War Machine

This repository was created for a semester project in Michigan State University's CMSE 202, Computational Modeling Tools and Techniques during the Fall of 2024 taught by Dr. Nathan Haut at the Department of Computational Mathematics, Science, and Engineering. This project comes under the social sciences.

Group members:

1. Kyle Cowden (Graph Theory)
2. Lowell Monis (Machine Learning)
3. Joseph Burke (Data Processing and Graph Theory)
4. Saif Sheikh (Machine Learning and Visualization)
5. Adhvik Kolar (Machine Learning and Visualization)

Running:

The primary code used to generate plots of how accurate our war predictions are is in the code.ipynb file. This file contains our primary submission for this project. You can also find code for making graphics and simulations of how alliances change in our raw data in archive/Correlates_of_war.ipynb. archive/svm.ipynb contains an exploratory attempt at using SVMs alone to predict alliance changes, but is not used in the main simulation that we are presenting. If you would like to view any visuals, you can view them in the folder titled visuals.

Abstract

Our project focuses on modeling and predicting international alliances and the likelihood of conflict using the Correlates of War (CoW) datasets. This work integrates computational modeling, data analysis, and machine learning to answer the following central questions:

How do alliance configurations shift over time?

Thus, when will war break out?

What factors in alliances historically correlate with wars?

Can graph theory and machine learning models predict alliance instability?

These questions are motivated by the need to better understand the dynamic nature of global alliances and the conditions under which conflict arises, contributing to the broader field of political science, international relations, and social relations.

Background and Motivation

The CoW datasets provide a comprehensive archive of historical and contemporary data on interstate conflicts, alliances, trade, and diplomatic exchanges. Leveraging this dataset allows us to analyze how various factors influence alliance stability and the onset of conflict. Our motivation lies in advancing predictive capabilities using computational tools and exploring the theoretical implications of alliance dynamics through graph theory and machine learning.

Objectives of this study:

• Understand stable alliance configurations using graph theory principles.
• Use these configurations to predict war likelihood.

Methodology

We employed a multi-faceted approach combining graph theory, and machine learning. The first phase involved constructing network graphs where nodes represented countries and edges depicted alliances. We implemented graph-theoretical stability rules to identify two configurations: complete graphs, which signify stable alliances, and disjoint subgraphs, which often predict conflict. For the second phase, we utilized Python-based libraries such as NetworkX for graph analysis, pandas for data processing, and sklearn for machine learning. We chose logistic regression to simplify the model. It was also chosen for its interpretability and effectiveness in binary classification tasks like predicting war likelihood and alliance shifts.

The logistic model is based on the logistic function, also known as the sigmoid function. [1]

$$f:\mathbb{R}\rightarrow[-1,1], f(x) = \frac{e^x}{1+e^x}$$

This makes it great to use as a binary classifier by using the probabilistic concept of likelihood.

Graph theory was used as a medium for this project [2]. Nodes were used to represent states, while edges were used to represent relationships or alliances. For the sake of simplicity, the lack of an edge indicates hostility. Relationships were assumed to be bi-directional, which removed the need to create directed graphs.

There were a few rules set up for the sake of stability.

1. Allies cannot share a mutual enemy.
2. Alliances must form; no isolated nodes are allowed.

From these rules, two stable configurations were achieved:

1. Complete Graph ($K_n$: All states are allies.
2. Disjoint Complete Subgraphs: States form two or more distinct alliances with hostility between the groups, making war inevitable.

Returning to computational techniques used, we used the following libraries and tools:

1. `NetworkX': For constructing and analyzing graphs, particularly for stability analysis.
2. Pandas and Numpy: For data processing and manipulation.
3. scikit-learn: For building machine learning models to predict the likelihood of war based on alliances and graph properties. [3]

This is a brief timeline of the steps followed to complete this project.

1. Data Processing
2. Graph Construction
3. Stability Analysis: Applying the rules and identifying stable configurations.
4. Machine Learning for War Prediction: Using features derived from the graph such as centrality measures, edge density, and community structure, models were trained to predict the likelihood of alliance changes based on historical data.

Exploring machine learning models to use was a bit challenging. We shortlisted three potential methods:

1. Binary classifier/Logistic Regression: Simplistic binary outcome.
2. Support Vector Machines: Can capture non-linear relationships in high-dimensional data, suitable for complex features like religion and diplomacy.
3. Multiple regression: Has potential for predicting the strength or likelihood of alliances.

Based on our exploratory analysis between different models, we understood that a simple logistic regression was the smart choice considering the time we had, the complexity of the data, and the exploration we had done into SVMs and Multiple Regression.

Data Source

In this study, the Correlates of War (COW) Datasets were used [4]. In particular, we used Version 4 of the Alliance Data [5], which has data of all defense, entente, and non-aggression alliance agreements from 1860 to 2007. The scope of this project entails data from 1860 to 1918, i.e., until the First World War. The data is publicly available and widely recognized in international relations research. There are a few quirks in the data set: there are more countries than are relevant, which is why we analyzed the number of graph components instead of the number of complete graph components. The data was preprocessed to filter relevant alliances, convert dates into numeric formats, and handle missing or incomplete data.

There was a lot of reformatting and trimming that had to be done. Country latitudes and longitudes were used for geographical graphing. We converted the dates from datetime format to numerical codes.

Results

We were able to predict alliance shifts with up to 60% accuracy using post-WWI data. Predicting alliance stability, however, was something we were not very successful at.

Discussion

We had two primary issues when using graph-based metrics:

1. Certain graphs had a tendency to cycle between two states.
2. We ended up with one complete graph most of the time. This does not happen often in the real world. This results in 0% accuracy.

Machine learning was slightly better with higher accuracy. We always knew that we would not get a 100% accuracy when compared to ground truth data due to the sheer complexity and intersectionality of the data.

Some general challenges in the problem itself are as follows:

1. Graph Complexity: Challenge in accurately detecting stability in large graphs, we could not use the metrics we wanted with accuracy due to the large graph sizes. Future projects could use clique identification: we did not have time to implement that since it was not our initial focus.
2. Class Imbalance: Possible imbalance between war and non-war instances in data.
3. Accuracy: Coping with low accuracy will be difficult. We will need to add more predictors to the model in order to streamline prediction as war is a very multidimensional concept.
4. Broad Assumptions: This was always going to limit applicability.

We also had problems of our own making:

1. We ended up with a lot of spaghetti code.
2. We identified alliance flips instead of formation and maintenance, making the code extremely convoluted.
3. The complexity of the project hurt our communication ability. We were unable to meet as an entire group often but we met in smaller groups depending on what we were working on. Unfortunately, we underestimated how strongly correlated the graph and the machine learning part would be leading to synchronization issues.

Conclusion

Success in this project depends on perspective:

1. In predicting war, we had a 60% accuracy, using only graph relations and no other context.
2. In predicting alliance stability, which was not our primary goal, we used graph metrics alone. We were terrible at this.

References

[1] Rai, Khushwant (2020). The math behind Logistic Regression. Accessed on Novermber 16, 2024 from https://medium.com/analytics-vidhya/the-math-behind-logistic-regression-c2f04ca27bca

[2] PBS Digital Studios. (2017). Network Mathematics and Rival Factions. (June 2017). Accessed on November 10, 2024 from https://www.pbs.org/video/network-mathematics-and-rival-factions-infinite-series-ijmbu2/

[3] https://scikit-learn.org/

[4] COW War Data, 1816 – 2007 (v4.0): Sarkees, Meredith Reid and Frank Wayman (2010). Resort to War: 1816 – 2007. Washington DC: CQ Press. Accessed on November 5, 2024 from https://correlatesofwar.org/data-sets/

[5] Gibler, Douglas M. (2009). International military alliances, 1648-2008. CQ Press.