arXiv subjects

Ralf Möller

Publications and source records attributed to Ralf Möller.

35 records · Page 2Linked to original sources

arXiv2024

Automated Computation of Therapies Using Failure Mode and Effects Analysis in the Medical Domain

Failure mode and effects analysis (FMEA) is a systematic approach to identify and analyse potential failures and their effects in a system or process. The FMEA approach, however, requires domain experts to manually analyse the FMEA model to derive risk-reducing actions that should be applied. In this paper, we provide a formal framework to allow for automatic planning and acting in FMEA models. More specifically, we cast the FMEA model into a Markov decision process which can then be solved by existing solvers. We show that the FMEA approach can not only be used to support medical experts during the modelling process but also to automatically derive optimal therapies for the treatment of patients.

cs.AI↗

arXiv2024

Enhancement of Subjective Content Descriptions by using Human Feedback

An agent providing an information retrieval service may work with a corpus of text documents. The documents in the corpus may contain annotations such as Subjective Content Descriptions (SCD) -- additional data associated with different sentences of the documents. Each SCD is associated with multiple sentences of the corpus and has relations among each other. The agent uses the SCDs to create its answers in response to queries supplied by users. However, the SCD the agent uses might reflect the subjective perspective of another user. Hence, answers may be considered faulty by an agent's user, because the SCDs may not exactly match the perceptions of an agent's user. A naive and very costly approach would be to ask each user to completely create all the SCD themselves. To use existing knowledge, this paper presents ReFrESH, an approach for Relation-preserving Feedback-reliant Enhancement of SCDs by Humans. An agent's user can give feedback about faulty answers to the agent. This feedback is then used by ReFrESH to update the SCDs incrementally. However, human feedback is not always unambiguous. Therefore, this paper additionally presents an approach to decide how to incorporate the feedback and when to update the SCDs. Altogether, SCDs can be updated with human feedback, allowing users to create even more specific SCDs for their needs.

cs.IR↗

arXiv2024

Lifted Causal Inference in Relational Domains

Lifted inference exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. Even though lifting is a well-established technique for the task of probabilistic inference in relational domains, it has not yet been applied to the task of causal inference. In this paper, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs as an extension of parametric factor graphs incorporating causal knowledge and give a formal semantics of interventions therein. We further present the lifted causal inference algorithm to compute causal effects on a lifted level, thereby drastically speeding up causal inference compared to propositional inference, e.g., in causal Bayesian networks. In our empirical evaluation, we demonstrate the effectiveness of our approach.

cs.AI↗

arXiv2024

A Lagrange-Newton Approach to Smoothing-and-Mapping

In this report we explore the application of the Lagrange-Newton method to the SAM (smoothing-and-mapping) problem in mobile robotics. In Lagrange-Newton SAM, the angular component of each pose vector is expressed by orientation vectors and treated through Lagrange constraints. This is different from the typical Gauss-Newton approach where variations need to be mapped back and forth between Euclidean space and a manifold suitable for rotational components. We derive equations for five different types of measurements between robot poses: translation, distance, and rotation from odometry in the plane, as well as home-vector angle and compass angle from visual homing. We demonstrate the feasibility of the Lagrange-Newton approach for a simple example related to a cleaning robot scenario.

cs.RO↗

arXiv2023

Colour Passing Revisited: Lifted Model Construction with Commutative Factors

Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes. To apply lifted inference, a lifted representation has to be obtained, and to do so, the so-called colour passing algorithm is the state of the art. The colour passing algorithm, however, is bound to a specific inference algorithm and we found that it ignores commutativity of factors while constructing a lifted representation. We contribute a modified version of the colour passing algorithm that uses logical variables to construct a lifted representation independent of a specific inference algorithm while at the same time exploiting commutativity of factors during an offline-step. Our proposed algorithm efficiently detects more symmetries than the state of the art and thereby drastically increases compression, yielding significantly faster online query times for probabilistic inference when the resulting model is applied.

cs.AI↗

arXiv2022

Derivation of Learning Rules for Coupled Principal Component Analysis in a Lagrange-Newton Framework

We describe a Lagrange-Newton framework for the derivation of learning rules with desirable convergence properties and apply it to the case of principal component analysis (PCA). In this framework, a Newton descent is applied to an extended variable vector which also includes Lagrange multipliers introduced with constraints. The Newton descent guarantees equal convergence speed from all directions, but is also required to produce stable fixed points in the system with the extended state vector. The framework produces "coupled" PCA learning rules which simultaneously estimate an eigenvector and the corresponding eigenvalue in cross-coupled differential equations. We demonstrate the feasibility of this approach for two PCA learning rules, one for the estimation of the principal, the other for the estimate of an arbitrary eigenvector-eigenvalue pair (eigenpair).

cs.NE↗

arXiv2021

Lifting DecPOMDPs for Nanoscale Systems -- A Work in Progress

DNA-based nanonetworks have a wide range of promising use cases, especially in the field of medicine. With a large set of agents, a partially observable stochastic environment, and noisy observations, such nanoscale systems can be modelled as a decentralised, partially observable, Markov decision process (DecPOMDP). As the agent set is a dominating factor, this paper presents (i) lifted DecPOMDPs, partitioning the agent set into sets of indistinguishable agents, reducing the worst-case space required, and (ii) a nanoscale medical system as an application. Future work turns to solving and implementing lifted DecPOMDPs.

cs.AI↗

arXiv2020

Improved Convergence Speed of Fully Symmetric Learning Rules for Principal Component Analysis

Fully symmetric learning rules for principal component analysis can be derived from a novel objective function suggested in our previous work. We observed that these learning rules suffer from slow convergence for covariance matrices where some principal eigenvalues are close to each other. Here we describe a modified objective function with an additional term which mitigates this convergence problem. We show that the learning rule derived from the modified objective function inherits all fixed points from the original learning rule (but may introduce additional ones). Also the stability of the inherited fixed points remains unchanged. Only the steepness of the objective function is increased in some directions. Simulations confirm that the convergence speed can be noticeably improved, depending on the weight factor of the additional term.

stat.ML↗

arXiv2020

Derivation of Symmetric PCA Learning Rules from a Novel Objective Function

Neural learning rules for principal component / subspace analysis (PCA / PSA) can be derived by maximizing an objective function (summed variance of the projection on the subspace axes) under an orthonormality constraint. For a subspace with a single axis, the optimization produces the principal eigenvector of the data covariance matrix. Hierarchical learning rules with deflation procedures can then be used to extract multiple eigenvectors. However, for a subspace with multiple axes, the optimization leads to PSA learning rules which only converge to axes spanning the principal subspace but not to the principal eigenvectors. A modified objective function with distinct weight factors had to be introduced produce PCA learning rules. Optimization of the objective function for multiple axes leads to symmetric learning rules which do not require deflation procedures. For the PCA case, the estimated principal eigenvectors are ordered (w.r.t. the corresponding eigenvalues) depending on the order of the weight factors. Here we introduce an alternative objective function where it is not necessary to introduce fixed weight factors; instead, the alternative objective function uses squared summands. Optimization leads to symmetric PCA learning rules which converge to the principal eigenvectors, but without imposing an order. In place of the diagonal matrices with fixed weight factors, variable diagonal matrices appear in the learning rules. We analyze this alternative approach by determining the fixed points of the constrained optimization. The behavior of the constrained objective function at the fixed points is analyzed which confirms both the PCA behavior and the fact that no order is imposed. Different ways to derive learning rules from the optimization of the objective function are presented. The role of the terms in the learning rules obtained from these derivations is explored.

math.OC↗

arXiv2020

Derivation of Coupled PCA and SVD Learning Rules from a Newton Zero-Finding Framework

In coupled learning rules for PCA (principal component analysis) and SVD (singular value decomposition), the update of the estimates of eigenvectors or singular vectors is influenced by the estimates of eigenvalues or singular values, respectively. This coupled update mitigates the speed-stability problem since the update equations converge from all directions with approximately the same speed. A method to derive coupled learning rules from information criteria by Newton optimization is known. However, these information criteria have to be designed, offer no explanatory value, and can only impose Euclidean constraints on the vector estimates. Here we describe an alternative approach where coupled PCA and SVD learning rules can systematically be derived from a Newton zero-finding framework. The derivation starts from an objective function, combines the equations for its extrema with arbitrary constraints on the vector estimates, and solves the resulting vector zero-point equation using Newton's zero-finding method. To demonstrate the framework, we derive PCA and SVD learning rules with constant Euclidean length or constant sum of the vector estimates.

cs.NE↗

arXiv2020

Exploring Unknown Universes in Probabilistic Relational Models

Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known, though, or may only described by assumptions such as "small universes are more likely". Without a universe, inference is no longer possible for lifted algorithms, losing their advantage of tractable inference. The aim of this paper is to define a semantics for models with unknown universes decoupled from a specific constraint language to enable lifted and thereby, tractable inference.

cs.AI↗

arXiv2019

Taming Reasoning in Temporal Probabilistic Relational Models

Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal approximate merging (TAMe), which incorporates (i) clustering for grouping submodels as well as (ii) statistical significance checks to test the fitness of the clustering outcome. In exchange for faster runtimes, TAMe introduces a bounded error that becomes negligible over time. Empirical results show that TAMe significantly improves the runtime performance of inference, while keeping errors small.

cs.AI↗

arXiv2018

Fusing First-order Knowledge Compilation and the Lifted Junction Tree Algorithm

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries as well as first-order knowledge compilation (FOKC) based on weighted model counting. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a model and LVE as a subroutine in its computations. For certain inputs, the implementations of LVE and, as a result, LJT ground parts of a model where FOKC has a lifted run. The purpose of this paper is to prepare LJT as a backbone for lifted inference and to use any exact inference algorithm as subroutine. Using FOKC in LJT allows us to compute answers faster than LJT, LVE, and FOKC for certain inputs.

cs.AI↗

arXiv2018

Preventing Unnecessary Groundings in the Lifted Dynamic Junction Tree Algorithm

The lifted dynamic junction tree algorithm (LDJT) efficiently answers filtering and prediction queries for probabilistic relational temporal models by building and then reusing a first-order cluster representation of a knowledge base for multiple queries and time steps. Unfortunately, a non-ideal elimination order can lead to groundings even though a lifted run is possible for a model. We extend LDJT (i) to identify unnecessary groundings while proceeding in time and (ii) to prevent groundings by delaying eliminations through changes in a temporal first-order cluster representation. The extended version of LDJT answers multiple temporal queries orders of magnitude faster than the original version.

cs.AI↗

arXiv2018

Answering Hindsight Queries with Lifted Dynamic Junction Trees

The lifted dynamic junction tree algorithm (LDJT) efficiently answers filtering and prediction queries for probabilistic relational temporal models by building and then reusing a first-order cluster representation of a knowledge base for multiple queries and time steps. We extend LDJT to (i) solve the smoothing inference problem to answer hindsight queries by introducing an efficient backward pass and (ii) discuss different options to instantiate a first-order cluster representation during a backward pass. Further, our relational forward backward algorithm makes hindsight queries to the very beginning feasible. LDJT answers multiple temporal queries faster than the static lifted junction tree algorithm on an unrolled model, which performs smoothing during message passing.

cs.AI↗

arXiv2016

Detecting Affordances by Visuomotor Simulation

The term "affordance" denotes the behavioral meaning of objects. We propose a cognitive architecture for the detection of affordances in the visual modality. This model is based on the internal simulation of movement sequences. For each movement step, the resulting sensory state is predicted by a forward model, which in turn triggers the generation of a new (simulated) motor command by an inverse model. Thus, a series of mental images in the sensory and in the motor domain is evoked. Starting from a real sensory state, a large number of such sequences is simulated in parallel. Final affordance detection is based on the generated motor commands. We apply this model to a real-world mobile robot which is faced with obstacle arrangements some of which are passable (corridor) and some of which are not (dead ends). The robot's task is to detect the right affordance ("pass-through-able" or "non-pass-through-able"). The required internal models are acquired in a hierarchical training process. Afterwards, the robotic agent is able to distinguish reliably between corridors and dead ends. This real-world result enhances the validity of the proposed mental simulation approach. In addition, we compare several key factors in the simulation process regarding performance and efficiency.

cs.AI↗

arXiv2016

Towards Analytics Aware Ontology Based Access to Static and Streaming Data (Extended Version)

Real-time analytics that requires integration and aggregation of heterogeneous and distributed streaming and static data is a typical task in many industrial scenarios such as diagnostics of turbines in Siemens. OBDA approach has a great potential to facilitate such tasks; however, it has a number of limitations in dealing with analytics that restrict its use in important industrial applications. Based on our experience with Siemens, we argue that in order to overcome those limitations OBDA should be extended and become analytics, source, and cost aware. In this work we propose such an extension. In particular, we propose an ontology, mapping, and query language for OBDA, where aggregate and other analytical functions are first class citizens. Moreover, we develop query optimisation techniques that allow to efficiently process analytical tasks over static and streaming data. We implement our approach in a system and evaluate our system with Siemens turbine data.

cs.AI↗