Wrapping Up Our ML Foundations Journey

Created in May 17, 2025

2025   ·   ML   Math   ·   ML-NYU

After completing 51 comprehensive blog posts on machine learning fundamentals, it’s time to wrap up this series. This journey has been both challenging and immensely rewarding.

There were several key motivations behind creating this content:

  1. To provide a structured approach that methodically builds intuition for a solid foundational understanding of machine learning
  2. To explain complex concepts in an accessible way that’s easy to remember and articulate
  3. To ensure mathematical rigor is maintained while keeping explanations clear and thorough
  4. To create a resource I wish I had when first learning these concepts

I believe I’ve accomplished these goals, and I’m genuinely satisfied with the outcome.

Looking back at our path:

  • We began with essential mathematical prerequisites (multivariate calculus, linear algebra, probability theory) to build a strong foundation
  • Progressed to the fundamentals of machine learning with supervised learning and empirical risk minimization
  • Explored optimization techniques through gradient descent and stochastic gradient descent
  • Examined various loss functions and regularization approaches to understand model development
  • Delved into linear models and their extensions with SVMs and margin classifiers
  • Advanced to nonlinear feature maps and kernels to tackle more complex problems
  • Investigated probabilistic modeling and Bayesian approaches for a different perspective on machine learning
  • Addressed multiclass classification methods and structured prediction
  • Introduced decision trees as our first truly non-linear classifiers
  • Concluded with ensemble methods from bagging and random forests to various boosting algorithms, culminating with gradient boosting

This progression represents a logical flow from fundamentals to advanced concepts, carefully designed to build upon each previous lesson.

I have several plans for the future:

  1. I intend to cover the foundational aspects of deep learning in a similar structured fashion, though not immediately. I will ensure this content aligns well with the machine learning material we’ve already covered.

  2. Following advice from a friend, I recognize the importance of focusing on depth in ML and practical applications. I’ll be dedicating time to projects that enhance my practical experience and will share insights as they develop.

  3. I welcome suggestions for specific topics you’d like to see broken down in this style, or if you have interesting ML ideas for collaboration. Feel free to DM me.

  4. With summer break approaching, I’ll be taking some time to rest and recharge after this challenging but highly educational semester.

I’d like to express my sincere gratitude to:

  • My professors for their excellent teaching of these complex subjects, especially Professor Mengye Ren, who taught me this course.
  • Everyone who supported me throughout this journey
  • You, the readers, for your engagement and feedback
Final Thoughts

This project began with the aim of clarifying machine learning concepts for myself and others. As we progressed from basic mathematical foundations all the way to advanced ensemble methods like gradient boosting, I hope these explanations have helped demystify machine learning and provided you with both theoretical understanding and practical insights.

The complete list of topics is available at: ML-NYU Category or This list

Until we meet again in future learning adventures, keep exploring, stay curious, and never stop learning!