Mathematics for Machine Learning
Nowdays people are becoming passionate about learning data science, artificial intelligence, machine learning and many more techniques in artificial intelligence domains (why should not afterall this is field has no end!)
We may change many fields or we can say we all are working in different fields but the one factor which is bonding us together is Mathematics. Machine is also not an exception for that! We all know Mathematics is a branch of science, which deals with numbers and their operations. It involves abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects, solving of problems etc.
Machine Learning theory is a field that intersects statistical, probabilistic, computer science and algorithmic aspects arising from learning iteratively from data and finding hidden insights which can be used to build intelligent applications. Despite the immense possibilities of Machine and Deep Learning, a thorough mathematical understanding of many of these techniques is necessary for a good grasp of the inner workings of the algorithms and getting good results.
Now a question may pop up in your mind is exactly what level of maths needed to understand machine learning techniques. The answer to this question is “depends on the level and interest of the individual.”
Before starting machine learning you must be familiar with some branches of mathematics including linear algebra, probability, calculus, etc
“Linear Algebra is the mathematics of the 21st century” In ML, Linear Algebra comes up everywhere. Topics such as Principal Component Analysis (PCA), Singular Value Decomposition (SVD), Eigendecomposition of a matrix, LU Decomposition, QR Decomposition or Factorization, Symmetric Matrices, Orthogonalization & Orthonormalization, Matrix Operations, Projections, Eigenvalues & Eigenvectors, Vector Spaces and Norms are needed for understanding the optimization methods used for machine learning. The amazing thing about Linear Algebra is that there are so many online resources.
Some study material and courses I’ll suggest for linear algebra required for machine learning are:
1. https://www.coursera.org/learn/linear-algebra-machine-learning
2. Linear Algebra
3. Linear Algebra — Foundations to Frontiers by Robert van de Geijn, University of Texas.
4. Foundations to Frontiers on edX
2. Probability Theory and Statistics
Machine Learning and Statistics aren’t very different fields. Some of the fundamental Statistical and Probability Theory needed for ML are Combinatorics, Probability Rules & Axioms, Bayes’ Theorem, Random Variables, Variance and Expectation, Conditional and Joint Distributions, Standard Distributions (Bernoulli, Binomial, Multinomial, Uniform and Gaussian), Moment Generating Functions, Maximum Likelihood Estimation (MLE), Prior and Posterior, Maximum a Posteriori Estimation (MAP) and Sampling Methods.
You can go for one of this courses:
1) https://www.coursera.org/browse/data-science/probability-and-statistics
2) Probability & Statistics
3) All of statistics: A Concise Course in Statistical Inference.
Some of the necessary topics include Differential and Integral Calculus, Partial Derivatives, Vector-Values Functions, Directional Gradient, Hessian, Jacobian, Laplacian and Lagragian Distribution.
Here I listed some online courses : (you can go any one of them or can go with another which you know)
1. Multivariable Calculus
2. https://www.coursera.org/learn/multivariate-calculus-machine-learning
3. https://nptel.ac.in/courses/111/107/111107108/
4. Algorithms and Complex Optimizations
This is important for understanding the computational efficiency and scalability of our Machine Learning Algorithm and for exploiting sparsity in our datasets. Knowledge of data structures (Binary Trees, Hashing, Heap, Stack etc), Dynamic Programming, Randomized & Sublinear Algorithm, Graphs, Gradient/Stochastic Descents and Primal-Dual methods are needed.
You can go for this course Optimization
5. Others
This comprises of other Math topics not covered in the four major areas described above. They include Real and Complex Analysis (Sets and Sequences, Topology, Metric Spaces, Single-Valued and Continuous Functions, Limits, Cauchy Kernel, Fourier Transforms), Information Theory (Entropy, Information Gain), Function Spaces and Manifolds.
For beginners, you don’t need a lot of Mathematics to start doing Machine Learning, you can learn the maths on the go as you master more techniques and algorithms.
Have a great learning!
