# Understanding the Basics of Mathematics for Machine Learning

In this article, we will be Understanding the basics of mathematics for Machine Learning.

## Introduction

Artificial Intelligence, Deep Learning/Machine Learning, Data Science, etc. technologies are becoming more popular now-a-days. But many people don’t know what are the skills required for learning them. Modern Data Science techniques, including Machine Learning, are mainly based on mathematics . The knowledge of programming skills, analytics and a curious mindset about data will inevitably be necessary to become an effective Data Scientist.

Mathematics is very important for machine learning, for example, classification, clustering, regression analysis, and dimensionality reduction are among the fundamentals of machine learning tools used in real-life applications. It is important to understand mathematical concepts such as vectors, sets and matrices for all these tasks and how these concepts can be used for data manipulation.

However, there are many more areas that need to be understood at the least at an introductory level for effective machine learning: multivariate calculus, stochastic process, numerical methods, optimization techniques, dynamical systems and differential equations.

But, not all of these concepts are strictly needed and will depend on the particular problem at hand. In fact, in many of the situations a really good understanding of linear algebra or even just some basic knowledge is more than enough to achieve good results when implementing machine learning algorithms. Simultaneously , you will get an advantage over your competitors if you have a good understanding of the mathematical machinery behind the cool machine learning /data science algorithms.

The mathematics is important for many reasons for machine learning below are some of them

• Choosing the right algorithm involves taking into consideration of factors such as accuracy, training time, number of parameters, model complexity, and number of features
• Setting parameters and choosing strategies for validation
• Helps to identify underfitting and overfitting by understanding the trade-off between bias and variation
• Choosing intervals and uncertainty estimations that are appropriate

## Applied Mathematics

Mathematics is quite an important skill in the arsenal of a Deep Learning engineer. It is the first major skill on our list. Mathematics have many uses in Deep Learning. Various mathematical formulas are applied in selecting the correct Deep Learning algorithm for your data, and also used to set parameters, approximate confidence levels. Algorithms of deep learning are the applications which are derived from procedures of statistical modeling and so it is very easy to understand them if you got a strong foundation in Mathematics. Linear algebra, multivariate calculus, statistics, probability, distributions like Poisson, normal, binomial, etc. are some of the important topics in mathematics. Some knowledge of Physics concepts also apart from mathematics can also be beneficial if you want to become a Deep Learning engineer.

## What level of mathematics do you need?

Understanding an interdisciplinary domain such as Machine Learning is especially a question of how much math is required, and how much math is necessary to comprehend these techniques. Answers to this questions is multifaceted and depend on the level and interests of the individual. Numerical formulations of Machine Learning, along with theoretical advancement, are at present being researched, with some researchers following more advanced methodologies.

The required math background includes

• Linear Algebra – vectors and matrices
• Probability Theory – random variables
• Statistics – sampling distributions

## Linear Algebra

Understanding of optimization methods used for machine learning requires knowledge of concepts such as Principal Component Analysis (PCA), Eigen decomposition of a matrix, Symmetric Matrices, Projections, Singular Value Decomposition (SVD), Orthogonalization & Orthonormalization, LU Decomposition, Matrix Operations, QR Decomposition/Factorization, Eigenvalues & Eigenvectors, Vector Spaces, and Norms.

Also understanding of vector operations like addition, subtraction and scalar multiplication are crucial for calculating inner product between vectors, which in turn is a necessary tool when building models used for classification tasks. Linear algebra also provides a strong foundation for interpreting higher order correlation within data points like as obtained from high dimensional datasets,  by drawing scatter plot with multiple variables or figuring out how the underlying distribution will look like.

## Probability Theory and Statistics

Machine Learning and Statistics are not diametrically opposed disciplines. Concepts include Combinatorics, Random Variables, Variance and Expectation, Probability Rules & Axioms, Bayes’ Theorem, Conditional and Joint Distributions, Standard Distributions – Bernoulli, Binomial, Multinomial, Uniform, and Gaussian; Moment Generating Functions, Maximum Likelihood Estimations (MLE), Prior and Posterior, Maximum a Posteriori Estimations (MAP), and Sampling Method.

Probability theory provides the mathematical and conceptual framework for describing uncertainty in a given dataset. The Bayesian framework is the most widely used approach, as it enables us to quantify how certain we are about our model predictions by linking them with assumptions regarding the world distribution that generated this dataset. And, statistics gives precise formulae for evaluating precisely what degree of confidence we can have on any machine learning classification techniques based on empirical observation such as cross-validations . Parallel concepts which is a probabilistic models build on including random variables and their probability distributions, that together constitute the central pillar for representing uncertainties . Additionally , it is often helpful to work with joint probability distribution ,basically a correlation between different instances , especially when modeling multi-class problems like categorizing images into different categories of objects .

## Multivariate Calculus

Differential and Integral Calculus, Vector-Valued Functions, Directional Gradient, Partial Derivatives, Hessian, Jacobian, Laplacian, and Lagrangian Distribution are some of the subjects covered in Multivariate Calculus.

Multi-variate calculus, is an extension of singled variable differential and integral calculus concepts, is important to model functions with multiple dimensions like images or basically any high dimensional dataset features. Furthermore, it is a necessity when constructing models based on optimization techniques for machine learning problems such as logistic regression for multi-class classification, that are heavily based on first principles in mathematics and often involving derivatives but can provide accurate results through the explicit minimization of a function.

## Algorithms and Complex Optimizations

Understanding of computational efficiency and scalability of Data science/ Machine Learning Algorithms, along with leveling up sparsity in our datasets, is crucial.

Data structures such as Binary Trees, Heaps, Hashing, Stacks, and so on; Dynamic Programming, Randomized & Sublinear Algorithms, Graphs, Gradient/Stochastic Descents, and Primal-Dual techniques are necessary.

## Miscellaneous Mathematics

This category consists of any Math subject which are not included in the four primary categories listed above.

Some of them are real and Complex Analysis – Sets, Sequences, Topology, and Information Theory including Entropy, Information Gain; Metric Spaces, Single-Valued and Continuous Functions, Limits, Fourier transforms, Cauchy Kernel, Function Spaces, and Manifolds.

## Conclusion

Machine Learning is used in almost every field these days and becoming more and more widespread. Whether be it in medicine, automobiles, cybersecurity, etc. all fields are exploring the machine learning capabilities. Learning more about Machine Learning and becoming a Machine Learning Engineer is a great idea and very wise move in career !

So, start learning all these skills, so you can enhance your capabilities and bag your dream job. It usually takes about 3 to 4 months to learn the mathematical concepts and put them in practical use. These were some basics of mathematics for Machine Learning.