Every day, computational fields like machine learning, artificial intelligence, neuroscience, cryptography, etc. are making great progress. Anyone pursuing a career in all such fields might be looking for a solid foundation. If we dig deeper, we often trace back to the Queen of Science- Mathematics.
How to learn mathematics for machine learning
To learn mathematics for machine learning, it is recommended to follow a structured approach that covers the essential topics. Here are some key topics that you should focus on:
- Linear Algebra: Linear algebra is the foundation of machine learning. You should have a good understanding of matrix operations, vector spaces, eigenvalues and eigenvectors, and linear transformations.
- Calculus: Calculus is essential for understanding optimization algorithms that are used in machine learning. You should have a good understanding of derivatives, integrals, and optimization techniques such as gradient descent.
- Probability and Statistics: Probability and statistics are critical for understanding uncertainty and making probabilistic predictions in machine learning. You should have a good understanding of probability distributions, hypothesis testing, and statistical inference.
- Optimization: Optimization is at the heart of many machine learning algorithms. You should have a good understanding of convex optimization, gradient descent, and stochastic gradient descent.
- Algorithms and Complexity: Finally, you should have a good understanding of algorithms and their complexity. You should be familiar with algorithmic complexity, big-O notation, and the time and space complexity of different algorithms.
To learn these topics, you can start with online courses or books that cover these subjects. It is essential to practice solving problems and implementing algorithms to gain a deeper understanding of the concepts. Additionally, working on machine learning projects and participating in online communities can help you develop practical skills and gain exposure to real-world applications of machine learning.
How to learn it intuitively
To understand the intuition of the mathematics behind machine learning algorithms, it is important to first have a strong foundation in the underlying mathematical concepts. Once you have a good understanding of linear algebra, calculus, probability, and statistics, you can begin to develop an intuition for how these concepts are used in machine learning.
Here are some tips to help you understand the intuition of the mathematics behind machine learning algorithms:
- Visualize the data: Visualization is an essential tool for understanding the patterns and relationships in data. Plotting the data and looking for patterns can help you develop an intuition for how the data is distributed and what features may be important for making predictions.
- Break down the algorithms: Try to break down the machine learning algorithms into their individual components and understand how each component works. For example, in linear regression, you can understand how the cost function is minimized using gradient descent to find the optimal values of the parameters.
- Work through examples: Working through examples can help you understand how the algorithms work in practice. Try implementing the algorithms in code and experimenting with different parameters and settings to see how they affect the results.
- Focus on the big picture: Understanding the mathematics behind machine learning algorithms is important, but it is also important to focus on the big picture. Understand the problem that the algorithm is trying to solve, the data that is being used, and the potential applications of the algorithm.
- Read and discuss with others: Reading papers and discussing the mathematics behind machine learning algorithms with others can help you gain new insights and perspectives. Join online communities or attend local meetups to connect with other machine learning enthusiasts.
By following these tips and practicing regularly, you can develop an intuition for the mathematics behind machine learning algorithms and gain a deeper understanding of how they work.
A solid foundation of the math concepts will be useful in not only understanding today’s technology but also let you create tomorrow’s. The huge interest in data science, machine learning, and artificial intelligence attracted people from multiple disciplines into these fields. There are a good number of resources freely available on the internet for them on the math foundations.
This is a curated list of some of my favorite resources.
- Essence of Calculus by Grant Sanderson
- Essence of Linear Algebra by Grant Sanderson
- Math Better Explained YouTube
- Multivariable Calculus by Grant Sanderson
- Crazy Muse YouTube
- Mirror Neuron MML
- Highlights of Calculus, Gilbert Strang
- Neuroscience Supplements by Rich Pang
- Coursera Mathematics for Machine Learning Linear Algebra
- Coursera Mathematics for Machine Learning Multivariate Calculus
- Coursera Mathematics for Machine Learning PCA Machine Learning
- CBMM Tutorial Linear Algebra by Joe Olson
- CBMM Probability Tutorial Andrei Barbu
- Introduction to Higher Mathematics by Bill Shillito
There are plenty of other resources. But these are the ones I have gone through and liked the most. If you are a visual person like me and prefer a mix of visuals, intuitions, and fundamental ideas, I am sure you will like these.