TY - CONF AB - We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data. AU - Kwitt, Roland AU - Huber, Stefan AU - Niethammer, Marc AU - Lin, Weili AU - Bauer, Ulrich ID - 1424 TI - Statistical topological data analysis-A kernel perspective VL - 28 ER - TY - CONF AB - Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrence of new mutations is much longer than the time it takes for a new beneficial mutation to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a (1+1)-type process where the probability of accepting a new genotype (improvements or worsenings) depends on the change in fitness. We present an initial runtime analysis of SSWM, quantifying its performance for various parameters and investigating differences to the (1+1) EA. We show that SSWM can have a moderate advantage over the (1+1) EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1) EA by taking advantage of information on the fitness gradient. AU - Paixao, Tiago AU - Sudholt, Dirk AU - Heredia, Jorge AU - Trubenova, Barbora ID - 1430 T2 - Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation TI - First steps towards a runtime comparison of natural and artificial evolution ER - TY - CONF AB - Cryptographic access control offers selective access to encrypted data via a combination of key management and functionality-rich cryptographic schemes, such as attribute-based encryption. Using this approach, publicly available meta-data may inadvertently leak information on the access policy that is enforced by cryptography, which renders cryptographic access control unusable in settings where this information is highly sensitive. We begin to address this problem by presenting rigorous definitions for policy privacy in cryptographic access control. For concreteness we set our results in the model of Role-Based Access Control (RBAC), where we identify and formalize several different flavors of privacy, however, our framework should serve as inspiration for other models of access control. Based on our insights we propose a new system which significantly improves on the privacy properties of state-of-the-art constructions. Our design is based on a novel type of privacy-preserving attribute-based encryption, which we introduce and show how to instantiate. We present our results in the context of a cryptographic RBAC system by Ferrara et al. (CSF'13), which uses cryptography to control read access to files, while write access is still delegated to trusted monitors. We give an extension of the construction that permits cryptographic control over write access. Our construction assumes that key management uses out-of-band channels between the policy enforcer and the users but eliminates completely the need for monitoring read/write access to the data. AU - Ferrara, Anna AU - Fuchsbauer, Georg AU - Liu, Bin AU - Warinschi, Bogdan ID - 1474 TI - Policy privacy in cryptographic access control ER - TY - GEN AB - In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkähler manifolds including toric hyperkähler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulting formulae for their Poincaré polynomials are combinatorial and representation theoretical in nature. In particular we will look at their Betti numbers and will establish some results and state some expectations on their asymptotic shape. AU - Tamas Hausel AU - Rodríguez Villegas, Fernando ID - 1473 IS - 370 T2 - Asterisque TI - Cohomology of large semiprojective hyperkähler varieties VL - 2015 ER - TY - CONF AB - Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes. AU - Reininghaus, Jan AU - Huber, Stefan AU - Bauer, Ulrich AU - Kwitt, Roland ID - 1483 TI - A stable multi-scale kernel for topological machine learning ER -