Multi-class SVMs: From Tighter Data-Dependent Generalization Bounds to Novel Algorithms

This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially improving the state-of-the-art linear dependence in the existing data-dependent generalization analysis. The theoretical analysis motivates us to introduce a new multi-class classification machine based on $\ell_p$-norm regularization, where the parameter $p$ controls the complexity of the corresponding bounds. We derive an efficient optimization algorithm based on Fenchel duality theory. Benchmarks on several real-world datasets show that the proposed algorithm can achieve significant accuracy gains over the state of the art

Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States

We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.Comment: 6 pages, 5 figures, 1 tabl

Understanding and Comparing Deep Neural Networks for Age and Gender Classification

Recently, deep neural networks have demonstrated excellent performances in recognizing the age and gender on human face images. However, these models were applied in a black-box manner with no information provided about which facial features are actually used for prediction and how these features depend on image preprocessing, model initialization and architecture choice. We present a study investigating these different effects. In detail, our work compares four popular neural network architectures, studies the effect of pretraining, evaluates the robustness of the considered alignment preprocessings via cross-method test set swapping and intuitively visualizes the model's prediction strategies in given preprocessing conditions using the recent Layer-wise Relevance Propagation (LRP) algorithm. Our evaluations on the challenging Adience benchmark show that suitable parameter initialization leads to a holistic perception of the input, compensating artefactual data representations. With a combination of simple preprocessing steps, we reach state of the art performance in gender recognition.Comment: 8 pages, 5 figures, 5 tables. Presented at ICCV 2017 Workshop: 7th IEEE International Workshop on Analysis and Modeling of Faces and Gesture