Knowledge graphs are graph-structured knowledge resources which are often expressed as triples such as ("UK", "hasCapital", "London") and ("London", "instanceOf", "City"). As well as such basic "facts", knowledge graphs often include structural knowledge about the domain, typically based on a hierarchy of entity types (AKA classes or concepts); e.g., ("City", "subClassOf", "HumanSettlement"). A knowledge graph that consist largely or wholly of structural knowledge is often called an ontology. Some knowledge graphs are general purpose, such as Wikidata and the Google knowledge graph, while others are developed for specific domains such as medicine. They are rapidly gaining in importance and are playing a key role in many applications. For example, Google uses its knowledge graph for search, question answering and Google Assistant, while Amazon and Apple also use knowledge graphs to power their personal assistants Alexa and Siri, respectively. Knowledge graphs are widely used in the domain of health and wellbeing, e.g., for organising and exchanging information and to power clinical artificial intelligence (AI). One example is FoodOn, an ontology representing food knowledge such as fine-grained food product categorization, nutrition and allergens, as well as related activities such as agriculture. Knowledge graph construction and maintenance is, however, very challenging, and may require a considerable amount of human effort. Notwithstanding the high cost of knowledge creation, knowledge graphs are often still biased, incomplete or too coarse-grained. Take HeLis, an ontology for health and lifestyle, as an example. Its food knowledge is quite simple and often represents many different variants with a single entity (e.g., "Banana" for all kinds and derivatives of bananas), and its knowledge of health is highly incomplete when compared with dedicated biomedical ontologies. In addition, it is hard to avoid errors such as incorrect facts and categorisations in knowledge graphs; e.g., FoodOn categorises soy milk as a kind of milk, but not as a kind of soy product. Such errors may be inherited from the information source or be caused by the construction procedure. These issues significantly impact the usefulness of knowledge graphs and the reliability of the systems that use them; e.g., the categorisation of soy milk could be dangerous if the knowledge graph were used in a food allergen alert system. Therefore, effective knowledge graph construction and curation is urgently required and will play a critical role in exploiting the full value of knowledge graphs. As there are now many available knowledge resources, one possible approach is to use multiple sources to address both coverage and quality issues, e.g., via integration and cross-checking. For example, integrating HeLis with FoodOn would combine fine-grained categorization of food products (including bananas) with lifestyle knowledge. Moreover, cross-checking FoodOn with HeLis will reveal the problem with soy milk, which is correctly categorized as a soy product in HeLis. Automating the integration of knowledge resources is challenging, but combining semantic and learning-based techniques seems to be a very promising approach, and we have already obtained some encouraging preliminary results in this direction. The proposed research will therefore study a range of semantic and machine learning techniques, and how to combine them to support knowledge graph construction and curation. As well as its application to knowledge graph construction and curation, this research will also contribute to the development of new neural-symbolic theories, paradigms and methods, such as deep semantic embedding for learning representations for expressive knowledge, and knowledge-guided learning for addressing sample shortage problems. These techniques promise to revolutionize many AI and big data technologies.

Our 21st century lives will be increasingly connected to our digital identities, representations of ourselves that are defined from trails of personal data and that connect us to commercial and public services, employers, schools, families and friends. The future health of our Digital Economy rests on training a new generation of leaders who can harness the emerging technologies of digital identity for both economic and societal value, but in a fair and transparent manner that accommodates growing public concern over the use of personal data. We will therefore train a community of 80 PhD students with the interdisciplinary skills needed to address the profound challenges of digital identity in the 21st century. Our training programme will equip students with a unique blend of interdisciplinary skills and knowledge across three thematic aspects of digital identity - enabling technologies, global impacts and people and society - while also providing them with the wider research and professional skills to deliver a research project across the intersection of at least two of these. Our students will be situated within Horizon, a leading centre for Digital Economy research and a vibrant environment that draws together a national research Hub, CDT and a network of over 100 industry, academic and international partners. Horizon currently provides access to a large network of over 75 potential supervisors, ranging from from leading Professors to talented early career researchers. Each student will work with an industry, public, third sector or international partner to ensure that their research is grounded in real user needs, to maximise its impact, and also to enhance their employability. These external partners will be involved in co-sponsorship, supervision, providing resources and hosting internships. Our external partners have already committed to co-sponsor 30 students so far, and we expect this number to grow. Our centre also has a strong international perspective, working with international partners to explore the global marketplace for digital identity services as well as the cross-cultural issues that this raises. This will build on our success in exporting the CDT model to China where we have recently established a £17M International Doctoral Innovation Centre to train 50 international students in digital economy research with funding from Chinese partners. We run an integrated four-year training programme that features a bespoke core covering key topics in digital identity, optional advanced specialist modules, practice-led team and individual projects, training in research methods and professional skills, public and external engagement, and cohort building activities including an annual writing retreat and summer school. The first year features a nine month structured process of PhD co-creation in which students, supervisors and external partners iteratively refine an initial PhD topic into a focused research proposal. Building on our experience of running the current Horizon CDT over the past five years, our management structure responds to external, university and student input and manages students through seven key stages of an extended PhD process: recruitment, induction, taught programme, PhD co-creation, PhD research, thesis, and alumni. Students will be recruited onto and managed through three distinct pathways - industry, international and institutional - that reflect the funding, supervision and visiting constraints of working with varied external partners.

The CDT will train the next generation of leaders in statistics and statistical machine learning, who will be able to develop widely-applicable novel methodology and theory, as well as create application-specific methods, leading to breakthroughs in real-world problems in government, medicine, industry and science. The research will focus on the development of applicable modern statistical theory and methods as well as on the underpinnings of statistical machine learning. The research will be strongly linked to applications. There is an urgent national need for graduates from this CDT. Large volumes of complicated data are now routinely collected in all sectors of society, encompassing electronic health records, massive scientific datasets, governmental data, and data collected through the advent of the digital economy. The underpinning techniques for exploiting these data come from statistics and machine learning. Exploiting such data is crucial for future UK prosperity. However, several reports from government and learned societies have identified a lack of individuals able to exploit this data. In many situations, existing methodology is insufficient. Off-the-shelf approaches may be misleading due to a lack of reproducibility or sampling biases which they do not correct. Furthermore, understanding the underlying mechanisms is often desired: scientifically valid, interpretable and reproducible results are needed to understand scientific phenomena and to justify decisions, particularly those affecting individuals. Bespoke, model-based statistical methods are needed, that may need to be blended with statistical machine learning approaches to deal with large data. Individuals that can fulfill these more sophisticated demands are doctoral level graduates in statistics who are well versed in the foundations of machine learning. Yet the UK only graduates a small number of statistics PhDs per year, and many of these graduates will not have been exposed to machine learning. The Centre will bring together Imperial and Oxford, two top statistics groups, as equal partners, offering an exceptional training environment and the direct involvement of absolute research leaders in their fields. The supervisor pool will include outstanding researchers in statistical methodology and theory as well as in statistical machine learning. We will use innovative and student-led teaching, focussing on PhD-level training. Teaching cuts across years and thus creates strong cohort cohesion not just within a year group but also between year groups. We will link theoretical advances to application areas through partner interactions as well as through a placement of students with users of statistics. The CDT has a large number of high profile partners that helped shape our application priority areas (digital economy, medicine, engineering, public health, science) and that will co-fund and co-supervise PhD students, as well as co-deliver teaching elements.