Machine learning has had the entire data science community brimming with questions regarding the framework and the hidden insights that are being used to build the intelligent applications of the future. There are immense possibilities when it comes to grasping the inner workings of algorithms related to machine learning. As mathematics is a big portion of the programming process, there are many important questions to ask and many reasons to include math in the machine learning development process.
The knowledge of mathematics is very important to understand and apply machine learning algorithms in different applications. From understanding uncertainty and intervals of prediction to choose a parameter settings with a strategy for validation, mathematics concepts help in implementing machine learning. Some of the other reasons are the selection of algorithms including choosing the right training time, complexity and accuracy and bias in variance trade-off for overfitting and underfitting with machine learning
To understand each of the above reasons, a person generally needs to have an advanced level of mathematics experience in their field. Delving into machine learning often requires a multidimensional effort and a series of mathematical formulations which can work to advance the theory and the efficiency of machine learning in the future.
Some of the main topics of mathematics that lend themselves to machine learning include:
Linear algebra: As one of the top solutions in mathematics for the 21st century, this is a type of mathematics that is so important for projections, vector spaces and norms in the future. The good news is that much of the coursework is available online through MIT courseware for free.
Multivariate calculus: Integral calculus, partial derivatives, and differential calculus can all be parts of this discipline of mathematics added to the development of machine learning.
Theory and statistics and probability: Statistics is a very different feel from machine learning, but the fundamental values of statistics are still essential for probability, adding in random variables, discovering variances and sampling with machine learning.
Complex optimizations and algorithms: This is a type of mathematics that so important for improving the efficiency of computations. Knowledge of various data structures as well as exploiting sparsity in any data set is required to properly scale and use a complex optimization within an algorithm.
Additional Topics: Other important disciplines can include continuous functions limits, information theory, real and complex analysis and sequences and function spaces and manifolds. These can all be forms of mathematics that can lead themselves beneficial to the development of new machine learning solutions.
Studying these types of mathematics can be surprisingly accessible. Gaining a basic knowledge of these mathematics topics which are required for the development of machine learning can be done through resources such as:
- The open course in machine learning by Andrew NG at Stanford Coursera.
- The Linear algebra course on EdX
- The convex optimization course from Stanford
- Larry Wasserman’s book on statistical inference.
- The Harvard Stat lectures of Joseph Blitzstein
- The Khan Academy linear algebra courses.
- Mathematics for Machine Learning Specialization by Imperial College London
- Mathematics for Machine Learning by MIT
- Data Science Math Skills by Duke University
- Intro to Inferential Statistics by Udacity
- Applications of Linear Algebra Part 1 by Davidson College (edX)
- Introduction to Mathematical Thinking by Stanford University (Coursera)
- Introduction to Linear Models and Matrix Algebra by Harvard University (edX)
These are just a few excellent starting points that you can use for starting your review and preparing accordingly for future educational programs. If you are interested in developing the future of machine learning these strategies for learning through mathematics can help with the development of software and systems that can forge a new path in machine learning for tomorrow.