arXiv subjects

Christian Knoll

Publications and source records attributed to Christian Knoll.

At least 19 recordsLinked to original sources

arXiv2026

AI-enhanced Direct SLAM: A Principled Approach to Unsupervised Learning in Bayesian Inference

In this paper, we propose an artificial intelligence (AI)-enhanced hybrid simultaneous localization and mapping (SLAM) method that performs Bayesian inference directly on raw radio-frequency (RF) signals while learning an environment model in an unsupervised manner. The approach combines a physically interpretable signal model for line-of-sight (LOS) components with an AI model that captures multipath component statistics. Building on this formulation, we develop a particle-based sumproduct algorithm (SPA) on a factor graph that jointly estimates the mobile terminal (MT) state, visibility, multipath parameters, and noise variances, and integrate it into a variational framework that maximizes the evidence lower bound (ELBO) to learn the neural network (NN) parametrization directly from measurements. We further present a highly efficient GPU-based implementation that enables parallel likelihood evaluation across particles and base stations (BSs). Simulation results in multipath environments demonstrate that the proposed method learns the generative, environment-dependent signal model in an unsupervised manner while accurately localizing the MT and effectively exploiting the learned map in obstructed-line-of-sight (OLOS) scenarios.

eess.SP↗

arXiv2024

Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensembles

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we discuss function space inference via particle optimization and present practical modifications that improve uncertainty estimation and, most importantly, make it applicable for large and pretrained networks. First, we demonstrate that the input samples, where particle predictions are enforced to be diverse, are detrimental to the model performance. While diversity on training data itself can lead to underfitting, the use of label-destroying data augmentation, or unlabeled out-of-distribution data can improve prediction diversity and uncertainty estimates. Furthermore, we take advantage of the function space formulation, which imposes no restrictions on network parameterization other than sufficient flexibility. Instead of using full deep ensembles to represent particles, we propose a single multi-headed network that introduces a minimal increase in parameters and computation. This allows seamless integration to pretrained networks, where this repulsive last-layer ensemble can be used for uncertainty aware fine-tuning at minimal additional cost. We achieve competitive results in disentangling aleatoric and epistemic uncertainty for active learning, detecting out-of-domain data, and providing calibrated uncertainty estimates under distribution shifts with minimal compute and memory.

cs.LG↗

arXiv2024

On the Convexity and Reliability of the Bethe Free Energy Approximation

The Bethe free energy approximation provides an effective way for relaxing NP-hard problems of probabilistic inference. However, its accuracy depends on the model parameters and particularly degrades if a phase transition in the model occurs. In this work, we analyze when the Bethe approximation is reliable and how this can be verified. We argue and show by experiment that it is mostly accurate if it is convex on a submanifold of its domain, the 'Bethe box'. For verifying its convexity, we derive two sufficient conditions that are based on the definiteness properties of the Bethe Hessian matrix: the first uses the concept of diagonal dominance, and the second decomposes the Bethe Hessian matrix into a sum of sparse matrices and characterizes the definiteness properties of the individual matrices in that sum. These theoretical results provide a simple way to estimate the critical phase transition temperature of a model. As a practical contribution we propose $\texttt{BETHE-MIN}$, a projected quasi-Newton method to efficiently find a minimum of the Bethe free energy.

stat.ML↗

arXiv2024

Tensions between Preference and Performance: Designing for Visual Exploration of Multi-frequency Medical Network Data

The analysis of complex high-dimensional data is a common task in many domains, resulting in bespoke visual exploration tools. Expectations and practices of domain experts as users do not always align with visualization theory. In this paper, we report on a design study in the medical domain where we developed two high-fidelity prototypes encoding EEG-derived brain network data with different types of visualizations. We evaluate these prototypes regarding effectiveness, efficiency, and preference with two groups: participants with domain knowledge (domain experts in medical research) and those without domain knowledge, both groups having little or no visualization experience. A requirement analysis and study of low-fidelity prototypes revealed a strong preference for a novel and aesthetically pleasing visualization design, as opposed to a design that is considered more optimal based on visualization theory. Our study highlights the pros and cons of both approaches, discussing trade-offs between task-specific measurements and subjective preference. While the aesthetically pleasing and novel low-fidelity prototype was favored, the results of our evaluation show that, in most cases, this was not reflected in participants' performance or subjective preference for the high-fidelity prototypes.

cs.HC↗

arXiv2024

Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders

The traditional two-stage approach to causal inference first identifies a single causal model (or equivalence class of models), which is then used to answer causal queries. However, this neglects any epistemic model uncertainty. In contrast, Bayesian causal inference does incorporate epistemic uncertainty into query estimates via Bayesian marginalisation (posterior averaging) over all causal models. While principled, this marginalisation over entire causal models, i.e., both causal structures (graphs) and mechanisms, poses a tremendous computational challenge. In this work, we address this challenge by decomposing structure marginalisation into the marginalisation over (i) causal orders and (ii) directed acyclic graphs (DAGs) given an order. We can marginalise the latter in closed form by limiting the number of parents per variable and utilising Gaussian processes to model mechanisms. To marginalise over orders, we use a sampling-based approximation, for which we devise a novel auto-regressive distribution over causal orders (ARCO). Our method outperforms state-of-the-art in structure learning on simulated non-linear additive noise benchmarks, and yields competitive results on real-world data. Furthermore, we can accurately infer interventional distributions and average causal effects.

cs.LG↗

arXiv2023

The Gulf of Interpretation: From Chart to Message and Back Again

Charts are used to communicate data visually, but often, we do not know whether a chart's intended message aligns with the message readers perceive. In this mixed-methods study, we investigate how data journalists encode data and how members of a broad audience engage with, experience, and understand these visualizations. We conducted workshops and interviews with school and university students, job seekers, designers, and senior citizens to collect perceived messages and feedback on eight real-world charts. We analyzed these messages and compared them to the intended message. Our results help to understand the gulf that can exist between messages (that producers encode) and viewer interpretations. In particular, we find that consumers are often overwhelmed with the amount of data provided and are easily confused with terms that are not well known. Chart producers tend to follow strong conventions on how to visually encode particular information that might not always benefit consumers.

cs.HC↗

arXiv2023

What is the message? Perspectives on Visual Data Communication

Data visualizations are widely used to communicate messages about urgent topics such as climate change and public health. However, we still know little about how these visualizations are produced and interpreted in popular science contexts. In this mixed-method study, we examine how data are visually communicated and understood in the popular science magazine Scientific American, focusing on the messages these visualizations convey. To capture this complexity, we analyze data visualizations about climate change and pandemics in Scientific American over the past fifty years from three complementary perspectives: reader, chart, and producer. From the reader's perspective, we articulate takeaway messages and document sensemaking, interpreting visualizations first without and then with textual elements. From the chart perspective, we examine how visual features and text shape interpretation. From the producer's perspective, we draw on interviews with Scientific American staff to understand message planning and compare a sample of their intended messages with those we interpreted. Using takeaway messages as our central analytic lens, we develop a message typology and show that messages vary systematically across dimensions such as granularity, articulation, and inference. A key finding is that text plays a pivotal role: approximately two-thirds of messages change when textual elements are added. While the interviews highlighted the central role of message planning in visualization production, intended and interpreted messages only partially aligned. Our findings underscore the importance of contextual clarity and audience-aware communication, and we derive recommendations for visualization designers and science communicators.

cs.HC↗

arXiv2023

Self-attention for Enhanced OAMP Detection in MIMO Systems

Multiple-Input Multiple-Output (MIMO) systems are essential for wireless communications. Sinceclassical algorithms for symbol detection in MIMO setups require large computational resourcesor provide poor results, data-driven algorithms are becoming more popular. Most of the proposedalgorithms, however, introduce approximations leading to degraded performance for realistic MIMOsystems. In this paper, we introduce a neural-enhanced hybrid model, augmenting the analyticbackbone algorithm with state-of-the-art neural network components. In particular, we introduce aself-attention model for the enhancement of the iterative Orthogonal Approximate Message Passing(OAMP)-based decoding algorithm. In our experiments, we show that the proposed model canoutperform existing data-driven approaches for OAMP while having improved generalization to otherSNR values at limited computational overhead.

cs.IT↗

arXiv2022

Active Bayesian Causal Inference

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.

cs.LG↗

arXiv2022

Understanding the Behavior of Belief Propagation

Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference; because of the high-dimensional nature, however, one must often use approximate methods for this purpose. Belief propagation performs approximate inference, is efficient, and looks back on a long success-story. Yet, in most cases, belief propagation lacks any performance and convergence guarantees. Many realistic problems are presented by graphical models with loops, however, in which case belief propagation is neither guaranteed to provide accurate estimates nor that it converges at all. This thesis investigates how the model parameters influence the performance of belief propagation. We are particularly interested in their influence on (i) the number of fixed points, (ii) the convergence properties, and (iii) the approximation quality.

cs.AI↗

arXiv2021

Distribution Mismatch Correction for Improved Robustness in Deep Neural Networks

Deep neural networks rely heavily on normalization methods to improve their performance and learning behavior. Although normalization methods spurred the development of increasingly deep and efficient architectures, they also increase the vulnerability with respect to noise and input corruptions. In most applications, however, noise is ubiquitous and diverse; this can often lead to complete failure of machine learning systems as they fail to cope with mismatches between the input distribution during training- and test-time. The most common normalization method, batch normalization, reduces the distribution shift during training but is agnostic to changes in the input distribution during test time. This makes batch normalization prone to performance degradation whenever noise is present during test-time. Sample-based normalization methods can correct linear transformations of the activation distribution but cannot mitigate changes in the distribution shape; this makes the network vulnerable to distribution changes that cannot be reflected in the normalization parameters. We propose an unsupervised non-parametric distribution correction method that adapts the activation distribution of each layer. This reduces the mismatch between the training and test-time distribution by minimizing the 1-D Wasserstein distance. In our experiments, we empirically show that the proposed method effectively reduces the impact of intense image corruptions and thus improves the classification performance without the need for retraining or fine-tuning the model.

cs.LG↗

arXiv2021

Einstein-Dirac-Maxwell wormholes: ansatz, construction and properties of symmetric solutions

We present a discussion of the traversable wormholes in Einstein-Dirac-Maxwell theory recently reported in e-Print: 2010.07317. This includes a detailed description of the ansatz and junction condition, together with an investigation of the domain of existence of the solutions. In this study, we assume symmetry under interchange of the two asymptotically flat regions of a wormhole. Possible issues and limitations of the approach are also discussed.

gr-qc↗

arXiv2021

Traversable wormholes in Einstein-Dirac-Maxwell theory

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordström black holes. They also possess a finite mass $M$ and electric charge $Q_e$, with $Q_e/M>1$. An exact wormhole solution with ungauged, massless fermions is also reported.

gr-qc↗

arXiv2020

Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions

In this paper we present a detailed calculation of an Ansatz that allows to obtain spherically symmetric Einstein-Dirac configurations in $d$-dimensions. We show that this is possible by combining $2^{\lfloor \frac{d-2}{2} \rfloor}$ Dirac fields, making use of the properties of the angular dependence of the spinors in a spherical background. By applying this Ansatz, we investigate some simple analytical solutions. One of them is a regular wormhole supported by the Dirac fields. Other solutions include a pathological black hole and a naked singularity. We analyze the domain of existence and properties of all these solutions.

gr-qc↗

arXiv2019

Boson and Dirac stars in $D\geq 4$ dimensions

We present a comparative study of spherically symmetric, localized, particle-like solutions for spin $s=0,1/2$ and $1$ gravitating fields in a $D$-dimensional, asymptotically flat spacetime. These fields are massive, possessing a harmonic time dependence and no self-interaction. Special attention is paid to the mathematical similarities and physical differences between the bosonic and fermonic cases. We find that the generic pattern of solutions is similar for any value of the spin $s$, depending only on the dimensionality of spacetime, the cases $D=4,5$ being special.

gr-qc↗

arXiv2018

Self-Guided Belief Propagation -- A Homotopy Continuation Method

Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually. This homotopy continuation method converges to a unique solution and increases the accuracy without increasing the computational burden. We provide a formal analysis to demonstrate that SBP finds the global optimum of the Bethe approximation for attractive models where all variables favor the same state. Moreover, we apply SBP to various graphs with random potentials and empirically show that: (i) SBP is superior in terms of accuracy whenever BP converges, and (ii) SBP obtains a unique, stable, and accurate solution whenever BP does not converge.

stat.ML↗

arXiv2018

Quasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensions

We study the quasinormal modes of massive Dirac spinors in the background of rotating black holes. In particular, we consider the Kerr geometry as well as the five dimensional Myers-Perry spacetime with equal angular momenta. We decouple the equations using the standard methods from the literature. In the five dimensional Myers-Perry black hole the angular equation is solved analytically. Using the continued fraction method, we calculate the spectrum of quasinormal modes for the ground modes and first excited modes. We analyze, in a systematic way, its dependence on the different parameters of the black hole and fermionic field. We compare our values with previous results available in the literature for Kerr and for the static limit. The numerical results show several differences between the four and five dimensional cases. For instance, in five dimensions the symmetry between the positive and negative (real) frequency of the modes breaks down, which results in a richer spectrum.

gr-qc↗

arXiv2018

Solutions of the massive Dirac equation in the near-horizon metric of the extremal five dimensional Myers-Perry black hole with equal angular momenta

We study massive Dirac fields in the background of the near-horizon limit of the extremal Myers-Perry black hole in five dimensions. We consider the case in which both angular momenta have equal magnitude. The resulting Dirac equation can be decoupled into an angular and a radial part. The solution of the angular part results in some algebraic relations that determine completely the angular quantum numbers of the fermionic field. The radial part can be analytically solved in terms of special functions, which allow us to analyze the near-horizon radial current of the Dirac field.

gr-qc↗