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The Mathematics Behind Machine Learning: What You Need to Know?

Last updated:
10th Mar, 2021
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The Mathematics Behind Machine Learning: What You Need to Know?

Machine learning is a division of AI that focuses on building applications by processing available data accurately. The primary aim of machine learning is to help computers process calculations without human intervention. This is made possible by allowing a machine to learn to mimic human intelligence via supervised or unsupervised learning methods. 

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Machine Learning is a combination of many fields which includes statistics, probability, linear algebra, calculus, and so on, based on which a machine learning model can create or be fed algorithms to improvise as per human intelligence. The more complex the application, the more complex its algorithm will be. 

From digital assistants, and smart devices to websites recommending your favourite products based on your activities online, and mobile phones notifying you of your flight schedule, machine learning-based products and tools are all around us. As our dependence on smart devices and appliances increases, so will the need for machine learning implementation. 

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To that end, in this article, we will explore the mathematical concepts required in writing machine learning algorithms and implementing them. 

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What is the Significance of Mathematics in Machine Learning?

Machine learning applications provide analytics and insights gleaned from available data which contribute to actionable decision-making in businesses. Since machine learning revolves around studying and implementing algorithms, it is important to bolster your mathematical skills. It helps in eliminating uncertainty and predicting data values accurately where complex data parameters and features are involved. It also aids us in better understanding the Bias-Variance trade-off. 

Mastering machine learning requires knowledge of mathematical concepts like linear algebra, vector calculus, analytical geometry, matrix decompositions, probability and statistics. A strong grasp of these helps in creating intuitive machine learning applications. 

Linear Algebra

Linear Algebra is concerned with vectors and matrices, and mostly revolves around computation. It plays an integral role in machine learning and deep learning techniques. According to Skyler Speakman, it is the mathematics of the 21st century. 

Linear Algebra is typically used by ML engineers and data scientists or researchers to build Linear algorithms, Logistic regressions, Decision trees, and Support Vector Machines.


Calculus drives machine learning algorithms. Without knowledge of its concepts, it wouldn’t be possible to predict outcomes using a given data set. Calculus helps to analyze the rate at which quantities change, and is concerned with the optimum performance of machine learning algorithms. Integrations, differentials, limits, and derivatives are a few concepts of calculus that help train deep Neural Networks


Probability in machine learning predicts the set of outcomes whereas statistics drive the favourable outcome to its conclusion. The event could be as simple as tossing a coin. Probability can be broken down into two categories: Conditional Probability and Joint Probability. Joint probability happens when the events are independent of each other, whereas conditional probability occurs when one event supersedes the other. 


Statistics focuses on the quantitative and qualitative aspects of the algorithm. It helps us to identify goals and transform collected data into precise observations by presenting it concisely. Statistics in machine learning focuses on Descriptive statistics and Inferential statistics. 

Descriptive statistics is concerned with describing and summarizing the small dataset a model is working on. The methods used here are mean, median, mode, standard deviation, and variation. The end results are presented as pictorial representations.

Inferential statistics deals with extracting insights from a given sample while working with a large dataset. Inferential statistics allow machines to analyse data beyond the scope of the provided information. Hypothesis tests, sampling distributions, analysis of variance, are some aspects of Inferential Statistics.

Apart from these, coding prowess is a crucial prerequisite for Machine learning. Expertise in languages such as Python and Java help in a better understanding of data modelling. String formatting, defining functions, loops with multiple variable iterators, if or else conditional expressions are some of its basic functions. 

As for data modelling, it is the process through which we estimate the structure of data sets and detect possible variations and patterns. To be able to make accurate predictions, one must be aware of the various properties of the collective data. 

How Can you Learn Machine Learning? 

While Machine learning is a lucrative field to get into, it requires plenty of practice and patience. Given its applications in almost every industry today, machine learning engineers are in heavy demand. 

The average salary of an entry-level engineer with a background in machine learning is Rs 686k /year. And with experience and upskilling, the potential to earn a higher salary increases exponentially. 

There are several courses available for someone who wishes to enhance their knowledge base in machine learning. It would take you a minimum of 6 months to 2 years to master the subject. 

With a minimum of a Bachelor’s Degree and one year of work experience, better yet a degree in Mathematics or Statistics, you can pursue any one of the following courses on upGrad to increase your chances of success in the field. 

  1. Advanced Certificate Program in Machine Learning and Deep Learning from IIT Bangalore (6 months) 
  2. Advanced Certificate Program in Machine Learning and NLP from IIT Bangalore (6 months)
  3. Executive PG Programme in Machine Learning & AI from IIT Bangalore (12 months)
  4. Master of Science in Machine Learning and AI from LJMU and IIT Bangalore (18 months)

All these courses offer a minimum of 240+ hours of learning and at least 5 case studies which would help you gain an in-depth understanding of machine learning and it’s various auxiliary fields. You can cover essential topics like Python, MySQL, Tensor, NLTK, statsmodels, excel, etc which form the backbone of coding. Here is a detailed look at the various upGrad courses in Machine learning so you can choose the one most suitable for you.

Join the artificial intelligence course online from the World’s top Universities – Masters, Executive Post Graduate Programs, and Advanced Certificate Program in ML & AI to fast-track your career.

Applications of Machine Learning

Machine learning plays a crucial role in our daily lives, both in the professional and personal sphere. Its analytical and intuitive capacities have the potential to drastically impact the way we carry out our daily tasks. It has proved resourceful in saving money and time for an organisation. 

While machine learning is a broad field with applications in almost every industry, here are a few most prominent examples:

  1. Image recognition is one of the most commonly used applications as it assists in face detection, thus, creating a separate database for each individual. It can be used to identify handwriting styles too. 
  2. Machine learning in the health sector has enhanced the capabilities of health care providers. It can be used in faster medical diagnosis. In many cases, AI has helped in the early diagnosis of diseases, thus, allowing doctors to suggest treatments and preventive measures that have the potential to save lives.
  3. Machine learning has major applications in the financial sector where investments, mergers and acquisitions are concerned. It assists banks and other economic institutions to make smart choices.
  4. Its effectiveness is possibly most apparent in the customer care and service industry as machine learning streamlines operations and provides solutions quickly and more efficiently.
  5. Machine learning automates tasks that would otherwise have to be performed by a human on the field. For example, if we were to consider virtual assistants, it could be as simple a task as changing the password, or evening checking your bank balance. With machine learning, it’s now possible to allocate human resources to more pressing tasks that require complicated decision-making or human touch to accomplish. 

Future Scope of Machine Learning

Even though machine learning has been around for decades, it’s application is most apparent today. The industry has yet to prosper, and improvise, which implies that the future of machine learning is bright. Most large-scale companies are already reaping the benefits of machine learning and scaling their services and products to drive growth.

Naturally, ML engineers are in heavy demand and machine learning presents itself as a lucrative career to get into. It stands to businesses the edge they need. AI has generated an estimated 2.3 million job opportunities until now. It’s been projected that, by the end of 2022, the global ML industry will grow at a CAGR of 42.2% to reach USD 9 billion.

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Here are a few top trends in machine learning: 

  1. More and more algorithms are learning toward unsupervised implementations. Businesses are investing in Quantum Computing based on these unsupervised algorithms which have the potential to transform machine learning. These contribute to analyzing and drawing meaningful insights, thus, helping businesses achieve better results that would not have been possible using classic machine learning techniques. 
  2. AI-powered robots are being deployed to carry out business operations. However, these technologies are in the nascent stage and as businesses invest in establishing an AI and ML foothold, robots will soon help increase productivity exponentially. To cite as an example, we have drones posing as powerful business tools in the consumer market where they are being put to use to accomplish commercial operations and simple tasks like delivering goods. 
  3. Machine learning algorithms support enhanced personalization. These algorithms survey potential customers’ online behaviour and send information back to the companies. The companies in turn send them products and service recommendations. These machine learning techniques help identify the likes and dislikes of customers. Through machine learning, companies give their customers what they desire, and when they desire it, which increases customer retention and attracts more business to the organization. Improved personalization is the future of machine learning. 
  4. Thanks to enhanced machine learning algorithms, mobile and web applications are now smarter than ever. Improved cognitive services allow developers to create separate databases for each client, based on visual recognition, their speech, sound, voice, and so on. 

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This brings us to the end of the article. We hope you found this information helpful!


Pavan Vadapalli

Blog Author
Director of Engineering @ upGrad. Motivated to leverage technology to solve problems. Seasoned leader for startups and fast moving orgs. Working on solving problems of scale and long term technology strategy.
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Frequently Asked Questions (FAQs)

1Why is homoscedasticity required in linear regression?

Homoscedasticity describes how similar or how far the data deviates from the mean. This is an important assumption to make because parametric statistical tests are sensitive to differences. Heteroscedasticity does not induce bias in coefficient estimations, but it does reduce their precision. With lower precision, the coefficient estimates are more likely to be off from the correct population value. To avoid this, homoscedasticity is a crucial assumption to assert.

2What are the two types of multicollinearity in linear regression?

Data and structural multicollinearity are the two basic types of multicollinearity. When we make a model term out of other terms, we get structural multicollinearity. In other words, rather than being present in the data itself, it is a result of the model that we provide. While data multicollinearity is not an artefact of our model, it is present in the data itself. Data multicollinearity is more common in observational investigations.

3What are the drawbacks of using t-test for independent tests?

There are issues with repeating measurements instead of differences across group designs when using paired sample t-tests, which leads to carry-over effects. Due to type I errors, the t-test cannot be used for multiple comparisons. It will be difficult to reject the null hypothesis when doing a paired t-test on a set of samples. Obtaining the subjects for the sample data is a time-consuming and costly aspect of the research process.

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