Math in the Real World: Tests, Simulations, and More
The best writing on math and stats pulls off a difficult feat: it takes lofty concepts and complex formulas and connects them to the practical challenges data professionals tackle in their daily jobs.
Some data scientists love sinking their teeth into new math topics, while others tiptoe into this field with caution, if not downright reluctance. No matter where you find yourself on this spectrum, we think you'll enjoy our selection of articles this week. From the inner workings of A/B tests to graph theory and statistical experiments, they effortlessly blend the theoretical and the pragmatic, the abstract and the concrete. Let's dive in.
- Whether you're new to Monte Carlo simulations or need a solid refresher, Sydney Nye‘s debut TDS article is an accessible deep dive into a statistical technique that "allows us to place strategic bets in the face of uncertainty, making probabilistic sense of complex, deterministic problems."
- Graph theory has been central to machine learning research for some time now, but for people outside that community it might still appear dauntingly hermetic. Hennie de Harder offers a beginner-friendly primer on what graphs are, how they function, and how data scientists can leverage their power to solve intricate real-world problems.
- If you hadn't devoted much thought to differential equations since high school, here's your chance to reexamine them from a new angle: Shuai Guo‘s series on physics-informed neural networks (PINN) is back with an installment devoted to differential equations and how they "provide insights into system dynamics and allow us to make predictions about the system's future behavior."
- For a hands-on take on permutation tests and how they can supplant more traditional formula-based statistical methods, follow along as Pan Cretan explains how to go about designing experiments with resampling. (Readers who came to Data Science from a less math-focused background will find this one especially useful!)
- Our final weekly highlight returns to the very same Monte Carlo simulations with which we started, but harnesses their power to a different end. Ida Johnsson, PhD shares a helpful introduction to A/B testing: it provides clear definitions of the statistical concepts involved, and focuses on the process of evaluating the performance of tests using Monte Carlo simulations.
Our other recommended reads this week aren't quite Math-free, but they nonetheless open up the space for fascinating conversations on other essential topics.
- In a methodical and timely study, Yennie Jun explores gender biases in large language models' built-in historical knowledge.
- Missed ICML 2023? Michael Galkin is here to help us catch up with a detailed recap of recent advances and emerging trends.
- Everybody loves complaining about data cleaning, but Vicky Yu‘s concise guide can help you streamline the process so it becomes less tedious.
- Transformers meet jazz chords in Francesco Foscarin‘s debut TDS post, which presents a data-driven approach to tree-based music analysis.
- Hans van Dam brings together mobile-app development and LLMs with a hands-on tutorial that leverages GPT-4 functions to navigate an app's Graphical User Interface (GUI).
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Until the next Variable,
TDS Editors
