# 1 Automated Syllabus of Math Papers

Built by Rex W. Douglass @RexDouglass ; Github ; LinkedIn

Papers curated by hand, summaries and taxonomy written by LLMs.

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# 2 Graph theory

## 2.1 Directed Acyclic Graph

• Consider the underlying causal mechanisms and context when analyzing data, as this enables better interpretation and generalization of results beyond statistical associations alone.

• Carefully consider the causal relationships between variables and avoid adjusting for variables that are descendants of an intermediate variable, as doing so can introduce bias into estimates of causal effects.

• Utilize directed acyclic graphs (DAGs) to identify and categorize effect modification in causal relationships, distinguishing between direct effect modification, indirect effect modification, effect modification by proxy, and effect modification by a common cause.

## 2.2 Graph

• Adopt an encoder-decoder framework when working with dynamic graphs, where the encoder generates embeddings for nodes and relationships, and the decoder uses those embeddings to make predictions or inferences about the graph structure or behavior.

## 2.3 Graph Theory

• Consider using a novel estimator for linear models with multi-way fixed effects, which involves solving a linear system on a weighted graph using recent advances in spectral graph theory, resulting in a nearly-linear time estimator that performs well with large datasets and high-dimensional fixed effects.

## References

Abraham, Ittai, and Ofer Neiman. 2012. “Using Petal-Decompositions to Build a Low Stretch Spanning Tree.” Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, May. https://doi.org/10.1145/2213977.2214015.
Howards, P. P., E. F. Schisterman, C. Poole, J. S. Kaufman, and C. R. Weinberg. 2012. “"Toward a Clearer Definition of Confounding" Revisited with Directed Acyclic Graphs.” American Journal of Epidemiology 176 (August). https://doi.org/10.1093/aje/kws127.
Kazemi, Seyed Mehran, Rishab Goel, Kshitij Jain, Ivan Kobyzev, Akshay Sethi, Peter Forsyth, and Pascal Poupart. 2019. “Representation Learning for Dynamic Graphs: A Survey.” arXiv. https://doi.org/10.48550/ARXIV.1905.11485.
Pearce, Neil, and Debbie A Lawlor. 2016. “Causal Inference—so Much More Than Statistics.” International Journal of Epidemiology 45 (December). https://doi.org/10.1093/ije/dyw328.
VanderWeele, Tyler J., and James M. Robins. 2007. “Four Types of Effect Modification.” Epidemiology 18 (September). https://doi.org/10.1097/ede.0b013e318127181b.