Future collaborative robots must be capable of finding objects. As such a fundamental skill, we expect object search to eventually become an off-the-shelf capability for any robot, similar to e.g., object detection, SLAM, and motion planning. However, existing approaches either make unrealistic compromises (e.g., reduce the problem from 3D to 2D), resort to ad-hoc, greedy search strategies, or attempt to learn end-to-end policies in simulation that are yet to generalize across real robots and environments. This thesis argues that through using Partially Observable Markov Decision Processes (POMDPs) to model object search while exploiting structures in the human world (e.g., octrees, correlations) and in human-robot interaction (e.g., spatial language), a practical and effective system for generalized object search can be achieved. In support of this argument, I develop methods and systems for (multi-)object search in 3D environments under uncertainty due to limited field of view, occlusion, noisy, unreliable detectors, spatial correlations between objects, and possibly ambiguous spatial language (e.g., "The red car is behind Chase Bank"). Besides evaluation in simulators such as PyGame, AirSim, and AI2-THOR, I design and implement a robot-independent, environment-agnostic system for generalized object search in 3D and deploy it on the Boston Dynamics Spot robot, the Kinova MOVO robot, and the Universal Robots UR5e robotic arm, to perform object search in different environments. The system enables, for example, a Spot robot to find a toy cat hidden underneath a couch in a kitchen area in under one minute. This thesis also broadly surveys the object search literature, proposing taxonomies in object search problem settings, methods and systems.

Backstepping is a mature and powerful Lyapunov-based design approach for a specific set of systems. Throughout the development over three decades, innovative theories and practices have extended backstepping to stabilization and tracking problems for nonlinear systems with growing complexity. The attractions of the backstepping-like approach are the recursive design processes and modularized design. A nonlinear system can be transferred into a group of simple problems and solved it by a sequential superposition of the corresponding approaches for each problem. To handle the complexities, backstepping designs always come up with adaptive control and robust control. The survey aims to review the milestone theoretical achievements among thousands of publications making the state-feedback backstepping designs of complex ODE systems to be systematic and modularized. Several selected elegant methods are reviewed, starting from the general designs, and then the finite-time control enhancing the convergence rate, the fuzzy logic system and neural network estimating the system unknowns, the Nussbaum function handling unknown control coefficients, barrier Lyapunov function solving state constraints, and the hyperbolic tangent function applying in robust designs. The associated assumptions and Lyapunov function candidates, inequalities, and the deduction key points are reviewed. The nonlinearity and complexities lay in state constraints, disturbance, input nonlinearities, time-delay effects, pure feedback systems, event-triggered systems, and stochastic systems. Instead of networked systems, the survey focuses on stand-alone systems.

International maritime crime is becoming increasingly sophisticated, often associated with wider criminal networks. Detecting maritime threats by means of fusing data purely related to physical movement (i.e., those generated by physical sensors, or hard data) is not sufficient. This has led to research and development efforts aimed at combining hard data with other types of data (especially human-generated or soft data). Existing work often assumes that input soft data is available in a structured format, or is focused on extracting certain relevant entities or concepts to accompany or annotate hard data. Much less attention has been given to extracting the rich knowledge about the situations of interest implicitly embedded in the large amount of soft data existing in unstructured formats (such as intelligence reports and news articles). In order to exploit the potentially useful and rich information from such sources, it is necessary to extract not only the relevant entities and concepts but also their semantic relations, together with the uncertainty associated with the extracted knowledge (i.e., in the form of probabilistic knowledge graphs). This will increase the accuracy of and confidence in, the extracted knowledge and facilitate subsequent reasoning and learning. To this end, we propose Maritime DeepDive, an initial prototype for the automated construction of probabilistic knowledge graphs from natural language data for the maritime domain. In this paper, we report on the current implementation of Maritime DeepDive, together with preliminary results on extracting probabilistic events from maritime piracy incidents. This pipeline was evaluated on a manually crafted gold standard, yielding promising results.

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable, while in linear regression, the direction of effect cannot be identified. For such linear models, non-Gaussianity of the (latent) variables has been shown to provide identifiability. In the case of factor analysis, this leads to independent component analysis, while in the case of the direction of effect, non-Gaussian versions of structural equation modelling solve the problem. More recently, we have shown how even general nonparametric nonlinear versions of such models can be estimated. Non-Gaussianity is not enough in this case, but assuming we have time series, or that the distributions are suitably modulated by some observed auxiliary variables, the models are identifiable. This paper reviews the identifiability theory for the linear and nonlinear cases, considering both factor analytic models and structural equation models.

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It can be performed in cost and memory that scale essentially linearly with the matrix size $N$, for kernels of finite differentiability, along with addition and multiplication of S-formatted matrices. We prove and exploit the fact that the inverse of a kernel matrix (if it exists) is compressible in the S-format as well. Selected inversion allows to directly compute the entries in the corresponding sparsity pattern. The S-formatted matrix operations enable the efficient, approximate computation of more complicated matrix functions such as ${\bm A}^\alpha$ or $\exp({\bm A})$. The matrix algebra is justified mathematically by pseudo differential calculus. As an application, efficient Gaussian process learning algorithms for spatial statistics is considered. Numerical results are presented to illustrate and quantify our findings.

Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples from a probability density $p$ given a score estimate (an estimate of $\nabla \ln p$) that is accurate in $L^2(p)$. Compared to previous works, we do not incur error that grows exponentially in time or that suffers from a curse of dimensionality. Our guarantee works for any smooth distribution and depends polynomially on its log-Sobolev constant. Using our guarantee, we give a theoretical analysis of score-based generative modeling, which transforms white-noise input into samples from a learned data distribution given score estimates at different noise scales. Our analysis gives theoretical grounding to the observation that an annealed procedure is required in practice to generate good samples, as our proof depends essentially on using annealing to obtain a warm start at each step. Moreover, we show that a predictor-corrector algorithm gives better convergence than using either portion alone.

Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address these difficulties by replacing the posterior density with a smooth approximation that is amenable to efficient exploration by using Langevin Markov chain Monte Carlo (MCMC) methods. An alternative approach is based on data augmentation and relaxation, where auxiliary variables are introduced in order to construct an approximate augmented posterior distribution that is amenable to efficient exploration by Gibbs sampling. This paper proposes a new accelerated proximal MCMC method called latent space SK-ROCK (ls SK-ROCK), which tightly combines the benefits of the two aforementioned strategies. Additionally, instead of viewing the augmented posterior distribution as an approximation of the original model, we propose to consider it as a generalisation of this model. Following on from this, we empirically show that there is a range of values for the relaxation parameter for which the accuracy of the model improves, and propose a stochastic optimisation algorithm to automatically identify the optimal amount of relaxation for a given problem. In this regime, ls SK-ROCK converges faster than competing approaches from the state of the art, and also achieves better accuracy since the underlying augmented Bayesian model has a higher Bayesian evidence. The proposed methodology is demonstrated with a range of numerical experiments related to image deblurring and inpainting, as well as with comparisons with alternative approaches from the state of the art. An open-source implementation of the proposed MCMC methods is available from https://github.com/luisvargasmieles/ls-MCMC.

The vehicle's perception sensors radar, lidar and camera, which must work continuously and without restriction, especially with regard to automated/autonomous driving, can lose performance due to unfavourable weather conditions. This paper analyzes the sensor signals of these three sensor technologies under rain and fog as well as day and night. A data set of a driving test vehicle as an object target under different weather conditions was recorded in a controlled environment with adjustable, defined, and reproducible weather conditions. Based on the sensor performance evaluation, a method has been developed to detect sensor degradation, including determining the affected data areas and estimating how severe they are. Through this sensor monitoring, measures can be taken in subsequent algorithms to reduce the influences or to take them into account in safety and assistance systems to avoid malfunctions.

Implicit neural representations (INRs) have achieved impressive results for scene reconstruction and computer graphics, where their performance has primarily been assessed on reconstruction accuracy. As INRs make their way into other domains, where model predictions inform high-stakes decision-making, uncertainty quantification of INR inference is becoming critical. To that end, we study a Bayesian reformulation of INRs, UncertaINR, in the context of computed tomography, and evaluate several Bayesian deep learning implementations in terms of accuracy and calibration. We find that they achieve well-calibrated uncertainty, while retaining accuracy competitive with other classical, INR-based, and CNN-based reconstruction techniques. Contrary to common intuition in the Bayesian deep learning literature, we find that INRs obtain the best calibration with computationally efficient Monte Carlo dropout, outperforming Hamiltonian Monte Carlo and deep ensembles. Moreover, in contrast to the best-performing prior approaches, UncertaINR does not require a large training dataset, but only a handful of validation images.

We formulated the sense of the presence of a remote participant in hybrid communication using a Bayesian framework. We also applied the knowledge gained from the simulation with the Bayesian model to the avatar robot's intervention behavior and encouraged the local participants to speak by intervening in the remote participant's behavior using an avatar robot. We then modeled the influence of the avatar robot's behavior on the local participants' statements using an active inference framework that included the presence of a remote participant as a latent variable. Based on the simulation results, we designed the gaze behavior of an avatar robot. Finally, we examined the effectiveness of the designed gaze behavior of the avatar robot. The gaze behavior expressed more of the remote participant's attention and interest in local participants, but local participants expressed fewer opinions in the meeting tasks. The results suggest that gaze behavior increased the presence of the remote participant and discouraged the local participant from speaking in the context of the experimental task. We believe that presence has a sufficiently large influence on whether participants want to express an opinion. It is worth investigating the influence of presence and its control methods using Bayesian models.