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Mathematics for Machine Learning and Data Science

Deep Learning_012924A
[Deep Learning - SpringerLink]

- Overview

Mathematics is the cornerstone of any contemporary scientific discipline. Almost all modern data science techniques, including machine learning, have a deep mathematical foundation. 

It goes without saying that you absolutely need all the other intellectual jewels — programming skills, some business acumen, and your unique analytical and curiosity - about data to become a top data scientist. 

But it's always worth knowing the mechanics under the hood, rather than just being behind the wheel as someone who knows nothing about cars. So having a solid understanding of the math behind cool algorithms will give you an edge over your peers. 

Machine learning (ML) and data science use four key mathematical concepts: Statistics, Linear algebra, Probability, Calculus. Statistics are the core of every model, while calculus helps learn and optimize a model. Linear algebra is used in ML to understand how algorithms work. It involves vector, matrix, and tensor operations. Calculus uses concepts to formulate functions that are used to train algorithms.

Mathematical concepts are crucial for developing models, making predictions, and evaluating the accuracy of algorithms. Here are some mathematical disciplines that are studied for machine learning: Linear algebra, Calculus, Probability theory, Optimization.

Some fundamental statistical and probability theories needed for ML include:

  • Probability rules and axioms
  • Bayes' theorem
  • Random variables
  • Variance and expectation
  • Conditional and joint distributions
  • Standard distributions


[Alberta, Canada]

- Mathematics for Machine Learning and Deep Learning

Machine learning (ML) theory is a field that intersects statistics, probability, computer science, and algorithms to iteratively learn from data and find hidden insights that can be used to build intelligent applications. 

Despite the enormous possibilities of ML and deep learning (DL), a solid mathematical understanding of many of these techniques is necessary to get a good grasp of the inner workings of algorithms and get good results.

Four Mathematics Pillars that are required for ML:

  • Linear Algebra & Matrix
  • Probability & Statistics
  • Calculus
  • Geometry & Graph Knowledge


Here are some other mathematical concepts used in ML and DL: 

  • Discrete mathematics: This is the foundation of computer science. It involves inductive and deductive reasoning, graph theory, recursion, and algorithm complexity.
  • Linear regression: This is a linear model that establishes the relationship between a dependent variable and one or more independent variables.
  • Integral calculus: This is a major branch of calculus that deals with integrating an infinite number of infinitesimal increments to a function.
  • Principal Component Analysis: This is used to reduce the dimensionality of data.
  • Gradient descent algorithm: This minimizes an error function based on the computation of the rate of change.


- Mathematics for Data Science

Data science is a broad field that requires a lot of expertise. While math is not the only requirement for a data science career, it is often one of the most important. 

Data scientists use math to analyze and understand data. They use mathematical concepts as tools to analyze data and predict results. 

Data science is an interdisciplinary field that uses statistics, scientific computing, and algorithms to extract knowledge and insights from data. It uses techniques and theories from many fields, including mathematics, statistics, computer science, and information science. 

Data scientists use a variety of mathematical concepts, including: 

  • Linear algebra
  • Calculus
  • Statistics
  • Probability
  • Discrete math
  • Geometry
  • Linear regression


[More to come ...]


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