Published as a workshop paper at ICLR 2020 N ON - LINEAR INTERLINKAGES AND KEY OBJECTIVES AMONGST THE PARIS AGREEMENT AND THE S USTAIN - ABLE D EVELOPMENT G OALS Felix Laumann Department of Mathematics Imperial College London fjl1218@ic.ac.uk Julius von K ¨ ugelgen Max Planck Institute for Intelligent Systems, T ¨ ubingen Department of Engineering, University of Cambridge Mauricio Barahona Department of Mathematics Imperial College London ABSTRACT The United Nations’ ambitions to combat climate change and prosper human de- velopment are manifested in the Paris Agreement and the Sustainable Develop- ment Goals (SDGs), respectively. These are inherently inter-linked as progress to- wards some of these objectives may accelerate or hinder progress towards others. We investigate how these two agendas influence each other by defining networks of 18 nodes, consisting of the 17 SDGs and climate change, for various groupings of countries. We compute a non-linear measure of conditional dependence, the partial distance correlation, given any subset of the remaining 16 variables. These correlations are treated as weights on edges, and weighted eigenvector centralities are calculated to determine the most important nodes. We find that SDG 6, clean water and sanitation, and SDG 4, quality education, are most central across nearly all groupings of countries. In developing regions, SDG 17, partnerships for the goals, is strongly connected to the progress of other objectives in the two agendas whilst, somewhat surprisingly, SDG 8, decent work and economic growth, is not as important in terms of eigenvector centrality. 1 I NTER- LINKED HUMAN AND NATURAL WORLDS The state-of-the-art in sustainability is described by two United Nations (UN) landmark agendas, the Paris Agreement (UN, 2015a) and the Sustainable Development Goals (SDGs) (UN, 2015b). Whilst the former focuses on preventing a global climate crisis with far reaching consequences by limiting global warming to 1.5 to 2 ◦ C above pre-industrial levels, the purpose of the latter is to end poverty, protect the planet and ensure that all people enjoy peace and prosperity by 2030. Any action for the progress on either agenda often has an influence on the other (UN Climate Change, 2019), reflecting the complexity of the human and natural worlds. This inter-linked nature gives rise to opportunities for the creation of synergistic interventions: civil, corporate and institutional actions can efficiently create impact across both agendas, thereby im- proving the world profoundly. On the other hand, this inter-linked construct can also be subject to trade-offs between objectives, i.e., progress towards one agenda constrains progress towards the other. In this work, we aim to discover how climate change, as measured by local temperature rises, and the 17 SDGs are inter-linked by learning the structure of undirected graphs over these variables from their (conditional) dependencies. Adding climate change as an 18 th variable is motivated by the observation that temperature rises (or any other direct metrics of climate change) are not actually tracked within SDG 13 (climate action). Indicators of SDG 13 only track inputs (such as investment), means (such as plans and strategies), 1 arXiv:2004.09318v1 [econ.EM] 16 Apr 2020