Non-linear interlinkages and key objectives amongst the Paris Agreement and the Sustainable Development Goals

1 Inter-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 improving 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 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), and impacts (number of people affected by disasters), but they do not account for outputs, such as changes in temperature or green house gas emissions.¹¹1Only recently (and after performing the present analysis) have ”total greenhouse gas emissions” been added as an output-quantifying indicator (13.2.2).

We use distance correlation (Székely et al., 2007) as a measure of non-linear dependence between variables of possibly varying dimensions. To account for possible interactions, each pair of variables is conditioned on any subset of the remaining variables, and the minimum resulting distance correlation is taken as the weight on an edge between these two variables. Subsequently, the weighted eigenvector centrality of every node is calculated to measure its importance within the network.

In summary, the contributions of this paper include: first, the application of a non-linear measure of (conditional) dependence to SDG data, thereby relaxing the linearity assumption on the nature of interlinkages between the SDGs, compared to the work of Lusseau and Mancini (2019); and secondly, the use of eigenvector centrality as a relative measure which also takes the importance of a node’s neighbours into account, as opposed to simple degree centrality as used by McGowan et al. (2019).

2 Methodology

We use data provided by the World Bank (2020b) and the UN (2020) in form of time-series for various indicators, which measure progress towards their associated SDGs, in conjunction with temperature recordings (World Bank, 2020a).²²2For detailed descriptions of indicators, see https://sustainabledevelopment.un.org/sdgs In total, these three sources provide 379 time-series, which are available on a country-level with annual measurements from 2000 to 2016³³3

We impute missing values (especially for the time 2000-2005) using a weighted average across countries (where data is available) with weights inversely proportional to the Euclidean distance between indicators.

. Apart from measurements for the 17 SDGs, we introduce climate change as an additional variable which we define by annual average temperature per country. We consider these 18 variables as the set of nodes

V

of an undirected graph

G

. We learn the graph structure by computing partial distance covariances (Székely et al., 2014) between any pair

(X, Y)

of nodes, given any subset

Z \subseteq V ∖ (X, Y)

of the remaining 16 nodes. This yields a sparsely-connected undirected graph with weighted edges

E

capturing non-linear dependencies between variables. Using these weights, we compute weighted eigenvector centralities (Newman, 2018, p.159; Appendix A.2) to find the most important nodes. Code to reproduce our findings and visualisations of networks may be found online at https://github.com/felix-laumann/SDG-dataset.

2.1 Distance covariance

Let $X \in R^{d_{X}}$ and $Y \in R^{d_{Y}}$

be two random vectors with finite first moments, i.e.,

E [X], E [Y] < \infty

. The distance covariance between

X

and

Y

, denoted by

V^{2} (X, Y)

, is a measure of dependence between

X

and

Y

with the following important properties: (i)

V^{2} (X, Y) \geq 0

, with equality if and only if

X

and

Y

are independent, i.e., it is a non-parametric measure that—unlike, e.g., standard correlation—is able to pick up complex non-linear dependencies; (ii)

V^{2} (X, Y) = V^{2} (Y, X)

, i.e., it is symmetric; and (iii) unlike many other dependence measures

V^{2} (X, Y)

is well-defined even for

d_{X} \neq d_{Y}

. This last point makes it particularly useful for our setting where, due to the different numbers of indicators per SDG, dimensionality varies considerably between variables.

Formally, the distance covariance between $X$ and $Y$ is defined as

V^{2} (X, Y) = ∥ f_{X, Y} (t, s) - f_{X} (t) f_{Y} (s) ∥^{2} := \int | f_{X, Y} (t, s) - f_{X} (t) f_{Y} (s) |^{2} w (t, s) d t d s

(1)

where $w (t, s) := (| t |_{d_{X}}^{1 + d_{X}} | s |_{d_{Y}}^{1 + d_{Y}})^{- 1}$ , and where the characteristic function $f$

of a random variable

Z

is denoted as

f_{Z} (t) = E [e^{i t Z}]

with

i^{2} = - 1

The corresponding distance correlation $R^{2}$ is the normalised distance covariance, computed by

R2(X,Y)=⎧⎪⎨⎪⎩V2(X,Y)√V2(X,X)V2(Y,Y),\quad if \quadV2(X,X)V2(Y,Y)>00,\quad if \quadV2(X,X)V2(Y,Y)=0.

(2)

Properties of $R^{2}$ include: (i) $0 \leq R^{2} (X, Y) \leq 1$ ; and (ii) $R^{2} (X, Y) = 1$ if and only if there exists a vector $a$ , a non-zero real number $b$

, and an orthogonal matrix

C

such that

Y = a + b C X

Since $V^{2} (X, Y)$ and therefore $R^{2} (X, Y)$

are defined in terms of the underlying joint distribution of

(X, Y)

which is usually not known, we require a way to estimate them from data. Definitions of biased and unbiased estimators, referred to as

A

and

~ A

, can be found in Appendix A.1.1 and A.1.2.

2.2 Partial distance covariance

As we deal with graphs of 18 nodes, any pairwise covariance may occur through the remaining 16 nodes. Thus, we condition any pair of nodes $(X, Y)$ on any subset $Z \subseteq V ∖ (X, Y)$ of the remaining 16 nodes. The pairwise distances $c_{i j} = ∥ Z_{i} - Z_{j} ∥$ and the distance matrix $C_{i j}$ for $Z$ are computed equivalently to $A_{i j}$ and $B_{i j}$ for $X$ and $Y$ as explained in Appendix A.1.1. For any number $n \geq 4$ of samples ${(x_{i}, y_{i}, z_{i})}_{i = 1}^{n}$ from $(X, Y, Z)$ , we define a Hilbert space $H_{n}$ over distance matrices computed on these $n$ points, with inner products $⟨ \cdot, \cdot ⟩$ as defined in Appendix A.1.2 (Székely et al., 2014). With this, we can compute partial distance covariances for random vectors of varying dimensions as follows.

Let $~ A (x)$ , $~ B (y)$ and $~ C (z)$ be elements of the Hilbert space $H_{n}$ corresponding to the distance matrices computed using the samples $x = (x_{1}, . . ., x_{n})$ , $y = (y_{1}, . . ., y_{n})$ , and $z = (z_{1}, . . ., z_{n})$ , respectively. The projection $P_{z} (x)$ of $~ A (x)$ onto $~ C (z)$ and the complementary orthogonal projection $P_{z^{⊥}} (x)$ are defined by

P_{z} (x) := \frac{⟨ ~ A (x), ~ C (z) ⟩}{⟨ ~ C (z), ~ C (z) ⟩} ~ C (z), and P_{z^{⊥}} (x) := ~ A (x) - P_{z} (x) = ~ A (x) - \frac{⟨ ~ A (x), ~ C (z) ⟩}{⟨ ~ C (z), ~ C (z) ⟩} ~ C (z),

(3)

respectively. The sample partial distance covariance is then defined as

V_{n}^{2} (X, Y | Z) = ⟨ P_{z^{⊥}} (x), P_{z^{⊥}} (y) ⟩ = \frac{1}{n (n - 3)} \sum_{i \neq j}^{n} (P_{z^{⊥}} (x))_{i j} (P_{z^{⊥}} (y))_{i j} .

(4)

Finally, we can normalise these covariances to arrive at the sample partial distance correlations

R_{n}^{2} (X, Y | Z) = ⎧ ⎨ ⎩ \begin{matrix} \frac{⟨ P_{z^{⊥}} (x), P_{z^{⊥}} (y) ⟩}{∥ P_{z^{⊥}} (x) ∥ ∥ P_{z^{⊥}} (y) ∥}, & if ∥ P_{z^{⊥}} (x) ∥ ∥ P_{z^{⊥}} (y) ∥ \neq 0 0, & if ∥ P_{z^{⊥}} (x) ∥ ∥ P_{z^{⊥}} (y) ∥ = 0 \end{matrix},

(5)

which serve as weights on edges between any two nodes.

3 Results

We apply this methodology to the data set of the aforementioned 379 indicators for various groupings of countries, for which countries are assumed to be independent samples. This assumption allows us to see the indicators’ non-stationary time-series as $d$

-dimensional probability distributions, where

d = # indicators \times # years

. Whilst we only describe the networks of a few groupings in this section, we would like to refer to Appendix B for results on all groupings.

Global South		Global North
SDG 6	0.48	SDG 6	0.43
SDG 4	0.42	SDG 4	0.40
SDG 7	0.38	SDG 9	0.33
SDG 17	0.37	SDG 3	0.32
SDG 3	0.26	SDG 17	0.29
SDG 15	0.25	SDG 7	0.27

Western Asia		Northern Europe
SDG 6	0.48	SDG 4	0.38
SDG 4	0.36	SDG 3	0.35
SDG 17	0.34	SDG 6	0.30
SDG 3	0.33	SDG 16	0.30
SDG 16	0.32	SDG 7	0.29
SDG 7	0.26	SDG 9	0.28

Table 1: Comparison of eigenvector centralities between the Global South and the Global North (left), and between Western Asia and Northern Europe (right). Results for all groupings can be found in B.2.

Firstly, we compare the Global South and the Global North (see Figure 1). The accompanied eigenvector centralities are shown in Table 1. In both groupings, SDG 6, clean water and sanitation, followed closely by SDG 4, quality education, are the most central objectives of the 18 variables. In the Global South, temperature rises are more strongly dependent on variables than in the Global North, which broadly aligns with King and Harrington (2018) who find that geographical areas in the Global South are more vulnerable to climate change than regions in the Global North. Further, SDG 1, no poverty, is strongly linked to SDG 14, life below water, in the Global South. This may be explained by the dependence of small island developing states (SIDS)—all of which lie in the Global South—on marine life to provide for their citizens’ living.

Contrarily, the Global North strongly depends on SDG 9, industry, innovation and infrastructure, to maintain its citizens’ high levels of living standards and to further progress towards other SDGs, as well as climate change mitigation and adaptation. Moreover, SDG 7, clean and affordable energy, is closely related to SDG 15, life on land, which could result from the increasing area of biodiverse land populated by wind turbines, solar panels, or water dams (e.g., Hernandez et al., 2015).

Next, we compare two geographical regions, Western Asia and Northern Europe, shown in Figure 2 with accompanied eigenvector centralities in Table 1. In Western Asia, SDG 6 together with SDG 4 are again the two most central nodes, but SDG 16, peace, justice and strong institutions, is also important, likely to be associated with the unstable political circumstances in this area during the period of recorded measurements. Additionally, SDG 5, gender equality, is strongly linked to SDG 17, partnerships for the goals, which coincides with the remarkably low percentage of women in managerial positions in Western Asia.⁴⁴4In Saudi Arabia, for example, only 5 to 9% of managerial positions were held by women from 2000 to 2015, whereas this number fluctuated between 32 and 36% in the United Kingdom in the same period (UN (2020), indicator 5.5.2)

In contrast, Northern Europe does not see a remarkable difference between the centralities of SDGs 6 and 4 to all others, but finds SDGs 4, 6, 3, and 17 with almost equivalently high centralities. As in the Global North, industry, innovation and infrastructure are of particular importance to progress towards the SDGs, and we fine that clean and affordable energy is closely linked to life on land.

We note, however, that most edges found in our network analysis are not statistically significant at $p = 0.05$ , using the test of Székely et al. (2014). This is likely linked to the high dimensionality of the data and the short recording period. The present work is thus only a first step, and further analysis is needed to better understand non-linear interlinkages between the SDGs and climate change.

4 Conclusions

We report findings of our work in progress towards discovering dependencies amongst the Sustainable Development Goals (SDGs) and climate change. As a first step, we compute partial distance correlations between the 17 SDGs and climate change, as measured by indicators associated to the SDGs and annual average temperature, respectively. Using these measurements of non-linear dependence as edge weights in a network over these variables, we determine eigenvector centralities to unveil which variables are of particular importance, given the available data. Our results indicate that SDG 6, clean water and sanitation, together with SDG 4, quality education, are the most central nodes in nearly all continents and other groupings of countries. In contrast to many contemporary policies, our preliminary results suggest that economic growth, as measured by SDG 8, appears not to play as central of a role for sustainable development or mitigating climate change as other SDGs.

References

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Appendix A Appendix A

a.1 Distance covariance estimators

a.1.1 Biased estimators

Suppose that we have access to a sample of pairs $(x_{1}, y_{1}), . . ., (x_{n}, y_{n}) i.i.d \sim P_{X, Y}$ . First, define the pairwise distances: $a_{i j} := ∥ x_{i} - x_{j} ∥$ and $b_{i j} = ∥ y_{i} - y_{j} ∥ \forall i, j = 1, . . ., n$ . Next, define the corresponding distance matrices, denoted by $(A_{i j})_{i, j = 1}^{n}$ and $(B_{i j})_{i, j = 1}^{n}$ , as follows:

A_{i j} = {\begin{matrix} a_{i j} - \frac{1}{n} \sum_{l = 1}^{n} a_{i l} - \frac{1}{n} \sum_{k = 1}^{n} a_{k j} + \frac{1}{n^{2}} \sum_{k, l = 1}^{n} a_{k l}, & if i \neq j 0, & if i = j \end{matrix}

(6)

and

B_{i j} = {\begin{matrix} b_{i j} - \frac{1}{n} \sum_{l = 1}^{n} b_{i l} - \frac{1}{n} \sum_{k = 1}^{n} b_{k j} + \frac{1}{n^{2}} \sum_{k, l = 1}^{n} b_{k l}, & if i \neq j 0, & if i = j . \end{matrix}

(7)

Having computed these, the sample distance covariance $V_{n}^{2} (X, Y)$ can be estimated by

V_{n}^{2} (X, Y) = \frac{1}{n^{2}} n \sum i, j = 1 A_{i j} B_{i j},

(8)

which converges almost surely to the population distance covariance $V^{2} (X, Y)$ as $n \to \infty$ (Székely et al., 2014).

a.1.2 Unbiased estimators

Unbiased estimators of the distance covariance are denoted as $Ω_{n} (x, y)$ . Firstly, we must redefine our distance matrices $(A_{i j})_{i, j = 1}^{n}$ and $(B_{i j})_{i, j = 1}^{n}$ , which we call $({~ A}_{i j})_{i, j = 1}^{n}$ and $({~ B}_{i j})_{i, j = 1}^{n}$ as

{~ A}_{i j} = {\begin{matrix} a_{i j} - \frac{1}{n - 2} \sum_{l = 1}^{n} a_{i l} - \frac{1}{n - 2} \sum_{k = 1}^{n} a_{k j} + \frac{1}{(n - 1) (n - 2)} \sum_{k, l = 1}^{n} a_{k l}, & if i \neq j; 0, & if i = j \end{matrix}

(9)

and

{~ B}_{i j} = {\begin{matrix} b_{i j} - \frac{1}{n - 2} \sum_{l = 1}^{n} b_{i l} - \frac{1}{n - 2} \sum_{k = 1}^{n} b_{k j} + \frac{1}{(n - 1) (n - 2)} \sum_{k, l = 1}^{n} b_{k l}, & if i \neq j; 0, & if i = j . \end{matrix}

(10)

Finally, we can compute the unbiased estimator $Ω_{n} (X, Y)$ for $V^{2} (X, Y)$ as the dot product $⟨ ~ A, ~ B ⟩$ :

Ω_{n} (X, Y) = ⟨ ~ A, ~ B ⟩ = \frac{1}{n (n - 3)} n \sum i, j = 1 {~ A}_{i j} {~ B}_{i j}

(11)

a.2 Eigenvector centrality

For any graph $G := (V, E)$ , let $K$ be the adjacency matrix of graph $G$ with $k_{v, t}$ equal to the weight on the edge between node $v$ and $t$ . The eigenvector centrality $x$ of node $v$ is a measure relative to all other nodes in $G$ , defined as

x_{v} = \frac{1}{λ} \sum t \in G k_{v, t} x_{t},

(12)

where $λ$

is the greatest eigenvalue in the eigenvector equation

K x = λ x

, subject to

x \neq 0

. Consequently, this centrality measure is an extension of the widely used degree centrality by considering the centrality of its neighbours besides its own.

Appendix B Appendix B

b.1 Networks of groupings

b.2 Eigenvector centralities

b.3 Groupings of countries

Northern Africa	Eastern Africa	Middle Africa	Southern Africa	Western Africa	Sub-Saharan Africa	Africa	Caribbean	Central America	South America	Latin America and the Caribbean	North America	Americas	Central Asia	Eastern Asia	South-eastern Asia	Southern Asia	Western Asia	Asia	Eastern Europe	Northern Europe	Southern Europe	Western Europe	Europe	Australia and New Zealand	Oceania (excl. AUS + NZ)	Oceania (incl. AUS + NZ)
Algeria	Burundi	Angola	Botswana	Benin	Burundi	Algeria	Antigua and Barbuda	Belize	Argentina	Antigua and Barbuda	Canada	Antigua and Barbuda	Kazakhstan	China	Brunei Darussalam	Afghanistan	Armenia	Kazakhstan	Belarus	Denmark	Albania	Austria	Belarus	Australia	Fiji	Australia
Egypt, Arab Rep.	Comoros	Cameroon	Lesotho	Burkina Faso	Comoros	Egypt, Arab Rep.	Bahamas, The	Costa Rica	Bolivia	Bahamas, The	Greenland	Bahamas, The	Kyrgyz Republic	Korea, Dem. People’s Rep.	Cambodia	Bangladesh	Azerbaijan	Kyrgyz Republic	Bulgaria	Estonia	Bosnia and Herzegovina	Belgium	Bulgaria	New Zealand	Papua New Guinea	New Zealand
Morocco	Djibouti	Central African Republic	Namibia	Cote d’Ivoire	Djibouti	Morocco	Barbados	El Salvador	Brazil	Barbados	United States	Barbados	Tajikistan	Japan	Indonesia	Bhutan	Bahrain	Tajikistan	Czech Republic	Finland	Croatia	France	Czech Republic		Solomon Islands	Fiji
Tunisia	Eritrea	Chad	South Africa	Gambia, The	Eritrea	Tunisia	Cuba	Guatemala	Chile	Cuba		Cuba	Turkmenistan	Mongolia	Lao PDR	India	Cyprus	Turkmenistan	Hungary	Iceland	Greece	Germany	Hungary		Vanuatu	Papua New Guinea
	Ethiopia	Congo, Rep.		Ghana	Ethiopia	Burundi	Dominica	Honduras	Colombia	Dominica		Dominica	Uzbekistan		Malaysia	Iran, Islamic Rep.	Georgia	Uzbekistan	Poland	Ireland	Italy	Liechtenstein	Poland		Micronesia, Fed. Sts.	Solomon Islands
	Kenya	Congo, Dem. Rep.		Guinea-Bissau	Kenya	Comoros	Grenada	Mexico	Ecuador	Grenada		Grenada			Myanmar	Maldives	Iraq	China	Moldova	Latvia	Malta	Luxembourg	Moldova		Palau	Vanuatu
	Madagascar	Equatorial Guinea		Liberia	Madagascar	Djibouti	Haiti	Nicaragua	Guyana	Haiti		Haiti			Philippines	Nepal	Israel	Korea, Dem. People’s Rep.	Romania	Lithuania	Montenegro	Netherlands	Romania		Kiribati	Micronesia, Fed. Sts.
	Malawi	Gabon		Mali	Malawi	Eritrea	Jamaica	Panama	Paraguay	Jamaica		Jamaica			Singapore	Pakistan	Jordan	Japan	Russian Federation	Norway	Portugal	Switzerland	Russian Federation		Samoa	Palau
	Mauritius	Sao Tome and Principe		Mauritania	Mauritius	Ethiopia	Puerto Rico		Peru	Puerto Rico		Puerto Rico			Thailand	Sri Lanka	Kuwait	Mongolia	Slovak Republic	Sweden	Serbia		Slovak Republic		Tonga	Kiribati
	Mozambique			Niger	Mozambique	Kenya	Trinidad and Tobago		Suriname	Trinidad and Tobago		Trinidad and Tobago			Timor-Leste		Lebanon	Brunei Darussalam	Ukraine	United Kingdom	Slovenia		Ukraine		Tuvalu	Samoa
	Rwanda			Nigeria	Rwanda	Madagascar			Uruguay	Belize		Belize			Vietnam		Oman	Cambodia			Spain		Denmark			Tonga
	Seychelles			Senegal	Seychelles	Malawi			Venezuela, RB	Costa Rica		Costa Rica					Qatar	Indonesia					Estonia			Tuvalu
	Somalia			Sierra Leone	Somalia	Mauritius				El Salvador		El Salvador					Saudi Arabia	Lao PDR					Finland
	South Sudan			Togo	South Sudan	Mozambique				Guatemala		Guatemala					Syrian Arab Republic	Malaysia					Iceland
	Uganda				Uganda	Rwanda				Honduras		Honduras					Turkey	Myanmar					Ireland
	Tanzania				Tanzania	Seychelles				Mexico		Mexico					United Arab Emirates	Philippines					Latvia
	Zambia				Zambia	Somalia				Nicaragua		Nicaragua					Yemen, Rep.	Singapore					Lithuania
	Zimbabwe				Zimbabwe	South Sudan				Panama		Panama						Thailand					Norway
					Angola	Uganda				Argentina		Argentina						Timor-Leste					Sweden
					Cameroon	Tanzania				Bolivia		Bolivia						Vietnam					United Kingdom
					Central African Republic	Zambia				Brazil		Brazil						Afghanistan					Albania
					Chad	Zimbabwe				Chile		Chile						Bangladesh					Bosnia and Herzegovina
					Congo, Rep.	Angola				Colombia		Colombia						Bhutan					Croatia
					Congo, Dem. Rep.	Cameroon				Ecuador		Ecuador						India					Greece
					Equatorial Guinea	Central African Republic				Guyana		Guyana						Iran, Islamic Rep.					Italy
					Gabon	Chad				Paraguay		Paraguay						Maldives					Malta
					Sao Tome and Principe	Congo, Rep.				Peru		Peru						Nepal					Montenegro
					Botswana	Congo, Dem. Rep.				Suriname		Suriname						Pakistan					Portugal
					Lesotho	Equatorial Guinea				Uruguay		Uruguay						Sri Lanka					Serbia
					Namibia	Gabon				Venezuela, RB		Venezuela, RB						Armenia					Slovenia
					South Africa	Sao Tome and Principe						Canada						Azerbaijan					Spain
					Benin	Botswana						Greenland						Bahrain					Austria
					Burkina Faso	Lesotho						United States						Cyprus					Belgium
					Cote d’Ivoire	Namibia												Georgia					France
					Gambia, The	South Africa												Iraq					Germany
					Ghana	Benin												Israel					Liechtenstein
					Guinea-Bissau	Burkina Faso												Jordan					Luxembourg
					Liberia	Cote d’Ivoire												Kuwait					Netherlands
					Mali	Gambia, The												Lebanon					Switzerland
					Mauritania	Ghana												Oman
					Niger	Guinea-Bissau												Qatar
					Nigeria	Liberia												Saudi Arabia
					Senegal	Mali												Syrian Arab Republic
					Sierra Leone	Mauritania												Turkey
					Togo	Niger												United Arab Emirates
						Nigeria												Yemen, Rep.
						Senegal
						Sierra Leone
						Togo

World contains all listed countries.

Global North	Global South	LDC	LLDC	SIDS	G20	Emerging Markets	OPEC	Low Income	Lower middle Income	Upper middle Income	High Income
Albania	Fiji	Yemen, Rep.	Afghanistan	Antigua and Barbuda	Australia	Bangladesh	Algeria	Afghanistan	Angola	Albania	Antigua and Barbuda
Austria	Micronesia, Fed. Sts.	Afghanistan	Armenia	Bahamas, The	Canada	Egypt, Arab Rep.	Angola	Benin	Bangladesh	Algeria	Australia
Belarus	Tonga	Burundi	Azerbaijan	Barbados	Saudi Arabia	Indonesia	Equatorial Guinea	Burkina Faso	Bhutan	Argentina	Austria
Belgium	Vanuatu	Angola	Bhutan	Belize	United States	Iran, Islamic Rep.	Gabon	Burundi	Bolivia	Armenia	Bahamas, The
Bosnia and Herzegovina	Tuvalu	Benin	Bolivia	Comoros	India	Mexico	Iran, Islamic Rep.	Central African Republic	Cambodia	Azerbaijan	Bahrain
Bulgaria	Solomon Islands	Mozambique	Botswana	Cuba	Russian Federation	Nigeria	Iraq	Chad	Cameroon	Belarus	Barbados
Croatia	Samoa	Burkina Faso	Burkina Faso	Dominica	South Africa	Pakistan	Kuwait	Congo, Dem. Rep.	Comoros	Belize	Belgium
Cyprus	Papua New Guinea	Niger	Burundi	Dominican Republic	Turkey	Philippines	Libya	Eritrea	Congo, Rep.	Bosnia and Herzegovina	Canada
Czech Republic	Palau	Central African Republic	Central African Republic	Fiji	Argentina	Turkey	Nigeria	Ethiopia	Cote d’Ivoire	Botswana	Chile
Denmark	Kiribati	Chad	Chad	Grenada	Brazil	Korea, Dem. People’s Rep.	Saudi Arabia	Gambia	Djibouti	Brazil	Croatia
Estonia	Bangladesh	Lesotho	Ethiopia	Guinea-Bissau	Mexico	Vietnam	United Arab Emirates	Guinea	Egypt, Arab Rep.	Bulgaria	Malta
Finland	Bhutan	Liberia	Kazakhstan	Guyana	France	Brazil	Congo, Dem. Rep.	Guinea-Bissau	El Salvador	China	Cyprus
France	Cambodia	Congo, Dem. Rep.	Kyrgyz Republic	Haiti	Germany	Russian Federation	Venezuela, RB	Haiti	Ghana	Colombia	Czech Republic
Greece	China	Djibouti	Lao PDR	Jamaica	Italy	India		Liberia	Honduras	Costa Rica	Denmark
Germany	India	Togo	Lesotho	Kiribati	United Kingdom	China		Madagascar	India	Cuba	Estonia
Greenland	Indonesia	Equatorial Guinea	Malawi	Maldives	China	South Africa		Malawi	Indonesia	Dominica	Finland
Hungary	Lao PDR	Eritrea	Mali	Mauritius	Indonesia			Mali	Kenya	Dominican Republic	France
Iceland	Malaysia	Ethiopia	Moldova	Palau	Japan			Mozambique	Kiribati	Ecuador	Germany
Ireland	Myanmar	Gambia	Mongolia	Papua New Guinea	Korea, Dem. People’s Rep.			Nepal	Kyrgyz Republic	Equatorial Guinea	Greece
Italy	Mongolia	Madagascar	Nepal	Puerto Rico				Niger	Lao PDR	Fiji	Greenland
Latvia	Nepal	Malawi	Niger	Samoa				Rwanda	Lesotho	Gabon	Hungary
Liechtenstein	Pakistan	Mali	Paraguay	Sao Tome and Principe				Sierra Leone	Mauritania	Georgia	Iceland
Lithuania	Philippines	Rwanda	Rwanda	Seychelles				Somalia	Moldova	Grenada	Ireland
Luxembourg	Sri Lanka	Senegal	South Sudan	Singapore				South Sudan	Mongolia	Guatemala	Israel
Malta	Thailand	Sierra Leone	Tajikistan	Solomon Islands				Syrian Arab Republic	Morocco	Guyana	Italy
Montenegro	Timor-Leste	Mauritania	Turkmenistan	Suriname				Tajikistan	Myanmar	Iran, Islamic Rep.	Japan
Netherlands	Vietnam	Guinea-Bissau	Uganda	Timor-Leste				Tanzania	Nicaragua	Iraq	Korea, Dem. People’s Rep.
Norway	Maldives	Guinea	Uzbekistan	Tuvalu				Togo	Nigeria	Jamaica	Kuwait
Poland	Grenada	Comoros	Zambia	Vanuatu				Uganda	Pakistan	Jordan	Latvia
Portugal	Dominica	Sao Tome and Principe	Zimbabwe					Yemen, Rep.	Papua New Guinea	Kazakhstan	Liechtenstein
Romania	Barbados	Zambia							Philippines	Lebanon	Lithuania
Serbia	Antigua and Barbuda	Uganda							Sao Tome and Principe	Libya	Luxembourg
Slovakia	Cuba	Tanzania							Senegal	Malaysia	Netherlands
Slovenia	Bahamas, The	South Sudan							Solomon Islands	Maldives	New Zealand
Spain	Puerto Rico	Sudan							Sudan	Mauritius	Norway
Sweden	Jamaica	Bhutan							Timor-Leste	Mexico	Oman
Switzerland	Algeria	Cambodia							Tunisia	Montenegro	Palau
Ukraine	Angola	Bangladesh							Ukraine	Namibia	Panama
United Kingdom	Benin	Haiti							Uzbekistan	Paraguay	Poland
Canada	Botswana	Kiribati							Vanuatu	Peru	Portugal
United States	Burkina Faso	Lao PDR							Vietnam	Romania	Puerto Rico
Azerbaijan	Cameroon	Myanmar							Zambia	Russian Federation	Qatar
Georgia	Central African Republic	Nepal							Zimbabwe	Samoa	Saudi Arabia
Israel	Chad	Vanuatu								Serbia	Seychelles
Russian Federation	Congo	Tuvalu								South Africa	Singapore
Turkey	Cote d’Ivoire	Solomon Islands								Sri Lanka	Slovak Republic
Australia	Congo, Dem. Rep.	Timor-Leste								Suriname	Slovenia
New Zealand	Djibouti									Thailand	Spain
Korea, Dem. People’s Rep.	Egypt, Arab Rep.									Tonga	Sweden
Japan	Equatorial Guinea									Turkey	Switzerland
Singapore	Eritrea									Turkmenistan	Trinidad and Tobago
	Ethiopia									Tuvalu	United Arab Emirates
	Gabon									Venezuela, RB	United Kingdom
	Gambia, The										United States
	Ghana										Uruguay
	Kenya
	Lesotho
	Liberia
	Libya
	Madagascar
	Malawi
	Mali
	Morocco
	Mozambique
	Namibia
	Niger
	Nigeria
	Rwanda
	Senegal
	Sierra Leone
	Somalia
	South Africa
	South Sudan
	Sudan
	Syrian Arab Republic
	Togo
	Tunisia
	Uganda
	Tanzania
	Zambia
	Zimbabwe
	Seychelles
	Sao Tome and Principe
	Mauritius
	Mauritania
	Guinea-Bissau
	Guinea
	Comoros
	Burundi
	Belize
	Bahamas, The
	Argentina
	Bolivia
	Brazil
	Chile
	Colombia
	Costa Rica
	Cuba
	Dominican Republic
	Ecuador
	El Salvador
	Guatemala
	Haiti
	Honduras
	Jamaica
	Mexico
	Panama
	Paraguay
	Peru
	Puerto Rico
	Suriname
	Trinidad and Tobago
	Uruguay
	Venezuela, RB
	Nicaragua
	Guyana
	Grenada
	Dominica
	Barbados
	Antigua and Barbuda
	Iraq
	Afghanistan
	Armenia
	Bahrain
	Iran, Islamic Rep.
	Jordan
	Kazakhstan
	Kuwait
	Kyrgyz Republic
	Lebanon
	Oman
	Qatar
	Saudi Arabia
	Tajikistan
	Turkmenistan
	United Arab Emirates
	Uzbekistan
	Yemen, Rep.

LDC: Least Developed Countries
LLDC: Land Locked Developing Countries
SIDS: Small Island Developing States
Emerging Markets: BRICS + N-11

Non-linear interlinkages and key objectives amongst the Paris Agreement and the Sustainable Development Goals

A large-scale bibliometric analysis of global climate change research between 2001 and 2018

SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning

The potential of artificial intelligence for achieving healthy and sustainable societies

Toward IoT enabled smart offices: Achieving Sustainable Development Goals

Climate Change Computer Audition: A Call to Action and Overview on Audio Intelligence to Help Save the Planet

The Sustainable Development Goals and Aerospace Engineering: A critical note through Artificial Intelligence

Revealing the Excitation Causality between Climate and Political Violence via a Neural Forward-Intensity Poisson Process

1 Inter-linked human and natural worlds

2 Methodology

2.1 Distance covariance

2.2 Partial distance covariance

3 Results

4 Conclusions

References

Appendix A Appendix A

a.1 Distance covariance estimators

a.1.1 Biased estimators

a.1.2 Unbiased estimators

a.2 Eigenvector centrality

Appendix B Appendix B

b.1 Networks of groupings

b.2 Eigenvector centralities

b.3 Groupings of countries

Non-linear interlinkages and key objectives amongst the Paris Agreement and the Sustainable Development Goals

Related Research

A large-scale bibliometric analysis of global climate change research between 2001 and 2018

SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning

The potential of artificial intelligence for achieving healthy and sustainable societies

Toward IoT enabled smart offices: Achieving Sustainable Development Goals

Climate Change Computer Audition: A Call to Action and Overview on Audio Intelligence to Help Save the Planet

The Sustainable Development Goals and Aerospace Engineering: A critical note through Artificial Intelligence

Revealing the Excitation Causality between Climate and Political Violence via a Neural Forward-Intensity Poisson Process

1 Inter-linked human and natural worlds

2 Methodology

2.1 Distance covariance

2.2 Partial distance covariance

3 Results

4 Conclusions

References

Appendix A Appendix A

a.1 Distance covariance estimators

a.1.1 Biased estimators

a.1.2 Unbiased estimators

a.2 Eigenvector centrality

Appendix B Appendix B

b.1 Networks of groupings

b.2 Eigenvector centralities

b.3 Groupings of countries