number of angles per digit to give similar accuracy Running time increases linearly as budget increases. Daozheng Chen (UMD, College Park), Dhruv Batra (TTI Chicago), Bill Freeman (MIT), Micah K. Johnson (GelSight, Inc.)