Mathematical Foundation for Machine Learning

Learning for human is very easy and we don't need any kind of algorithm or huge datasets. We can simply recognize, represent and understand real world. Our brain is capable of processing sensory inputs from our sense organs and visualize them. Instead, it is very hard for computer to understand the same things that are very common to us. For example, computer sees only 1s and 0s in an image of cat and it doesn't know what that image contains. That's why, math is very essential for machine to represent real world scenario and manipulate the data.

Machine Learning is all about creating an algorithm that can learn from data to make a prediction. Writing algorithms for Machine Learning is difficult and requires extensive programming and mathematical knowledge. Whether it is to gather and manipulate data or to learn and make prediction, Machine Learning is all about maths.

Mathematics in Machine Learning

The main four math disciplines required for Machine Learning are:
  • Statistics
  • Calculus
  • Linear Algebra
  • Probability Theory

Statistics

Statistics acts as a collection of techniques that extract useful information from data. It's a tool for creating an understanding from a set of numbers. Statistical inference is the process of making a prediction about a larger population of data based on a smaller sample.
Ultimately, Statistics is at the core of everything. Mean, Standard Deviation, Correlation, Regression are few essential statistical methods.

Calculus

Calculus tells us how to learn and optimize our Machine Learning model. Calculus is the study of change which also helps us find the direction of change. Gradient Descent optimization algorithm is the most common implementation of calculus in Machine Learning.

Most common topics are:
  • Derivatives
  • Integrals
  • Gradients

Linear Algebra

Linear algebra is used in Machine Learning to describe the parameters and structure of different machine learning algorithms.It gives set of operations to perform on matrices and vectors. Having Linear Algebra knowledge is helpful to understand how neural networks are put together and how they are operating.
Linear algebra makes running Machine Learning algorithms feasible on huge datasets.

Most common topics are:
  • Scalars, Vectors, Matrices, Tensors
  • Eigen Values and Eigen Vectors

Probability Theory

Probability theory is the branch of mathematics concerned with probability. Probability helps predict the likelihood of  event occurring in an experiment. During classification task, a trained ML model predicts the probability of an instance to be in any specific class.

Consists of topics such as:
  • Discrete Distribution
  • Conditional Probability

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