Variational Inference as Iterative Projection in a Bayesian Hilbert Space

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense `closest' to the full Bayesian posterior. Closeness is typically defined through the selection of an appropriate loss functional such as the Kullback-Leibler (KL) divergence. In this paper, we explore a new formulation of variational inference by exploiting the fact that the set of PDFs constitutes a Bayesian Hilbert space under careful definitions of vector addition, scalar multiplication and an inner product. We show that variational inference based on KL divergence then amounts to an iterative projection of the Bayesian posterior onto a subspace corresponding to the selected approximation family. In fact, the inner product chosen for the Bayesian Hilbert space suggests the definition of a new measure of the information contained in a PDF and in turn a new divergence is introduced. Each step in the iterative projection is equivalent to a local minimization of this divergence. We present an example Bayesian subspace based on exponentiated Hermite polynomials as well as work through the details of this general framework for the specific case of the multivariate Gaussian approximation family and show the equivalence to another Gaussian variational inference approach. We furthermore discuss the implications for systems that exhibit sparsity, which is handled naturally in Bayesian space.Comment: 28 pages, 7 figures, submitted to Annals of Mathematics and Artificial Intelligenc

Fault-tolerant formation driving mechanism designed for heterogeneous MAVs-UGVs groups

A fault-tolerant method for stabilization and navigation of 3D heterogeneous formations is proposed in this paper. The presented Model Predictive Control (MPC) based approach enables to deploy compact formations of closely cooperating autonomous aerial and ground robots in surveillance scenarios without the necessity of a precise external localization. Instead, the proposed method relies on a top-view visual relative localization provided by the micro aerial vehicles flying above the ground robots and on a simple yet stable visual based navigation using images from an onboard monocular camera. The MPC based schema together with a fault detection and recovery mechanism provide a robust solution applicable in complex environments with static and dynamic obstacles. The core of the proposed leader-follower based formation driving method consists in a representation of the entire 3D formation as a convex hull projected along a desired path that has to be followed by the group. Such an approach provides non-collision solution and respects requirements of the direct visibility between the team members. The uninterrupted visibility is crucial for the employed top-view localization and therefore for the stabilization of the group. The proposed formation driving method and the fault recovery mechanisms are verified by simulations and hardware experiments presented in the paper

Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond

We have discovered 7 intimate connections between the published results for the radiative corrections, \Ck, to the Gross--Llewellyn Smith (GLS) sum rule, in deep-inelastic lepton scattering, and the radiative corrections, \Cr, to the Adler function of the flavour-singlet vector current, in \ee annihilation. These include a surprising relation between the scheme-independent single-electron-loop contributions to the 4-loop QED $\beta$\/-function and the zero-fermion-loop abelian terms in the 3-loop GLS sum rule. The combined effect of all 7 relations is to give the factorization of the 2-loop $\beta$\/-function in \Ds\equiv\Ck\Cr-1=\frac{\Be}{\Aq}\left\{S_1\Cf\Aq+\left[S_2\Tf\Nf +\Sa\Ca+\Sf\Cf\right]\Cf\Aq^2\right\}+O(\Aq^4)\,, where \Aq=\al(\mu^2=Q^2)/4\pi is the \MS coupling of an arbitrary colour gauge theory, and S_1=-\Df{21}{2}+12\Ze3\,;\quad S_2=\Df{326}{3}-\Df{304}{3}\Ze3\,;\quad \Sa=-\Df{629}{2}+\Df{884}{3}\Ze3\,;\quad \Sf=\Df{397}{6}+136\Ze3-240\Ze5 specify the sole content of \Ck that is not already encoded in \Cr and \Be=Q^2\rd\Aq/\rd Q^2 at O(\Aq^3). The same result is obtained by combining the radiative corrections to Bjorken's polarized sum rule with those for the Adler function of the non-singlet axial current. We suggest possible origins of $\beta$ in the `Crewther discrepancy', \Ds, and determine \Ds/(\Be/\Aq), to all orders in \Nf\Aq, in the large-\Nf limit, obtaining the {\em entire\/} series of coefficients of which $S_1$ and $S_2$ are merely the first two members.Comment: 11 pages, LATEX, preprint INR-820/93, OUT-4102-45; In memoriam Sergei Grogorievich Corishny, 1958-198

Development of machine learning support for reading whole body diffusion-weighted MRI (WB-MRI) in myeloma for the detection and quantification of the extent of disease before and after treatment (MALIMAR): protocol for a cross-sectional diagnostic test accuracy study.

INTRODUCTION: Whole-body MRI (WB-MRI) is recommended by the National Institute of Clinical Excellence as the first-line imaging tool for diagnosis of multiple myeloma. Reporting WB-MRI scans requires expertise to interpret and can be challenging for radiologists who need to meet rapid turn-around requirements. Automated computational tools based on machine learning (ML) could assist the radiologist in terms of sensitivity and reading speed and would facilitate improved accuracy, productivity and cost-effectiveness. The MALIMAR study aims to develop and validate a ML algorithm to increase the diagnostic accuracy and reading speed of radiological interpretation of WB-MRI compared with standard methods. METHODS AND ANALYSIS: This phase II/III imaging trial will perform retrospective analysis of previously obtained clinical radiology MRI scans and scans from healthy volunteers obtained prospectively to implement training and validation of an ML algorithm. The study will comprise three project phases using approximately 633 scans to (1) train the ML algorithm to identify active disease, (2) clinically validate the ML algorithm and (3) determine change in disease status following treatment via a quantification of burden of disease in patients with myeloma. Phase 1 will primarily train the ML algorithm to detect active myeloma against an expert assessment ('reference standard'). Phase 2 will use the ML output in the setting of radiology reader study to assess the difference in sensitivity when using ML-assisted reading or human-alone reading. Phase 3 will assess the agreement between experienced readers (with and without ML) and the reference standard in scoring both overall burden of disease before and after treatment, and response. ETHICS AND DISSEMINATION: MALIMAR has ethical approval from South Central-Oxford C Research Ethics Committee (REC Reference: 17/SC/0630). IRAS Project ID: 233501. CPMS Portfolio adoption (CPMS ID: 36766). Participants gave informed consent to participate in the study before taking part. MALIMAR is funded by National Institute for Healthcare Research Efficacy and Mechanism Evaluation funding (NIHR EME Project ID: 16/68/34). Findings will be made available through peer-reviewed publications and conference dissemination. TRIAL REGISTRATION NUMBER: NCT03574454

Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals

The old "glue--and--cut" symmetry of massless propagators, first established in [1], leads --- after reduction to master integrals is performed --- to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (zeta_{2n}) in the Adler function and other similar functions essentially reducible to the massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicit performing the corresponding five-loop master integrals.Comment: 34 pages, few typos have been fixed, references and acknowledgements have been updated. Results for master integrals (together with some auxiliary information) are now available in http://www-ttp.physik.uni-karlsruhe.de/Progdata/ttp10/ttp10-18

A mission control architecture for robotic lunar sample return as field tested in an analogue deployment to the Sudbury impact structure

A Mission Control Architecture is presented for a Robotic Lunar Sample Return Mission which builds upon the experience of the landed missions of the NASA Mars Exploration Program. This architecture consists of four separate processes working in parallel at Mission Control and achieving buy-in for plans sequentially instead of simultaneously from all members of the team. These four processes were: Science Processing, Science Interpretation, Planning and Mission Evaluation. Science Processing was responsible for creating products from data downlinked from the field and is organized by instrument. Science Interpretation was responsible for determining whether or not science goals are being met and what measurements need to be taken to satisfy these goals. The Planning process, responsible for scheduling and sequencing observations, and the Evaluation process that fostered inter-process communications, reporting and documentation assisted these processes. This organization is advantageous for its flexibility as shown by the ability of the structure to produce plans for the rover every two hours, for the rapidity with which Mission Control team members may be trained and for the relatively small size of each individual team. This architecture was tested in an analogue mission to the Sudbury impact structure from June 6-17, 2011. A rover was used which was capable of developing a network of locations that could be revisited using a teach and repeat method. This allowed the science team to process several different outcrops in parallel, downselecting at each stage to ensure that the samples selected for caching were the most representative of the site. Over the course of 10 days, 18 rock samples were collected from 5 different outcrops, 182 individual field activities - such as roving or acquiring an image mosaic or other data product - were completed within 43 command cycles, and the rover travelled over 2,200 m. Data transfer from communications passes were filled to 74%. Sample triage was simulated to allow down-selection to 1kg of material for return to Earth

System for deployment of groups of unmanned micro aerial vehicles in GPS-denied environments using onboard visual relative localization

A complex system for control of swarms of micro aerial vehicles (MAV), in literature also called as unmanned aerial vehicles (UAV) or unmanned aerial systems (UAS), stabilized via an onboard visual relative localization is described in this paper. The main purpose of this work is to verify the possibility of self-stabilization of multi-MAV groups without an external global positioning system. This approach enables the deployment of MAV swarms outside laboratory conditions, and it may be considered an enabling technique for utilizing fleets of MAVs in real-world scenarios. The proposed visual-based stabilization approach has been designed for numerous different multi-UAV robotic applications (leader-follower UAV formation stabilization, UAV swarm stabilization and deployment in surveillance scenarios, cooperative UAV sensory measurement) in this paper. Deployment of the system in real-world scenarios truthfully verifies its operational constraints, given by limited onboard sensing suites and processing capabilities. The performance of the presented approach (MAV control, motion planning, MAV stabilization, and trajectory planning) in multi-MAV applications has been validated by experimental results in indoor as well as in challenging outdoor environments (e.g., in windy conditions and in a former pit mine)

Safeguarding pollinators and their values to human well-being

Wild and managed pollinators provide a wide range of benefits to society in terms of contributions to food security, farmer and beekeeper livelihoods, social and cultural values, as well as the maintenance of wider biodiversity and ecosystem stability. Pollinators face numerous threats, including changes in land-use and management intensity, climate change, pesticides and genetically modified crops, pollinator management and pathogens, and invasive alien species. There are well-documented declines in some wild and managed pollinators in several regions of the world. However, many effective policy and management responses can be implemented to safeguard pollinators and sustain pollination services