The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate non-linear utility. However, when repeated gambles are played over time -- especially in intertemporal choice where rewards compound multiplicatively -- the standard additive combination axiom fails to capture the appropriate long-run evaluation. In this paper we extend the framework by relaxing the additive combination axiom and introducing a nonlinear combination operator that effectively aggregates repeated gambles in the log-domain. This operator preserves the time-average (geometric) growth rate and addresses the ergodicity problem. We prove the key algebraic properties of the operator, discuss its impact on coherence, risk assessment, and representation, and provide a series of illustrative examples. Our approach bridges the gap between expectation values and time averages and unifies normative theory with empirically observed non-stationary reward dynamics.

The quality of ontologies and their alignments is crucial for developing high-quality semantics-based applications. Traditional debugging techniques repair ontology networks by removing unwanted axioms and mappings, but may thereby remove consequences that are correct in the domain of the ontology network. In this paper we propose a framework for repairing ontology networks that deals with this issue. It defines basic operations such as debugging, weakening and completing. Further, it defines combination operators that reflect choices in how and when to use the basic operators, as well as choices regarding the autonomy level of the ontologies and alignments in the ontology network. We show the influence of the combination operators on the quality of the repaired network and present an implemented tool. By using our framework together with existing algorithms for debugging, weakening and completing, we essentially provide a blueprint for extending previous work and systems.

We study the task of gesture recognition from electromyography (EMG), with the goal of enabling expressive human-computer interaction at high accuracy, while minimizing the time required for new subjects to provide calibration data. To fulfill these goals, we define combination gestures consisting of a direction component and a modifier component. New subjects only demonstrate the single component gestures and we seek to extrapolate from these to all possible single or combination gestures. We extrapolate to unseen combination gestures by combining the feature vectors of real single gestures to produce synthetic training data. This strategy allows us to provide a large and flexible gesture vocabulary, while not requiring new subjects to demonstrate combinatorially many example gestures. We pre-train an encoder and a combination operator using self-supervision, so that we can produce useful synthetic training data for unseen test subjects. To evaluate the proposed method, we collect a real-world EMG dataset, and measure the effect of augmented supervision against two baselines: a partially-supervised model trained with only single gesture data from the unseen subject, and a fully-supervised model trained with real single and real combination gesture data from the unseen subject. We find that the proposed method provides a dramatic improvement over the partially-supervised model, and achieves a useful classification accuracy that in some cases approaches the performance of the fully-supervised model.

Combining predictions from different models is a central problem in Bayesian inference and machine learning more broadly. Currently, these predictive distributions are almost exclusively combined using linear mixtures such as Bayesian model averaging, Bayesian stacking, and mixture of experts. Such linear mixtures impose idiosyncrasies that might be undesirable for some applications, such as multi-modality. While there exist alternative strategies (e.g. geometric bridge or superposition), optimising their parameters usually involves computing an intractable normalising constant repeatedly. We present two novel Bayesian model combination tools. These are generalisations of model stacking, but combine posterior densities by log-linear pooling (locking) and quantum superposition (quacking). To optimise model weights while avoiding the burden of normalising constants, we investigate the Hyvarinen score of the combined posterior predictions. We demonstrate locking with an illustrative example and discuss its practical application with importance sampling.

Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine the power space and the union of ordered elements for the disjunctive combination. We also study distances on ordered elements and their use. In particular, from a membership function, we redefine the cardinality of the intersection of ordered elements, considering them fuzzy. Keywords: ordinal variable ordered frame of discernment ordered and fuzzy elements ordered power set distance.

A bipolar framework is introduced for combining agents' beliefs so as to enable them to reach a common shared position or viewpoint. Our approach exploits the truth-gaps inherent to propositions involving vague concepts, by allowing agents to soften directly conflicting opinions. To this end we adopt a bipolar truth-model for propositional logic characterised by lower and upper valuations on the sentences of the language. According to this model sentences may be absolutely true, absolutely false or borderline (i.e.

Knowledge graph embedding is an important task and it will benefit lots of downstream applications. Currently, deep neural networks based methods achieve state-of-the-art performance. However, most of these existing methods are very complex and need much time for training and inference. To address this issue, we propose a simple but effective atrous convolution based knowledge graph embedding method. Compared with existing state-of-the-art methods, our method has following main characteristics. First, it effectively increases feature interactions by using atrous convolutions. Second, to address the original information forgotten issue and vanishing/exploding gradient issue, it uses the residual learning method. Third, it has simpler structure but much higher parameter efficiency. We evaluate our method on six benchmark datasets with different evaluation metrics. Extensive experiments show that our model is very effective. On these diverse datasets, it achieves better results than the compared state-of-the-art methods on most of evaluation metrics. The source codes of our model could be found at https://github.com/neukg/AcrE.

We study the effectiveness of consensus formation in multi-agent systems where there is both belief updating based on direct evidence and also belief combination between agents. In particular, we consider the scenario in which a population of agents collaborate on the best-of-n problem where the aim is to reach a consensus about which is the best (alternatively, true) state from amongst a set of states, each with a different quality value (or level of evidence). Agents' beliefs are represented within Dempster-Shafer theory by mass functions and we invegate the macro-level properties of four well-known belief combination operators for this multi-agent consensus formation problem: Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging operator. The convergence properties of the operators are considered and simulation experiments are conducted for different evidence rates and noise levels. Results show that a combination of updating from direct evidence and belief combination between agents results in better consensus to the best state than does evidence updating alone. We also find that in this framework the operators are robust to noise. Broadly, Dubois & Prade's operator results in better convergence to the best state. Finally, we consider how well the Dempster-Shafer approach to the best-of-n problem scales to large numbers of states.

Distributions over rankings are used to model user preferences in various settings including political elections and electronic commerce. The Repeated Insertion Model (RIM) gives rise to various known probability distributions over rankings, in particular to the popular Mallows model. However, probabilistic inference on RIM is computationally challenging, and provably intractable in the general case. In this paper we propose an algorithm for computing the marginal probability of an arbitrary partially ordered set over RIM. We analyze the complexity of the algorithm in terms of properties of the model and the partial order, captured by a novel measure termed the "cover width." We also conduct an experimental study of the algorithm over serial and parallelized implementations. Building upon the relationship between inference with rank distributions and counting linear extensions, we investigate the inference problem when restricted to partial orders that lend themselves to efficient counting of their linear extensions.

Consensus formation is investigated for multi-agent systems in which agents' beliefs are both vague and uncertain. Vagueness is represented by a third truth state meaning \emph{borderline}. This is combined with a probabilistic model of uncertainty. A belief combination operator is then proposed which exploits borderline truth values to enable agents with conflicting beliefs to reach a compromise. A number of simulation experiments are carried out in which agents apply this operator in pairwise interactions, under the bounded confidence restriction that the two agents' beliefs must be sufficiently consistent with each other before agreement can be reached. As well as studying the consensus operator in isolation we also investigate scenarios in which agents are influenced either directly or indirectly by the state of the world. For the former we conduct simulations which combine consensus formation with belief updating based on evidence. For the latter we investigate the effect of assuming that the closer an agent's beliefs are to the truth the more visible they are in the consensus building process. In all cases applying the consensus operators results in the population converging to a single shared belief which is both crisp and certain. Furthermore, simulations which combine consensus formation with evidential updating converge faster to a shared opinion which is closer to the actual state of the world than those in which beliefs are only changed as a result of directly receiving new evidence. Finally, if agent interactions are guided by belief quality measured as similarity to the true state of the world, then applying the consensus operator alone results in the population converging to a high quality shared belief.