Dependencies on the relative frequency of a state in the domain are common when modelling probabilistic dependencies on relational data. For instance, the likelihood of a school closure during an epidemic might depend on the proportion of infected pupils exceeding a threshold. Often, rather than depending on discrete thresholds, dependencies are continuous: for instance, the likelihood of any one mosquito bite transmitting an illness depends on the proportion of carrier mosquitoes. Current approaches usually only consider probabilities over possible worlds rather than over domain elements themselves. An exception are the recently introduced Lifted Bayesian Networks for Conditional Probability Logic, which express discrete dependencies on probabilistic data. We introduce functional lifted Bayesian networks, a formalism that explicitly incorporates continuous dependencies on relative frequencies into statistical relational artificial intelligence. and compare and contrast them with ifted Bayesian Networks for Conditional Probability Logic. Incorporating relative frequencies is not only beneficial to modelling; it also provides a more rigorous approach to learning problems where training and test or application domains have different sizes. To this end, we provide a representation of the asymptotic probability distributions induced by functional lifted Bayesian networks on domains of increasing sizes. Since that representation has well-understood scaling behaviour across domain sizes, it can be used to estimate parameters for a large domain consistently from randomly sampled subpopulations. Furthermore, we show that in parametric families of FLBN, convergence is uniform in the parameters, which ensures a meaningful dependence of the asymptotic probabilities on the parameters of the model.

Many of us are familiar with Google Translate, translation applications for travellers' smartphones and the instruction manuals of various devices and products. Professional translators also make use of machines. Training a computer to translate between two specific languages takes millions of sentences or billions of words worth of text. Maarit Koponen, a postdoctoral researcher at the University of Helsinki, is investigating which errors made by machines lead to misunderstandings and how those mistakes could be identified. The learning algorithms behind machine translation are called artificial intelligence, but machines are not intelligent in the way humans or the super AIs of science-fiction films are.

BRUSSELS--For Apple Inc. AAPL -2.05 % and Ireland, the European Commission's decision ordering Dublin to collect billions of euros from Apple in unpaid taxes isn't the end of the story. They have a chance to turn the tables on the commission at the bloc's highest courts, where they are preparing to appeal. The European Commission, the bloc's antitrust regulator, has ordered Ireland to recoup about 13 billion, or roughly 14.6 billion, in taxes that the commission has estimated Apple avoided paying in Europe for more than a decade. There is a strong record of the European Union's top court ruling in favor of the European Commission's decisions. But lawyers say there is one area where that trend isn't as clear-cut: state-aid cases dealing with tax matters.

The latest report on artificial intelligence evolution suggests the possibility that the line separating physical and digital realities might dissolve soon. Did you know that the future of artificial intelligence (AI) technologies could invisibly entwine human and machine intelligence? Well, the latest report on AI evolution suggests the possibility that the line separating physical and digital realities might dissolve soon. Due to the depiction of artificial intelligence in science fiction films and novels, humans have the tendency to see AI where it does not exist, The Guardian notes. But media discovery startup Random cofounder Jarno M. Koponen believes AI is beginning to turn invisible from the outside in and vice versa.