Neural ODEs with stochastic vector field mixtures

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to the set that baseline methods cannot solve, and proposes mixtures of stochastic vector fields as a model class that is capable of solving these essential problems. Dynamic vector field selection is of critical importance for our model, and our approach is to propagate component uncertainty over the integration interval with a technique based on forward filtering. We also formalise several loss functions that encourage desirable properties on the trajectory paths, and of particular interest are those that directly encourage fewer expected function evaluations. Experimentally, we demonstrate that our model class is capable of capturing the natural dynamics of human behaviour; a notoriously volatile application area. Baseline approaches cannot adequately model this problem

Security Analysis of an Untrusted Source for Quantum Key Distribution: Passive Approach

We present a passive approach to the security analysis of quantum key distribution (QKD) with an untrusted source. A complete proof of its unconditional security is also presented. This scheme has significant advantages in real-life implementations as it does not require fast optical switching or a quantum random number generator. The essential idea is to use a beam splitter to split each input pulse. We show that we can characterize the source using a cross-estimate technique without active routing of each pulse. We have derived analytical expressions for the passive estimation scheme. Moreover, using simulations, we have considered four real-life imperfections: Additional loss introduced by the "plug & play" structure, inefficiency of the intensity monitor, noise of the intensity monitor, and statistical fluctuation introduced by finite data size. Our simulation results show that the passive estimate of an untrusted source remains useful in practice, despite these four imperfections. Also, we have performed preliminary experiments, confirming the utility of our proposal in real-life applications. Our proposal makes it possible to implement the "plug & play" QKD with the security guaranteed, while keeping the implementation practical.Comment: 35 pages, 19 figures. Published Versio

Discussion of "Geodesic Monte Carlo on Embedded Manifolds"

Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)Comment: Discussion of arXiv:1301.6064. To appear in the Scandinavian Journal of Statistics. 18 page

Pitfall of the Detection Rate Optimized Bit Allocation within template protection and a remedy

One of the requirements of a biometric template protection system is that the protected template ideally should not leak any information about the biometric sample or its derivatives. In the literature, several proposed template protection techniques are based on binary vectors. Hence, they require the extraction of a binary representation from the real- valued biometric sample. In this work we focus on the Detection Rate Optimized Bit Allocation (DROBA) quantization scheme that extracts multiple bits per feature component while maximizing the overall detection rate. The allocation strategy has to be stored as auxiliary data for reuse in the verification phase and is considered as public. This implies that the auxiliary data should not leak any information about the extracted binary representation. Experiments in our work show that the original DROBA algorithm, as known in the literature, creates auxiliary data that leaks a significant amount of information. We show how an adversary is able to exploit this information and significantly increase its success rate on obtaining a false accept. Fortunately, the information leakage can be mitigated by restricting the allocation freedom of the DROBA algorithm. We propose a method based on population statistics and empirically illustrate its effectiveness. All the experiments are based on the MCYT fingerprint database using two different texture based feature extraction algorithms

Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set $\mathcal E$ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if $\mathcal E$ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyse the Boltzmann operator in the geometric setting from the point of its Maxwell's weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyv\"arinen divergence. This requires to generalise our approach to Orlicz-Sobolev spaces to include derivatives.%Comment: 39 pages, 1 figure. Expanded version of a paper presente at the conference SigmaPhi 2014 Rhodes GR. Under revision for Entrop