Belief Functions: Theory and Algorithms

The subject of this thesis is belief function theory and its application in different contexts. Belief function theory can be interpreted as a generalization of Bayesian probability theory and makes it possible to distinguish between different types of uncertainty. In this thesis, applications of belief function theory are explored both on a theoretical and on an algorithmic level. The problem of exponential complexity associated with belief function inference is addressed in this thesis by showing how efficient algorithms can be developed based on Monte-Carlo approximations and exploitation of independence. The effectiveness of these algorithms is demonstrated in applications to particle filtering, simultaneous localization and mapping, and active classification

Scientific discovery in a model-centric framework: Reproducibility, innovation, and epistemic diversity

Consistent confirmations obtained independently of each other lend credibility to a scientific result. We refer to results satisfying this consistency as reproducible and assume that reproducibility is a desirable property of scientific discovery. Yet seemingly science also progresses despite irreproducible results, indicating that the relationship between reproducibility and other desirable properties of scientific discovery is not well understood. These properties include early discovery of truth, persistence on truth once it is discovered, and time spent on truth in a long-term scientific inquiry. We build a mathematical model of scientific discovery that presents a viable framework to study its desirable properties including reproducibility. In this framework, we assume that scientists adopt a model-centric approach to discover the true model generating data in a stochastic process of scientific discovery. We analyze the properties of this process using Markov chain theory, Monte Carlo methods, and agent-based modeling. We show that the scientific process may not converge to truth even if scientific results are reproducible and that irreproducible results do not necessarily imply untrue results. The proportion of different research strategies represented in the scientific population, scientists' choice of methodology, the complexity of truth, and the strength of signal contribute to this counter-intuitive finding. Important insights include that innovative research speeds up the discovery of scientific truth by facilitating the exploration of model space and epistemic diversity optimizes across desirable properties of scientific discovery.Comment: EDITS: New title, corrected typos and errors, extended model and results descriptio

Context Exploitation in Data Fusion

Complex and dynamic environments constitute a challenge for existing tracking algorithms. For this reason, modern solutions are trying to utilize any available information which could help to constrain, improve or explain the measurements. So called Context Information (CI) is understood as information that surrounds an element of interest, whose knowledge may help understanding the (estimated) situation and also in reacting to that situation. However, context discovery and exploitation are still largely unexplored research topics. Until now, the context has been extensively exploited as a parameter in system and measurement models which led to the development of numerous approaches for the linear or non-linear constrained estimation and target tracking. More specifically, the spatial or static context is the most common source of the ambient information, i.e. features, utilized for recursive enhancement of the state variables either in the prediction or the measurement update of the filters. In the case of multiple model estimators, context can not only be related to the state but also to a certain mode of the filter. Common practice for multiple model scenarios is to represent states and context as a joint distribution of Gaussian mixtures. These approaches are commonly referred as the join tracking and classification. Alternatively, the usefulness of context was also demonstrated in aiding the measurement data association. Process of formulating a hypothesis, which assigns a particular measurement to the track, is traditionally governed by the empirical knowledge of the noise characteristics of sensors and operating environment, i.e. probability of detection, false alarm, clutter noise, which can be further enhanced by conditioning on context. We believe that interactions between the environment and the object could be classified into actions, activities and intents, and formed into structured graphs with contextual links translated into arcs. By learning the environment model we will be able to make prediction on the target\u2019s future actions based on its past observation. Probability of target future action could be utilized in the fusion process to adjust tracker confidence on measurements. By incorporating contextual knowledge of the environment, in the form of a likelihood function, in the filter measurement update step, we have been able to reduce uncertainties of the tracking solution and improve the consistency of the track. The promising results demonstrate that the fusion of CI brings a significant performance improvement in comparison to the regular tracking approaches

Distributed Random Set Theoretic Soft/Hard Data Fusion

Research on multisensor data fusion aims at providing the enabling technology to combine information from several sources in order to form a unifi ed picture. The literature work on fusion of conventional data provided by non-human (hard) sensors is vast and well-established. In comparison to conventional fusion systems where input data are generated by calibrated electronic sensor systems with well-defi ned characteristics, research on soft data fusion considers combining human-based data expressed preferably in unconstrained natural language form. Fusion of soft and hard data is even more challenging, yet necessary in some applications, and has received little attention in the past. Due to being a rather new area of research, soft/hard data fusion is still in a edging stage with even its challenging problems yet to be adequately de fined and explored. This dissertation develops a framework to enable fusion of both soft and hard data with the Random Set (RS) theory as the underlying mathematical foundation. Random set theory is an emerging theory within the data fusion community that, due to its powerful representational and computational capabilities, is gaining more and more attention among the data fusion researchers. Motivated by the unique characteristics of the random set theory and the main challenge of soft/hard data fusion systems, i.e. the need for a unifying framework capable of processing both unconventional soft data and conventional hard data, this dissertation argues in favor of a random set theoretic approach as the first step towards realizing a soft/hard data fusion framework. Several challenging problems related to soft/hard fusion systems are addressed in the proposed framework. First, an extension of the well-known Kalman lter within random set theory, called Kalman evidential filter (KEF), is adopted as a common data processing framework for both soft and hard data. Second, a novel ontology (syntax+semantics) is developed to allow for modeling soft (human-generated) data assuming target tracking as the application. Third, as soft/hard data fusion is mostly aimed at large networks of information processing, a new approach is proposed to enable distributed estimation of soft, as well as hard data, addressing the scalability requirement of such fusion systems. Fourth, a method for modeling trust in the human agents is developed, which enables the fusion system to protect itself from erroneous/misleading soft data through discounting such data on-the-fly. Fifth, leveraging the recent developments in the RS theoretic data fusion literature a novel soft data association algorithm is developed and deployed to extend the proposed target tracking framework into multi-target tracking case. Finally, the multi-target tracking framework is complemented by introducing a distributed classi fication approach applicable to target classes described with soft human-generated data. In addition, this dissertation presents a novel data-centric taxonomy of data fusion methodologies. In particular, several categories of fusion algorithms have been identifi ed and discussed based on the data-related challenging aspect(s) addressed. It is intended to provide the reader with a generic and comprehensive view of the contemporary data fusion literature, which could also serve as a reference for data fusion practitioners by providing them with conducive design guidelines, in terms of algorithm choice, regarding the specifi c data-related challenges expected in a given application

A survey of uncertainty in deep neural networks

Over the last decade, neural networks have reached almost every field of science and become a crucial part of various real world applications. Due to the increasing spread, confidence in neural network predictions has become more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over- or under-confidence, i.e. are badly calibrated. To overcome this, many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and various approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. For that, a comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and irreducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks (BNNs), ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for calibrating neural networks, and give an overview of existing baselines and available implementations. Different examples from the wide spectrum of challenges in the fields of medical image analysis, robotics, and earth observation give an idea of the needs and challenges regarding uncertainties in the practical applications of neural networks. Additionally, the practical limitations of uncertainty quantification methods in neural networks for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given

Quantum Monte Carlo simulations for estimating FOREX markets: A speculative attacks experience

The foreign exchange markets, renowned as the largest financial markets globally, also stand out as one of the most intricate due to their substantial volatility, nonlinearity, and irregular nature. Owing to these challenging attributes, various research endeavors have been undertaken to effectively forecast future currency prices in foreign exchange with precision. The studies performed have built models utilizing statistical methods, being the Monte Carlo algorithm the most popular. In this study, we propose to apply Auxiliary-Field Quantum Monte Carlo to increase the precision of the FOREX markets models from different sample sizes to test simulations in different stress contexts. Our findings reveal that the implementation of Auxiliary-Field Quantum Monte Carlo significantly enhances the accuracy of these models, as evidenced by the minimal error and consistent estimations achieved in the FOREX market. This research holds valuable implications for both the general public and financial institutions, empowering them to effectively anticipate significant volatility in exchange rate trends and the associated risks. These insights provide crucial guidance for future decision-making processes

Classification-Aided Robust Multiple Target Tracking Using Neural Enhanced Message Passing

We address the challenge of tracking an unknown number of targets in strong clutter environments using measurements from a radar sensor. Leveraging the range-Doppler spectra information, we identify the measurement classes, which serve as additional information to enhance clutter rejection and data association, thus bolstering the robustness of target tracking. We first introduce a novel neural enhanced message passing approach, where the beliefs obtained by the unified message passing are fed into the neural network as additional information. The output beliefs are then utilized to refine the original beliefs. Then, we propose a classification-aided robust multiple target tracking algorithm, employing the neural enhanced message passing technique. This algorithm is comprised of three modules: a message-passing module, a neural network module, and a Dempster-Shafer module. The message-passing module is used to represent the statistical model by the factor graph and infers target kinematic states, visibility states, and data associations based on the spatial measurement information. The neural network module is employed to extract features from range-Doppler spectra and derive beliefs on whether a measurement is target-generated or clutter-generated. The Dempster-Shafer module is used to fuse the beliefs obtained from both the factor graph and the neural network. As a result, our proposed algorithm adopts a model-and-data-driven framework, effectively enhancing clutter suppression and data association, leading to significant improvements in multiple target tracking performance. We validate the effectiveness of our approach using both simulated and real data scenarios, demonstrating its capability to handle challenging tracking scenarios in practical radar applications.Comment: 15 page