Ralf Möller

Malte Luttermann, Ralf Möller, Marcel Gehrke

Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain sizes. A central building block for the exploitation of indistinguishable objects in factor graphs is the identification of commutative factors, i.e., factors whose output values are invariant under permutations of input values assigned to a subset of their arguments. In this paper, we revisit the theoretical foundations underlying the state-of-the-art algorithm to detect commutative factors. Specifically, we show that in its current form, the state-of-the-art algorithm relies on a central theorem that is mistakenly regarded as a sufficient condition to identify commutative factors, while it actually only implies necessary condition. Consequently, the state of the art might, as we show in this paper, deliver incorrect results. To fix the flaws currently present in the state of the art, we prove a slightly modified version of the aforementioned theorem, which serves as a necessary condition to identify commutative factors. Moreover, we present a corrected version of the state-of-the-art algorithm, which keeps its efficiency while ensuring correctness and introduce a complementary algorithm with tighter worst-case bounds.

Malte Luttermann, Tanya Braun, Ralf Möller et al.

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.

Björn Filter, Ralf Möller, Özgür Lütfü Özçep

Collaborative causal inference (CCI) is a federated learning method for pooling data from multiple, often self-interested, parties, to achieve a common learning goal over causal structures, e.g. estimation and optimization of treatment variables in a medical setting. Since obtaining data can be costly for the participants and sharing unique data poses the risk of losing competitive advantages, motivating the participation of all parties through equitable rewards and incentives is necessary. This paper devises an evaluation scheme to measure the value of each party's data contribution to the common learning task, tailored to causal inference's statistical demands, by comparing completed partially directed acyclic graphs (CPDAGs) inferred from observational data contributed by the participants. The Data Valuation Scheme thus obtained can then be used to introduce mechanisms that incentivize the agents to contribute data. It can be leveraged to reward agents fairly, according to the quality of their data, or to maximize all agents' data contributions.

Malte Luttermann, Ralf Möller, Mattis Hartwig

Probabilistic relational models provide a well-established formalism to combine first-order logic and probabilistic models, thereby allowing to represent relationships between objects in a relational domain. At the same time, the field of artificial intelligence requires increasingly large amounts of relational training data for various machine learning tasks. Collecting real-world data, however, is often challenging due to privacy concerns, data protection regulations, high costs, and so on. To mitigate these challenges, the generation of synthetic data is a promising approach. In this paper, we solve the problem of generating synthetic relational data via probabilistic relational models. In particular, we propose a fully-fledged pipeline to go from relational database to probabilistic relational model, which can then be used to sample new synthetic relational data points from its underlying probability distribution. As part of our proposed pipeline, we introduce a learning algorithm to construct a probabilistic relational model from a given relational database.

Malte Luttermann, Mattis Hartwig, Tanya Braun et al.

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.

Malte Luttermann, Ralf Möller, Marcel Gehrke

Lifting exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, allowing to carry out query answering more efficiently while maintaining exact answers. In this paper, we investigate how lifting enables us to perform probabilistic inference for factor graphs containing unknown factors, i.e., factors whose underlying function of potential mappings is unknown. We present the Lifting Factor Graphs with Some Unknown Factors (LIFAGU) algorithm to identify indistinguishable subgraphs in a factor graph containing unknown factors, thereby enabling the transfer of known potentials to unknown potentials to ensure a well-defined semantics of the model and allow for (lifted) probabilistic inference. We further extend LIFAGU to incorporate additional background knowledge about groups of factors belonging to the same individual object. By incorporating such background knowledge, LIFAGU is able to further reduce the ambiguity of possible transfers of known potentials to unknown potentials.

Malte Luttermann, Ralf Möller, Marcel Gehrke

Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes of logical variables. We found that the current state-of-the-art algorithm to construct a lifted representation in form of a parametric factor graph misses symmetries between factors that are exchangeable but scaled differently, thereby leading to a less compact representation. In this paper, we propose a generalisation of the advanced colour passing (ACP) algorithm, which is the state of the art to construct a parametric factor graph. Our proposed algorithm allows for potentials of factors to be scaled arbitrarily and efficiently detects more symmetries than the original ACP algorithm. By detecting strictly more symmetries than ACP, our algorithm significantly reduces online query times for probabilistic inference when the resulting model is applied, which we also confirm in our experiments.

Malte Luttermann, Tanya Braun, Ralf Möller et al.

Lifting uses a representative of indistinguishable individuals to exploit symmetries in probabilistic relational models, denoted as parametric factor graphs, to speed up inference while maintaining exact answers. In this paper, we show how lifting can be applied to causal inference in partially directed graphs, i.e., graphs that contain both directed and undirected edges to represent causal relationships between random variables. We present partially directed parametric causal factor graphs (PPCFGs) as a generalisation of previously introduced parametric causal factor graphs, which require a fully directed graph. We further show how causal inference can be performed on a lifted level in PPCFGs, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.

Felix Mächtle, Nils Loose, Tim Schulz et al.

As the number of web applications and API endpoints exposed to the Internet continues to grow, so does the number of exploitable vulnerabilities. Manually identifying such vulnerabilities is tedious. Meanwhile, static security scanners tend to produce many false positives. While machine learning-based approaches are promising, they typically perform well only in scenarios where training and test data are closely related. A key challenge for ML-based vulnerability detection is providing suitable and concise code context, as excessively long contexts negatively affect the code comprehension capabilities of machine learning models, particularly smaller ones. This work introduces Trace Gadgets, a novel code representation that minimizes code context by removing non-related code. Trace Gadgets precisely capture the statements that cover the path to the vulnerability. As input for ML models, Trace Gadgets provide a minimal but complete context, thereby improving the detection performance. Moreover, we collect a large-scale dataset generated from real-world applications with manually curated labels to further improve the performance of ML-based vulnerability detectors. Our results show that state-of-the-art machine learning models perform best when using Trace Gadgets compared to previous code representations, surpassing the detection capabilities of industry-standard static scanners such as GitHub's CodeQL by at least 4% on a fully unseen dataset. By applying our framework to real-world applications, we identify and report previously unknown vulnerabilities in widely deployed software.

Magnus Bender, Tanya Braun, Ralf Möller et al.

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.

Malte Luttermann, Jan Speller, Marcel Gehrke et al.

Probabilistic relational models such as parametric factor graphs enable efficient (lifted) inference by exploiting the indistinguishability of objects. In lifted inference, a representative of indistinguishable objects is used for computations. To obtain a relational (i.e., lifted) representation, the Advanced Colour Passing (ACP) algorithm is the state of the art. The ACP algorithm, however, requires underlying distributions, encoded as potential-based factorisations, to exactly match to identify and exploit indistinguishabilities. Hence, ACP is unsuitable for practical applications where potentials learned from data inevitably deviate even if associated objects are indistinguishable. To mitigate this problem, we introduce the $\varepsilon$-Advanced Colour Passing ($\varepsilon$-ACP) algorithm, which allows for a deviation of potentials depending on a hyperparameter $\varepsilon$. $\varepsilon$-ACP efficiently uncovers and exploits indistinguishabilities that are not exact. We prove that the approximation error induced by $\varepsilon$-ACP is strictly bounded and our experiments show that the approximation error is close to zero in practice.

Björn Filter, Ralf Möller, Özgür Lütfü Özçep

Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work by Sim and colleagues (Rachel Hwee Ling Sim et al: Collaborative machine learning with incentive-aware model rewards. In: International conference on machine learning. PMLR. 2020, pp. 8927-8963) addressed this by allocating model rewards, which are non-monetary and freely replicable, based on the Shapley value of each party's data contribution, measured via information gain. In this paper, we introduce a ratio-based Shapley value that replaces the standard additive formulation with a relative contribution measure. While our overall reward framework, including the incentive definitions and model-reward setting, remains aligned with that of Sim and colleagues, the underlying value function is fundamentally different. Our alternative valuation induces a different distribution of model rewards and offers a new lens through which to analyze incentive properties. We formally define the ratio-based value and prove that it satisfies the same set of incentive conditions as the additive formulation, including adapted versions of fairness, individual rationality, and stability. Like the original approach, our method faces the same fundamental trade-offs between these incentives. Our contribution is a mathematically grounded alternative to the additive Shapley framework, potentially better suited to contexts where proportionality among contributors is more meaningful than additive differences.

Björn Filter, Ralf Möller, Özgür Lütfü Özçep

The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A major challenge in designing such systems is to guarantee safety and alignment with human values, particularly a fair distribution of rewards upon achieving the global goal. Cooperative game theory offers useful abstractions of cooperating agents via value functions, which assign value to each coalition, and via reward functions. With these, the idea of fair allocation can be formalized by specifying fairness axioms and designing concrete mechanisms. Classical cooperative game theory, exemplified by the Shapley value, does not fully capture scenarios like collaborative learning, as it assumes nonreplicable resources, whereas data and models can be replicated. Infinite replicability requires a generalized notion of fairness, formalized through new axioms and mechanisms. These must address imbalances in reciprocal benefits among participants, which can lead to strategic exploitation and unfair allocations. The main contribution of this paper is a mechanism and a proof that it fulfills the property of mutual fairness, formalized by the Balanced Reciprocity Axiom. It ensures that, for every pair of players, each benefits equally from the participation of the other.

Florian Andreas Marwitz, Ralf Möller, Magnus Bender et al.

Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities are considered, resulting in computational inefficiency and increased noise due to the propagation of unlikely probability mass. We propose to denoise the future and speed up inference by using only the top-p states, i.e., the most probable states with accumulated probability p. We show that the error introduced by using only the top-p states is bound by p and the so-called minimal mixing rate of the underlying model. Moreover, in our empirical evaluation, we show that we can expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09.

Florian Andreas Marwitz, Tanya Braun, Ralf Möller et al.

Decision making is a central problem in AI that can be formalized using a Markov Decision Process. A problem is that, with increasing numbers of (indistinguishable) objects, the state space grows exponentially. To compute policies, the state space has to be enumerated. Even more possibilities have to be enumerated if the size of the action space depends on the size of the state space, especially if we allow concurrent actions. To tackle the exponential blow-up in the action and state space, we present a first-order representation to store the spaces in polynomial instead of exponential size in the number of objects and introduce Foreplan, a relational forward planner, which uses this representation to efficiently compute policies for numerous indistinguishable objects and actions. Additionally, we introduce an even faster approximate version of Foreplan. Moreover, Foreplan identifies how many objects an agent should act on to achieve a certain task given restrictions. Further, we provide a theoretical analysis and an empirical evaluation of Foreplan, demonstrating a speedup of at least four orders of magnitude.

Jinghua Groppe, Sven Groppe, Ralf Möller

Deep learning-based approaches for software vulnerability prediction currently mainly rely on the original text of software code as the feature of nodes in the graph of code and thus could learn a representation that is only specific to the code text, rather than the representation that depicts the 'intrinsic' functionality of a program hidden in the text representation. One curse that causes this problem is an infinite number of possibilities to name a variable. In order to lift the curse, in this work we introduce a new type of edge called name dependence, a type of abstract syntax graph based on the name dependence, and an efficient node representation method named 3-property encoding scheme. These techniques will allow us to remove the concrete variable names from code, and facilitate deep learning models to learn the functionality of software hidden in diverse code expressions. The experimental results show that the deep learning models built on these techniques outperform the ones based on existing approaches not only in the prediction of vulnerabilities but also in the memory need. The factor of memory usage reductions of our techniques can be up to the order of 30,000 in comparison to existing approaches.

Malte Luttermann, Ralf Möller, Marcel Gehrke

Lifting exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, allowing to carry out query answering more efficiently while maintaining exact answers. In this paper, we investigate how lifting enables us to perform probabilistic inference for factor graphs containing factors whose potentials are unknown. We introduce the Lifting Factor Graphs with Some Unknown Factors (LIFAGU) algorithm to identify symmetric subgraphs in a factor graph containing unknown factors, thereby enabling the transfer of known potentials to unknown potentials to ensure a well-defined semantics and allow for (lifted) probabilistic inference.

Malte Luttermann, Edgar Baake, Juljan Bouchagiar et al.

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.

Tanya Braun, Stefan Fischer, Florian Lau et al.

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.

Ralf Möller

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.

Ralf Möller

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.

Ralf Möller

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.

Tanya Braun, Ralf Möller

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.

Marcel Gehrke, Ralf Möller, Tanya Braun

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.

Marcel Gehrke, Tanya Braun, Ralf Möller

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.

Marcel Gehrke, Tanya Braun, Ralf Möller

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.

Tanya Braun, Ralf Möller

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.

Wolfram Schenck, Hendrik Hasenbein, Ralf Möller

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.

Evgeny Kharlamov, Yannis Kotidis, Theofilos Mailis et al.

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.