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Maths for Machine Learning Specialisation

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20th Feb, 2023
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Maths for Machine Learning Specialisation

Is machine learning possible without maths? Absolutely Not. Machine learning is entirely about maths. It is an application of artificial intelligence that uses raw data, processes it, and further builds a model or conclusion. 

As imagining what an item would look like three-dimensionally just by looking at a picture. It is all about understanding and reasoning.

How is machine learning possible? Well, that’s because a lot of data is transmitted and generated every second of the day. Even Right now, when you’re reading this, some information is being developed. This data is further used for analysis, and at the end, conclusions are drawn. It is Fun, and one can relate it in our daily life by wanting to know why something works and how. There are very few who have not been impacted by artificial intelligence in today’s world. Because we encounter it in some or the other way, be it in healthcare, screen lock, photo tagging, Online Shopping etc.

Each concept learnt in this field is in some or the other way related to mathematics, either directly or indirectly.

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Maths For Machine Learning

To understand maths for machine learning, you must Excel in the following topics-

1)   Statistics

2)   Multivariate Calculus

3)   Linear algebra

4)   Probability

These are the four pillars. Let’s understand each of them in detail, as all these are equally essential to building an algorithm and solving real-life problems.

Machine Learning is all about working with data. For every modification performed on data, there is one bridge that helps us reach our goals through computation, and that is math.

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1)   Statistics-

This topic is more familiar to us than the others, which we will be covered because we have been learning this since high school, and it is the most critically important component of maths for machine learning. It is the application of probability theory and is used for drawing conclusions from the data which has been collected. It is playing with the raw data to get the findings from it.

  •   The first step is the collection of data. It is possible through 2 sources-
  • Primary source and
  • Secondary source.

This is the foundation for our further steps.

  •   The data collected is raw, and it needs some processing to make it meaningful and valuable. The data is processed, and information is extracted from it.
  •   The processed data should be represented in a manner that is easy to read and understand.
  •   Lastly, conclusions are drawn from the data collected because just numbers are not enough!

There are two types of statistics used in machine learning-

  1. A)  Descriptive statistics-

Descriptive statistics is a measure that summarises the processed data for ease of visualization, and it can be presented in a manner that is meaningful and understandable.

  1. B)   Inferential statistics-

It allows you to make conclusions based on the data taken from the population and also give reasoning.

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2)   Probability-

To start from scratch, the probability is the chance or likelihood of the occurrence of a particular event to happen. In machine learning, it is used in predicting the possibility of a specific event happening. The probability of an event is calculated as-.

P(event)= favourable outcomes/ total number of possible outcomes

Some basic concepts of probability are-

  •   Joint probability-

It is a measure that shows how much are the chances of two different events taking place simultaneously.

It is denoted by P(A∩B )-

  •   Conditional probability-

Conditional probability means the chances of some event occurring given that another event has already happened.

It is denoted by P(A|B)

  •   Bayes theorem-

It gives results on the probability of an event based on new information. It renews a set of old chances with the new one ( after adding additional information) to derive a new set of possibilities.

Bayes theorem helps us to understand the Confusion Matrix. It is also known as the error matrix in the field of machine. It is a method used for extracting the results of the performance of a classification model. A comparison is made between the actual and predicted classes. It has four outcomes-

True Positive (TP):

predicted values = predicted actual positive

     False-positive (FP):

Negative values predicted as positive

     False-negative (FN):

Positive values predicted as negative

     True negative (TN):

Predicted values = predicted actual negative

Machine learning professionals use this concept to note down inputs and predict possible outcomes.

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3)   Multivariate Calculus-

Multivariate calculus is also known as multivariable calculus. It is an intrinsic field of maths in machine learning algorithms, and without understanding this, you cannot think of going any further. It is the branch that tells us how to learn and optimize our models or algorithms. Without apprehending this concept, it is difficult to predict the outcomes from the data that has been collected.

Multivariate Calculus is divided into two types which are-

  •  Differential calculus-

Differential calculus breaks the data into small pieces to know how it works individually.

  • Inferential calculus-

Inferential calculus glues the broken pieces to find how much there is.

Some other types are Vector Values Function, Partial Derivatives, Hessian, Directional Gradient, Laplacian, Lagragian distribution.

Multivariate Calculus is mainly used in enhancing the machine learning process.

4)   Linear algebra-

Linear algebra is the backbone of machine learning. It makes running the algorithms feasible on substantial data sets. It also makes us understand the working of algorithms which we use in our daily life and help us make a better choice.

There are quite a few tasks which cannot be done without the use of linear algebra. Which are-

  •   Development of machine learning models.
  •   Operation of complex data structures.

Machine learning professionals use linear algebra to build their algorithms. Linear algebra is widely known as the mathematics of the 21st century, as many believe it will transform every industry in the future. It is a platform on which all the algorithms come together and lead to a result.

Some machine learning algorithms are fundamental and should be applied to any data problem. They are as follows-

1)   Logistic regression

2)   Linear regression

3)   SVM (Support Vector Machine)

4)   Naïve Bayes

5)   Decision Tree

6)   KNN (K- Nearest Neighbour)

7)   K- means

8)   Dimensionality Reduction Algorithms

9)   Gradient Boosting Algorithms

10) Random Forest

We need a plan for building a model because direct implementation will lead to a lot of errors. We need a high-level programming language such as Python to test our strategies and get better results than using the trial and error method, which is a very time-consuming process. Python is one of the best languages used for programming and software development.

Importance of machine learning-

Let’s think of one day without the use of artificial intelligence. Difficult, right? The applications provided have become part and parcel of our lives because of their ability to provide quick solutions to our problems and answering tedious questions effectively, efficiently and quickly. It is convenient and works as a saviour when a person is short on time. It also saves time, money and provides security. Tasks get done quickly and efficiently with not much physical movement.

Our life cannot get easier. Making payments is just a few fingertips away. Privacy is protected through face lock and fingerprint lock. Features with which we play from day to night are all because of the gift of artificial learning. Every question in the world can be answered by Siri or Google assistant. It helps us to buy the best for ourselves. For instance, while purchasing a phone, one can compare one device better than the other and the algorithm behind it. The applications of it are never-ending like, use in google maps where it uses location data from smartphones, in riding apps like ola, uber in which we fix the price of our ride and minimize the waiting time, in commercial flights to use auto-pilot, in spam filters whenever we receive an email from an unknown address while giving smart replies in gmail- it automatically suggests replies to us, and most importantly in the bank to prevent fraud and check deposits on mobile.

They are widely used in the healthcare department in machine learning; not only this, but we need maths right from sunrise to sundown because we make several transactions during a day. Our learning maths journey starts when we are in 11th and 12th grades, and when we start realizing that life is so unfair. At that time of life, you might wonder where I am going to use this math. Well, we use it here, and all the theoretical knowledge comes into practicality. The best way to get yourself fascinated in this field is by taking a machine learning algorithm and understanding why and how it works.

Not everything which is helpful comes to you quickly. You have to make efforts to achieve it. Though maths for machine learning can be complex, once you excel in it, you can not only use it for work but also implement it in your daily life to understand the working of certain things.

Many people still aren’t aware of how important it is to learn maths for machine learning as we saw some pointers on why and where we require mathematics not only in this field but also in our day-to-day life. 

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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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