Bellʼs theorem in physics, as well as causal discovery in machine learning, both face the problem of deciding whether observed data is compatible with a presumed causal relationship between the variables (for example, a local hidden variable model). Traditionally, Bell inequalities have been used to describe the restrictions imposed by causal structures on marginal distributions. However, some structures give rise to non-convex constraints on the accessible data, and it has recently been noted that linear inequalities on the observable entropies capture these situations more naturally. In this paper, we show the versatility of the entropic approach by greatly expanding the set of scenarios for which entropic constraints are known. For the first time, we treat Bell scenarios involving multiple parties and multiple observables per party. Going beyond the usual Bell setup, we exhibit inequalities for scenarios with extra conditional independence assumptions, as well as a limited amount of shared randomness between the parties. Many of our results are based on a geometric observation: Bell polytopes for two-outcome measurements can be naturally imbedded into the convex cone of attainable marginal entropies. Thus, any entropic inequality can be translated into one valid for probabilities. In some situations the converse also holds, which provides us with a rich source of candidate entropic inequalities.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New J. Phys. 16 (2014) 043001 R Chaves et al 2 1The notion of quantum non-locality is arguably somewhat unfortunate, as it seems to imply that an unspecified super-luminal mechanism is responsible for the strong correlations observed in quantum experiments. Bellʼs theorem only asserts that no local hidden variable (LHV) theory can reproduce these correlations. It does not put forward any alternative mechanism-certainly none involving actions at a distance. It has, however, become customary [1] to refer to statistics that cannot arise in LHV models as 'non-local'. We prefer sticking to commonly accepted language over inventing a possibly better-suited term that will not be widely understood. New J. Phys. 16 (2014) 043001 R Chaves et al New J. Phys. 16 (2014) 043001 R Chaves et al New J. Phys. 16 (2014) 043001 R Chaves et al 6 New J. Phys. 16 (2014) 043001 R Chaves et al 7 New J. Phys. 16 (2014) 043001 R Chaves et al 8 New J. Phys. 16 (2014) 043001 R Chaves et al 9 New J. Phys. 16 (2014) 043001 R Chaves et al 10 T n . We have stated this primarily to clarify the geometric nature of Q n (i.e. as an orthant, up to a linear isomorphism). New J. Phys. 16 (2014) 043001 R Chaves et al New J. Phys. 16 (2014) 043001 R Chaves et al 24

While an increasing interest in deep models for single-image depth estimation (SIDE) can be observed, established schemes for their evaluation are still limited. We propose a set of novel quality criteria, allowing for a more detailed analysis by focusing on specific characteristics of depth maps. In particular, we address the preservation of edges and planar regions, depth consistency, and absolute distance accuracy. In order to employ these metrics to evaluate and compare state-of-the-art SIDE approaches, we provide a new high-quality RGB-D dataset. We used a digital single-lens reflex (DSLR) camera together with a laser scanner to acquire high-resolution images and highly accurate depth maps. Experimental results show the validity of our proposed evaluation protocol.

Due to their ubiquity and long-term stability, polelike objects are well suited to serve as landmarks for vehicle localization in urban environments. In this work, we present a complete mapping and long-term localization system based on pole landmarks extracted from 3-D lidar data. Our approach features a novel pole detector, a mapping module, and an online localization module, each of which are described in detail, and for which we provide an open-source implementation [1].In extensive experiments, we demonstrate that our method improves on the state of the art with respect to long-term reliability and accuracy: First, we prove reliability by tasking the system with localizing a mobile robot over the course of 15 months in an urban area based on an initial map, confronting it with constantly varying routes, differing weather conditions, seasonal changes, and construction sites. Second, we show that the proposed approach clearly outperforms a recently published method in terms of accuracy.

This paper provides a fully decentralized algorithm for collaborative localization based on the extended Kalman filter. The major challenge in decentralized collaborative localization is to track inter-robot dependencies, which is particularly difficult when sustained synchronous communication between the robots cannot be guaranteed. Current approaches suffer from the need for particular communication schemes, extensive bookkeeping of measurements, overly conservative assumptions, or the restriction to specific measurement models. This paper introduces a localization algorithm that is able to approximate the inter-robot correlations while fulfilling all of the following conditions: communication is limited to two robots that obtain a relative measurement, the algorithm is recursive in the sense that it does not require storage of measurements and each robot maintains only the latest estimate of its own pose, and it supports generic measurement models. The fact that the proposed approach can handle these particularly difficult conditions ensures that it is applicable to a wide range of multi-robot scenarios. We provide mathematical details on our approximation. Extensive experiments carried out using real-world datasets demonstrate the improved performance of our method compared with several existing approaches.