Essential Mathematics for Machine Learning

In this page, We will learn about Essential Mathematics for Machine Learning | Why to learn Mathematics for Machine Learning? | Linear Algebra for Machine Learning | Calculus for Machine Learning | Probability in Machine Learning | Statistics in Machine Learning | Discrete Mathematics in Machine Learning | Algorithms and Complex Optimization | Best Way / Resources to learn Mathematics for Machine learning | Text-Books to learn Maths for Machine Learning | Online Videos to Learn Maths for Machine Learning"


Machine learning is currently one of the most popular technologies among researchers, businesses, and eager learners due to its ability to make human life easier. From Google Assistant to self-driving cars, it's being used in practically every aspect of real life. It's all about creating models that can extract key information and patterns from data automatically. However, this raises an important question: what is the magic behind ML? The solution is mathematics. Designing ML algorithms that can automatically learn from data and generate predictions relies heavily on mathematics. As a result, prior to delving into the intricacies of machine learning algorithms, it's critical to first grasp the basics of mathematics

For some people, mathematics has always been a dear friend, while for others, it has always been a source of phobia or dread. Many students around the world are uninterested in mathematics because they believe that the concepts addressed in mathematics are unrelated to practical or real-world situations. However, as machine learning becomes more popular, individuals are bec

Coming more encouraged to learn mathematics because it is directly used in the development of ML algorithms. Learning the fundamentals behind this is also highly beneficial. We will learn all of the fundamental mathematical ideas that are employed in Machine Learning in this topic.

[ Note: Working with simple machine learning models does not necessitate a thorough understanding of mathematics; rather, understanding basic math principles is sufficient to grasp how it is applied in ML. ]

Why to learn Mathematics for Machine Learning?

What is the necessity for mathematics in machine learning? This is a question that many enthusiastic learners have. Computers are faster than humans at solving mathematical problems. So, mastering mathematics in machine learning is not about solving a math issue, but rather about knowing how math is used in ML algorithms and how they work. Other arguments below show the importance of math in ML:

  • Mathematics defines the concept behind machine learning algorithms and aids in algorithm selection by taking into account accuracy, training time, model complexity, and number of features.
  • Computers interpret data differently than humans, for example, an image is interpreted as a 2D-3D matrix by a computer, which necessitates the use of mathematics.
  • We can appropriately determine the interval and uncertainty using math.
  • It aids in the selection of appropriate parameter values and validation techniques.
  • Understanding the Bias-Variance trade-off allows us to spot underfitting and overfitting problems in machine learning models.

Essential Mathematics for Machine Learning

After recognizing the importance of math, the next question is what level of arithmetic is required and what ideas must be grasped. We have provided the basic level of mathematics required for an ML Engineer/ Scientist to answer this topic. Aside from the ideas listed below, a person's math level is determined by their interest and the type of research they are conducting.

essential mathematics for machine learning 2
  • Linear algebra
  • Multivariate Calculus
  • Probability Theory
  • Discrete Mathematics
  • Statistics
  • Algorithm & Optimization
  • Others

The graph below depicts the significance of various Math principles in Machine Learning. Linear Algebra, which is commonly utilized in ML, is the most significant section of Mathematics, as indicated in the graph.

1. Linear Algebra for Machine Learning

Linear algebra is concerned with the study of vectors and the principles for manipulating them. The fundamentals of linear algebra are commonly used in the development of machine learning algorithms. It allows ML algorithms to be applied to a large number of datasets. It is capable of completing the following tasks:

  • In the domain of machine learning, it is virtually universally utilized.
  • Data can be optimized with the use of linear algebra.
  • Loss functions, regularisation, covariance matrices, Singular Value Decomposition (SVD), Matrix Operations, and support vector machine classification are all examples of its applications.
  • It's also utilized in Machine Learning's Linear Regression.

Principal Component Analysis (PCA), Singular Value Decomposition (SVD), Eigen decomposition of a matrix, LU Decomposition, QR Decomposition/Factorization, Symmetric Matrices, Orthogonalization & Orthonormalization, Matrix Operations, Projections, Eigenvalues & Eigenvectors, Vector Spaces, and Norms are some of the linear algebra topics covered in ML. Understanding the optimization approaches necessitates knowledge of these areas.

Aside from these applications, linear algebra is widely employed in neural networks and data science. In a nutshell, Linear Algebra serves as a platform or foundation for all machine learning algorithms to display their results.

Although linear algebra is a necessary aspect of mathematics for machine learning, it is not necessary to go overboard. It means that you don't need to be an expert in linear algebra to use machine learning; instead, a basic understanding of these principles is sufficient.

2. Calculus for Machine Learning

Calculus Although mathematics is an important aspect of Machine Learning, mastery of the subject is not required; rather, a fundamental understanding of the ideas is sufficient. Multivariate calculus aids in the solution of machine learning optimization issues. Different machine learning algorithms maximize an objective function in relation to a set of model parameters that influence how well a model describes the data. Optimization is the process of finding the best parameters, and multivariate calculus aids in solving optimization problems in the ML model. It aids in model optimization and yielding good outcomes.

In algorithm training and gradient descent, multivariate calculus is applied. Derivatives, divergence, curvature, and quadratic approximations are all significant ideas in multivariate calculus that we must master and apply.

The following are some of the most important aspects of multivariate calculus:

  • Partial Derivatives
  • Vector-Values Functions
  • Directional Gradient
  • Hessian, Jacobian
  • Laplacian and Lagrangian Distribution.

3. Probability in Machine Learning

Probability is an important and fascinating aspect of mathematics that determines the likelihood of an event occurring. The higher an event's probability, the more likely it is to happen. Machine learning also aids in the prediction of future events. To successfully work with an ML prediction and modeling project, probability is essential. It also aids hypothesis testing and distributions like the Gaussian distribution and the Probability density function.

The following are some key probabilistic notions to be aware of:

  • Joint, Marginal, and Conditional Probability,
  • Probability Distributions (Discrete, Continuous),
  • Density Estimation
  • Maximum Likelihood Estimation
  • Regression with Maximum Likelihood
  • Bayes Theorem, etc.

4. Statistics in Machine Learning

Statistics aids in the derivation of logical conclusions from data. It is an essential idea for any machine learning engineer or scientist to grasp in order to comprehend the operation of classification algorithms such as logistic regression, distributions, discrimination analysis, and hypothesis testing in Machine Learning. It aids in the completion of the following tasks:

  • It is a set of tools that assists in determining the goal from the facts and information available.
  • Statistics aids in the comprehension of data and the transformation of sample observations into useful knowledge.
  • There is no system in the world that has perfect data stored and accessible whenever it is needed. Data anomalies, such as incomplete or corrupted data, exist in every system. In such difficult situations, statistical notions will be your best friend.
  • It may be used to answer queries like "Who scored the highest and lowest in a cricket tournament?" "Which technology is on-trend in 2021?" and many others.

The following are some basic statistics ideas that are required for machine learning:

  • Combinatorics
  • Axioms
  • Bayes'Bayes' Theorem
  • Variance and Expectation
  • Random Variables
  • Conditional and Joint Distributions.

5. Discrete Mathematics in Machine Learning

Discrete mathematics is the study of mathematical concepts that are based on discrete (non-continuous) numbers, most commonly integers. Algorithms, programming languages, cryptography, software development, and other industries all benefit from discrete mathematics.

Discrete mathematics is necessary in many situations in machine learning and AI. A neural network, for example, can have.56 nodes and integer number of nodes and interconnections. A discrete element is necessary in such circumstances, necessitating discrete mathematics. For machine learning, graph structure and graph algorithms are essential discrete mathematics subjects.

Only the essentials of discrete mathematics are required for most ML applications. At the same time, you'll need a discrete mathematics book if you wish to work with graphical models, relational domains, structured prediction, and so on. However, most of the ideas are addressed in college for science graduates.

6. Algorithms and Complex Optimization

To better understand the computational efficiency and scalability of machine learning systems, optimization methods are required. The understanding of data structures on a conceptual level (Binary Trees, Hashing, Heap, Stack, etc.), Dynamic Programming, Randomized & Sublinear Algorithm, Graphs, Gradient/Stochastic Descents and Primal-Dual methods are needed.

Best Way/Resources to learn Mathematics for Machine learning

Learning math for machine learning is not difficult because there are a variety of resources available, such as books, online courses, and various blogs. All of these resources provide a wealth of information on various arithmetic topics. However, because each site is useful for specific ideas, we've compiled a list of all the essential resources that will assist you in learning math in a more efficient and straightforward manner.

1. Text-Books to learn Maths for Machine Learning

  • One of the best books to start your mathematical journey for machine learning is Mathematics for Machine Learning by Marc Peter Deisenroth. The practical applications of the algorithms, as well as the arithmetic that underpins them, are thoroughly presented in this book. The topic of machine learning's core mathematics has been described in the greatest possible way. This link will take you to a page where you can download the book.
  • Jay Dawani's book Hands-on Mathematics for Deep Learning is another resource for advanced math ideas that aid in the understanding of sophisticated machine learning algorithms and deep learning models. A basic introduction to linear algebra, calculus, probability, and statistics is also included in this book. The mathematics of multilayer perceptron, convolutional neural networks (CNN), and recurrent neural networks are all explained in length in the second version of the book (RNN). It also covers important topics like regularization (L1 and L2 norms), dropout layers, and more.

1. Online Videos to Learn Maths for Machine Learning

  • Khan Academy
    Khan Academy is a well-known online resource that offers free math and science courses with excellent explanations. You may easily study diverse ideas of mathematics such as linear algebra, probability and statistics, multivariable calculus, and optimization by watching these videos.
  • Udacity
    Udacity's Introduction to Statistics is another free video resource for learning the core ideas of statistics required for Machine Learning and Data Science.
  • Multivariate Calculus by Imperial College London:
    Imperial College London has created a YouTube series that explains some multivariate calculus ideas and how they're used in various ML algorithms. If you want to take the whole Machine Learning mathematics course, you'll have to sign up with Coursera; however, Imperial College London has made the Multivariate calculus available for free to all interested students.

Conclusion

One of the most significant aspects of Machine Learning is mathematics. How much math you need to study, on the other hand, is entirely dependent on what you want to learn and how deep you want to delve into that field. It means that while a basic understanding of Maths concepts (as covered in college) is sufficient for constructing simple ML models, you will also need to grasp the maths underlying them if you wish to develop complicated models and get into advanced concepts. It will take 3-4 months to learn math and put it into practice using machine learning techniques.