Probabilistic graphical models that encode indistinguishable objects and relations among them use first-order logic constructs to compress a propositional factorised model for more efficient (lifted) inference. To obtain a lifted representation, the state-of-the-art algorithm Advanced Colour Passing (ACP) groups factors that represent matching distributions. In an approximate version using ε as a hyperparameter, factors are grouped that differ by a factor of at most (1 ± ε). However, finding a suitable ε is not obvious and may need a lot of exploration, possibly requiring many ACP runs with different ε values. Additionally, varying ε can yield wildly different models, leading to decreased interpretability. Therefore, this paper presents a hierarchical approach to lifted model construction that is hyperparameter-free. It efficiently computes a hierarchy of ε values that ensures a hierarchy of models, meaning that once factors are grouped together given some ε, these factors will be grouped together for larger ε as well. The hierarchy of ε values also leads to a hierarchy of error bounds. This allows for explicitly weighing compression versus accuracy when choosing specific ε values to run ACP with and enables interpretability between the different models.

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 ε-Advanced Colour Passing (ε-ACP) algorithm, which allows for a deviation of potentials depending on a hyperparameter ε. ε-ACP efficiently uncovers and exploits indistinguishabilities that are not exact. We prove that the approximation error induced by ε-ACP is strictly bounded and our experiments show that the approximation error is close to zero in practice.

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.

A decentralised partially observable Markov decision problem (DecPOMDP) formalises collaborative multi-agent decision making. A solution to a DecPOMDP is a joint policy for the agents, fulfilling an optimality criterion such as maximum expected utility. A crux is that the problem is intractable regarding the number of agents. Inspired by lifted inference, this paper examines symmetries within the agent set for a potential tractability. Specifically, this paper contributes (i) specifications of counting and isomorphic symmetries, (ii) a compact encoding of symmetric DecPOMDPs as partitioned DecPOMDPs, and (iii) a formal analysis of complexity and tractability. This works allows tractability in terms of agent numbers and a new query type for isomorphic DecPOMDPs.

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.