arXiv subjects

Ralf Möller

Publications and source records attributed to Ralf Möller.

At least 19 recordsLinked to original sources

arXiv2026

Lifted Model Construction under Approximate Commutativity

Lifted inference algorithms enable scalable probabilistic inference even for large object domains by leveraging the indistinguishability of objects in a probability distribution. An essential prerequisite for constructing a lifted representation is to identify commutative factors, i.e., functions whose output values are invariant under permutations of a subset of their input values, in a potential-based factorisation. In practice, however, parameters learned from data inevitably deviate even if associated objects are indistinguishable, causing their corresponding factors to be only approximately commutative instead of being exactly commutative. We address this problem by introducing the concept of ε-commutativity, a relaxation of commutativity where output values are only approximately invariant under permutations of input values. Specifically, we show how ε-commutativity can be exploited for lifted model construction, downstream probabilistic inference, and prove strict bounds on the induced approximation error, thereby ensuring the practical applicability of lifted model construction while maintaining highly accurate query results. These theoretical guarantees are confirmed empirically, demonstrating comparable query accuracy at lower runtime.

cs.AI↗

arXiv2026

On the Detection of Commutative Factors in Factor Graphs: Necessary and Sufficient Conditions

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.

cs.AI↗

arXiv2026

Lifted Causal Inference

Lifted inference exploits indistinguishabilities in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. In this article, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs (PCFGs) to incorporate causal knowledge in lifted models and give a formal semantics of interventions therein. We further present the Lifted Causal Inference (LCI) 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 addition, we present partially directed parametric causal factor graphs (PD-PCFGs) as a generalisation of PCFGs to handle partial causal knowledge and extend LCI to perform lifted causal inference in a PD-PCFG, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.

cs.AI↗

arXiv2026

Denoising the Future: Top-p Distributions for Moving Through Time

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 possibly 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 transitions, i.e., the most probable transitions with accumulated probability p. We show that the error introduced by using only the top-p transitions is bound by $p$ and the so-called minimal mixing rate of the underlying model. We also show the same bound when using only the top-p states, which is the same, just for the states. Moreover, in our empirical evaluation, we show that we can, when using top-p transitions, expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09. Using the top-p states is slower than top-p transitions since we iterate over all states in each time step and sometimes lead empirically to a higher error. With a more sophisticated implementation, the speed-up, if any, would be really small. While top-p transitions look really promising, we cannot recommend top-p states and discuss why it is of the slower, while the error does not necessarily decrease.

cs.LG↗

arXiv2026

A First Step Towards Even More Sparse Encodings of Probability Distributions

Real world scenarios can be captured with lifted probability distributions. However, distributions are usually encoded in a table or list, requiring an exponential number of values. Hence, we propose a method for extracting first-order formulas from probability distributions that require significantly less values by reducing the number of values in a distribution and then extracting, for each value, a logical formula to be further minimized. This reduction and minimization allows for increasing the sparsity in the encoding while also generalizing a given distribution. Our evaluation shows that sparsity can increase immensely by extracting a small set of short formulas while preserving core information.

cs.AI↗

arXiv2026

Lifted Forward Planning in Relational Factored Markov Decision Processes with Concurrent Actions

When allowing concurrent actions in Markov Decision Processes, whose state and action spaces grow exponentially in the number of objects, computing a policy becomes highly inefficient, as it requires enumerating the joint of the two spaces. For the case of indistinguishable objects, we present a first-order representation to tackle the exponential blow-up in the action and state spaces. We propose Foreplan, an efficient relational forward planner, which uses the first-order representation allowing to compute policies in space and time polynomially in the number of objects. Thus, Foreplan significantly increases the number of planning problems solvable in an exact manner in reasonable time, which we underscore with a theoretical analysis. To speed up computations even further, we also introduce an approximate version of Foreplan, including guarantees on the error. Further, we provide an empirical evaluation of both Foreplan versions, demonstrating a speedup of several orders of magnitude. For the approximate version of Foreplan, we also empirically show that the induced error is often negligible.

cs.AI↗

arXiv2026

Exploring an Alternative Line-Search Method for Lagrange-Newton Optimization

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the value of the objective function; instead, the line search can operate on merit functions. In this report, we explore an alternative line-search method which is applicable to this case; it particulary addresses the damping of the step length in tight valleys. We propose a line-search criterion based on the divergence of the field of Newton step vectors. The visualization of the criterion for two-dimensional test functions reveals a network of ravines with flat bottom at the zero points of the criterion. The ravines are typically connected to stationary points. To traverse this ravine network in order to approach a stationary point, a zigzag strategy is devised. Numerical experiments demonstrate that the novel line-search strategy succeeds from most starting points in all test functions, but only exhibits the desired damping of the step length in some situations. At the present stage it is therefore difficult to appraise the utility of this contribution.

math.OC↗

arXiv2025

Trace Gadgets: Minimizing Code Context for Machine Learning-Based Vulnerability Prediction

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.

cs.CR↗

arXiv2025

A Ratio-Based Shapley Value for Collaborative Machine Learning - Extended Version

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.

cs.GT↗

arXiv2025

Approximate Lifted Model Construction

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.

cs.AI↗

arXiv2025

A Mechanism for Mutual Fairness in Cooperative Games with Replicable Resources -- Extended Version

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.

cs.GT↗

arXiv2025

Lifting Factor Graphs with Some Unknown Factors for New Individuals

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.

cs.AI↗

arXiv2024

Lifted Model Construction without Normalisation: A Vectorised Approach to Exploit Symmetries in Factor Graphs

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.

cs.AI↗

arXiv2024

Estimating Causal Effects in Partially Directed Parametric Causal Factor Graphs

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.

cs.AI↗

arXiv2024

Towards Privacy-Preserving Relational Data Synthesis via Probabilistic Relational Models

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.

cs.AI↗

arXiv2024

Mechanisms for Data Sharing in Collaborative Causal Inference (Extended Version)

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.

cs.LG↗

arXiv2024

Variables are a Curse in Software Vulnerability Prediction

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.

cs.SE↗

arXiv2024

Lifting Factor Graphs with Some Unknown Factors

cs.AI↗