907 research outputs found
Extended Object Tracking: Introduction, Overview and Applications
This article provides an elaborate overview of current research in extended
object tracking. We provide a clear definition of the extended object tracking
problem and discuss its delimitation to other types of object tracking. Next,
different aspects of extended object modelling are extensively discussed.
Subsequently, we give a tutorial introduction to two basic and well used
extended object tracking approaches - the random matrix approach and the Kalman
filter-based approach for star-convex shapes. The next part treats the tracking
of multiple extended objects and elaborates how the large number of feasible
association hypotheses can be tackled using both Random Finite Set (RFS) and
Non-RFS multi-object trackers. The article concludes with a summary of current
applications, where four example applications involving camera, X-band radar,
light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are
highlighted.Comment: 30 pages, 19 figure
Ranking relations using analogies in biological and information networks
Analogical reasoning depends fundamentally on the ability to learn and
generalize about relations between objects. We develop an approach to
relational learning which, given a set of pairs of objects
,
measures how well other pairs A:B fit in with the set . Our work
addresses the following question: is the relation between objects A and B
analogous to those relations found in ? Such questions are
particularly relevant in information retrieval, where an investigator might
want to search for analogous pairs of objects that match the query set of
interest. There are many ways in which objects can be related, making the task
of measuring analogies very challenging. Our approach combines a similarity
measure on function spaces with Bayesian analysis to produce a ranking. It
requires data containing features of the objects of interest and a link matrix
specifying which relationships exist; no further attributes of such
relationships are necessary. We illustrate the potential of our method on text
analysis and information networks. An application on discovering functional
interactions between pairs of proteins is discussed in detail, where we show
that our approach can work in practice even if a small set of protein pairs is
provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS321 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Time Dynamic Topic Models
Information extraction from large corpora can be a useful tool for many applications in industry and academia. For instance, political communication science has just recently begun to use the opportunities that come with the availability of massive amounts of information available through the Internet and the computational tools that natural language processing can provide. We give a linguistically motivated interpretation of topic modeling, a state-of-the-art algorithm for extracting latent semantic sets of words from large text corpora, and extend this interpretation to cover issues and issue-cycles as theoretical constructs coming from political communication science. We build on a dynamic topic model, a model whose semantic sets of words are allowed to evolve over time governed by a Brownian motion stochastic process and apply a new form of analysis to its result. Generally this analysis is based on the notion of volatility as in the rate of change of stocks or derivatives known from econometrics. We claim that the rate of change of sets of semantically related words can be interpreted as issue-cycles, the word sets as describing the underlying issue. Generalizing over the existing work, we introduce dynamic topic models that are driven by general (Brownian motion is a special case of our model) Gaussian processes, a family of stochastic processes defined by the function that determines their covariance structure. We use the above assumption and apply a certain class of covariance functions to allow for an appropriate rate of change in word sets while preserving the semantic relatedness among words. Applying our findings to a large newspaper data set, the New York Times Annotated corpus (all articles between 1987 and 2007), we are able to identify sub-topics in time, \\\\textit{time-localized topics} and find patterns in their behavior over time. However, we have to drop the assumption of semantic relatedness over all available time for any one topic. Time-localized topics are consistent in themselves but do not necessarily share semantic meaning between each other. They can, however, be interpreted to capture the notion of issues and their behavior that of issue-cycles
Arithmetic Average Density Fusion -- Part I: Some Statistic and Information-theoretic Results
Finite mixture such as the Gaussian mixture is a flexible and powerful
probabilistic modeling tool for representing the multimodal distribution widely
involved in many estimation and learning problems. The core of it is
representing the target distribution by the arithmetic average (AA) of a finite
number of sub-distributions which constitute a mixture. While the mixture has
been widely used for single sensor filter design, it is only recent that the AA
fusion demonstrates compelling performance for multi-sensor filter design. In
this paper, some statistic and information-theoretic results are given on the
covariance consistency, mean square error, mode-preservation capacity, and the
information divergence of the AA fusion approach. In particular, based on the
concept of conservative fusion, the relationship of the AA fusion with the
existing conservative fusion approaches such as covariance union and covariance
intersection is exposed. A suboptimal weighting approach has been proposed,
which jointly with the best mixture-fit property of the AA fusion leads to a
max-min optimization problem. Linear Gaussian models are considered for
algorithm illustration and simulation comparison, resulting in the first-ever
AA fusion-based multi-sensor Kalman filter.Comment: 30 pages, 14 figures, 3 tables. Information Fusion, 202
Deep probabilistic methods for improved radar sensor modelling and pose estimation
Radar’s ability to sense under adverse conditions and at far-range makes it a valuable alternative to vision and lidar for mobile robotic applications. However, its complex, scene-dependent sensing process and significant noise artefacts makes working with radar challenging. Moving past classical rule-based approaches, which have dominated the literature to date, this thesis investigates deep and data-driven solutions across a range of tasks in robotics.
Firstly, a deep approach is developed for mapping raw sensor measurements to a grid-map of occupancy probabilities, outperforming classical filtering approaches by a significant margin. A distribution over the occupancy state is captured, additionally allowing uncertainty in predictions to be identified and managed. The approach is trained entirely using partial labels generated automatically from lidar, without requiring manual labelling.
Next, a deep model is proposed for generating stochastic radar measurements from simulated elevation maps. The model is trained by learning the forward and backward processes side-by-side, using a combination of adversarial and cyclical consistency constraints in combination with a partial alignment loss, using labels generated in lidar. By faithfully replicating the radar sensing process, new models can be trained for down-stream tasks, using labels that are readily available in simulation. In this case, segmentation models trained on simulated radar measurements, when deployed in the real world, are shown to approach the performance of a model trained entirely on real-world measurements.
Finally, the potential of deep approaches applied to the radar odometry task are explored. A learnt feature space is combined with a classical correlative scan matching procedure and optimised for pose prediction, allowing the proposed method to outperform the previous state-of-the-art by a significant margin. Through a probabilistic consideration the uncertainty in the pose is also successfully characterised. Building upon this success, properties of the Fourier Transform are then utilised to separate the search for translation and angle. It is shown that this decoupled search results in a significant boost to run-time performance, allowing the approach to run in real-time on CPUs and embedded devices, whilst remaining competitive with other radar odometry methods proposed in the literature
Metric Gaussian variational inference
One main result of this dissertation is the development of Metric Gaussian Variational Inference (MGVI), a method to perform approximate inference in extremely high dimensions and for complex probabilistic models. The problem with high-dimensional and complex models is twofold. Fist, to capture the true posterior distribution accurately, a sufficiently rich approximation for it is required. Second, the number of parameters to express this richness scales dramatically with the number of model parameters. For example, explicitly expressing the correlation between all model parameters requires their squared number of correlation coefficients. In settings with millions of model parameter, this is unfeasible.
MGVI overcomes this limitation by replacing the explicit covariance with an implicit approximation, which does not have to be stored and is accessed via samples. This procedure scales linearly with the problem size and allows to account for the full correlations in even extremely large problems. This makes it also applicable to significantly more complex setups.
MGVI enabled a series of ambitious signal reconstructions by me and others, which will be showcased. This involves a time- and frequency-resolved reconstruction of the shadow around the black hole M87* using data provided by the Event Horizon Telescope Collaboration, a three-dimensional tomographic reconstruction of interstellar dust within 300pc around the sun from Gaia starlight-absorption and parallax data, novel medical imaging methods for computed tomography, an all-sky Faraday rotation map, combining distinct data sources, and simultaneous calibration and imaging with a radio-interferometer.
The second main result is an an approach to use several, independently trained and deep neural networks to reason on complex tasks. Deep learning allows to capture abstract concepts by extracting them from large amounts of training data, which alleviates the necessity of an explicit mathematical formulation. Here a generative neural network is used as a prior distribution and certain properties are imposed via classification and regression networks. The inference is then performed in terms of the latent variables of the generator, which is done using MGVI and other methods. This allows to flexibly answer novel questions without having to re-train any neural network and to come up with novel answers through Bayesian reasoning. This novel approach of Bayesian reasoning with neural networks can also be combined with conventional measurement data
Large Scale Inverse Problems
This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences
Probabilistic models for data efficient reinforcement learning
Trial-and-error based reinforcement learning (RL) has seen rapid advancements
in recent times, especially with the advent of deep neural networks. However, the
standard deep learning methods often overlook the progress made in control theory
by treating systems as black-box. We propose a model-based RL framework based
on probabilistic Model Predictive Control (MPC). In particular, we propose to learn
a probabilistic transition model using Gaussian Processes (GPs) to incorporate model
uncertainty into long-term predictions, thereby, reducing the impact of model errors. We
provide theoretical guarantees for first-order optimality in the GP-based transition models
with deterministic approximate inference for long-term planning. We demonstrate that
our approach not only achieves the state-of-the-art data efficiency, but also is a principled
way for RL in constrained environments.
When the true state of the dynamical system cannot be fully observed the standard
model based methods cannot be directly applied. For these systems an additional step of
state estimation is needed. We propose distributed message passing for state estimation in
non-linear dynamical systems. In particular, we propose to use expectation propagation
(EP) to iteratively refine the state estimate, i.e., the Gaussian posterior distribution on the
latent state. We show two things: (a) Classical Rauch-Tung-Striebel (RTS) smoothers,
such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS),
are special cases of our message passing scheme; (b) running the message passing
scheme more than once can lead to significant improvements over the classical RTS
smoothers. We show the explicit connection between message passing with EP and
well-known RTS smoothers and provide a practical implementation of the suggested
algorithm. Furthermore, we address convergence issues of EP by generalising this
framework to damped updates and the consideration of general -divergences.
Probabilistic models can also be used to generate synthetic data. In model based RL
we use ’synthetic’ data as a proxy to real environments and in order to achieve high data
efficiency. The ability to generate high-fidelity synthetic data is crucial when available
(real) data is limited as in RL or where privacy and data protection standards allow
only for limited use of the given data, e.g., in medical and financial data-sets. Current
state-of-the-art methods for synthetic data generation are based on generative models,
such as Generative Adversarial Networks (GANs). Even though GANs have achieved
remarkable results in synthetic data generation, they are often challenging to interpret.
Furthermore, GAN-based methods can suffer when used with mixed real and categorical
variables. Moreover, the loss function (discriminator loss) design itself is problem
specific, i.e., the generative model may not be useful for tasks it was not explicitly trained
for. In this paper, we propose to use a probabilistic model as a synthetic data generator.
Learning the probabilistic model for the data is equivalent to estimating the density of
the data. Based on the copula theory, we divide the density estimation task into two parts,
i.e., estimating univariate marginals and estimating the multivariate copula density over
the univariate marginals. We use normalising flows to learn both the copula density and
univariate marginals. We benchmark our method on both simulated and real data-sets in
terms of density estimation as well as the ability to generate high-fidelity synthetic data.Open Acces
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