Trust-Region Variational Inference with Gaussian Mixture Models

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by using information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. Our use of the lower bound ensures convergence to a stationary point of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multimodal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-theart MCMC samplers while requiring up to three orders of magnitude less computational resources

Trust-region variational inference with gaussian mixture models

Funding Information: This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 645582 (RoMaNS). Calculations for this research were conducted on the Lichtenberg high performance computer of the TU Darmstadt. Publisher Copyright: © 2020 Oleg Arenz, Mingjun Zhong and Gerhard Neumann.Peer reviewe

Robust and Efficient Inference of Scene and Object Motion in Multi-Camera Systems

Multi-camera systems have the ability to overcome some of the fundamental limitations of single camera based systems. Having multiple view points of a scene goes a long way in limiting the influence of field of view, occlusion, blur and poor resolution of an individual camera. This dissertation addresses robust and efficient inference of object motion and scene in multi-camera and multi-sensor systems. The first part of the dissertation discusses the role of constraints introduced by projective imaging towards robust inference of multi-camera/sensor based object motion. We discuss the role of the homography and epipolar constraints for fusing object motion perceived by individual cameras. For planar scenes, the homography constraints provide a natural mechanism for data association. For scenes that are not planar, the epipolar constraint provides a weaker multi-view relationship. We use the epipolar constraint for tracking in multi-camera and multi-sensor networks. In particular, we show that the epipolar constraint reduces the dimensionality of the state space of the problem by introducing a ``shared'' state space for the joint tracking problem. This allows for robust tracking even when one of the sensors fail due to poor SNR or occlusion. The second part of the dissertation deals with challenges in the computational aspects of tracking algorithms that are common to such systems. Much of the inference in the multi-camera and multi-sensor networks deal with complex non-linear models corrupted with non-Gaussian noise. Particle filters provide approximate Bayesian inference in such settings. We analyze the computational drawbacks of traditional particle filtering algorithms, and present a method for implementing the particle filter using the Independent Metropolis Hastings sampler, that is highly amenable to pipelined implementations and parallelization. We analyze the implementations of the proposed algorithm, and in particular concentrate on implementations that have minimum processing times. The last part of the dissertation deals with the efficient sensing paradigm of compressing sensing (CS) applied to signals in imaging, such as natural images and reflectance fields. We propose a hybrid signal model on the assumption that most real-world signals exhibit subspace compressibility as well as sparse representations. We show that several real-world visual signals such as images, reflectance fields, videos etc., are better approximated by this hybrid of two models. We derive optimal hybrid linear projections of the signal and show that theoretical guarantees and algorithms designed for CS can be easily extended to hybrid subspace-compressive sensing. Such methods reduce the amount of information sensed by a camera, and help in reducing the so called data deluge problem in large multi-camera systems

Advances in Simultaneous Localization and Mapping in Confined Underwater Environments Using Sonar and Optical Imaging.

This thesis reports on the incorporation of surface information into a probabilistic simultaneous localization and mapping (SLAM) framework used on an autonomous underwater vehicle (AUV) designed for underwater inspection. AUVs operating in cluttered underwater environments, such as ship hulls or dams, are commonly equipped with Doppler-based sensors, which---in addition to navigation---provide a sparse representation of the environment in the form of a three-dimensional (3D) point cloud. The goal of this thesis is to develop perceptual algorithms that take full advantage of these sparse observations for correcting navigational drift and building a model of the environment. In particular, we focus on three objectives. First, we introduce a novel representation of this 3D point cloud as collections of planar features arranged in a factor graph. This factor graph representation probabalistically infers the spatial arrangement of each planar segment and can effectively model smooth surfaces (such as a ship hull). Second, we show how this technique can produce 3D models that serve as input to our pipeline that produces the first-ever 3D photomosaics using a two-dimensional (2D) imaging sonar. Finally, we propose a model-assisted bundle adjustment (BA) framework that allows for robust registration between surfaces observed from a Doppler sensor and visual features detected from optical images. Throughout this thesis, we show methods that produce 3D photomosaics using a combination of triangular meshes (derived from our SLAM framework or given a-priori), optical images, and sonar images. Overall, the contributions of this thesis greatly increase the accuracy, reliability, and utility of in-water ship hull inspection with AUVs despite the challenges they face in underwater environments. We provide results using the Hovering Autonomous Underwater Vehicle (HAUV) for autonomous ship hull inspection, which serves as the primary testbed for the algorithms presented in this thesis. The sensor payload of the HAUV consists primarily of: a Doppler velocity log (DVL) for underwater navigation and ranging, monocular and stereo cameras, and---for some applications---an imaging sonar.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120750/1/paulozog_1.pd

Deterministic Sampling for Nonlinear Dynamic State Estimation

The goal of this work is improving existing and suggesting novel filtering algorithms for nonlinear dynamic state estimation. Nonlinearity is considered in two ways: First, propagation is improved by proposing novel methods for approximating continuous probability distributions by discrete distributions defined on the same continuous domain. Second, nonlinear underlying domains are considered by proposing novel filters that inherently take the underlying geometry of these domains into account