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.

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. Keywords: causal models; probabilistic relational models; lifted inference.

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.

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.

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.

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.

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.

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.

Smoothing-and-mapping (SAM) is a fairly modern approach to building graph-based maps of the environment; a tutorial is given by Grisetti et al. (2010) (see also the tutorial on Newton-type methods with applications in graph-based SLAM by Toussaint (2017)). Following the tutorial by Grisetti et al. (2010), the SAM problem (1) is solved in a Gauss-Newton framework and (2) involves transformations between manifolds for the rotational components. In the Gauss-Newton framework, error vectors (between true and expected measurements) are approximated to first order by a Taylor expansion, thus the resulting scalar error terms are second-order equations. A Newton descent is then performed based on the approximated Hessian (computed from the Jacobian) in these equations. However, while the Gauss-Newton framework allows for straightforward derivations, it suffers from a drawback with respect to rotational cost functions: In the quadratic approximation of the scalar error functions, the cyclic character of angular terms is lost. Therefore, to handle rotational components (e.g.

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.