Mathematics for Machine Learning Archive

The Fourier Transform and Its Math Explained From Scratch

In this post we will build the mathematical knowledge for understanding the Fourier Transform from the very foundations. In the first section we will briefly discuss sinusoidal function and complex numbers as they relate to Fourier transforms. Next, we will develop an understanding of Fourier series and how we can approximate periodic functions using

How to Find Vector Projections

In this post, we learn how to perform vector projections and scalar projections. In the process, we also look at the basis of a vector space and how to perform a change of basis. What is a Vector Projection? A vector projection of a vector a onto another vector b is the orthogonal projection

T-Tests: A comprehensive introduction

In this post, we define the t-test in statistics, explain what different t-tests exist, and demonstrate by example how we can use them to find the differences between means in various scenarios. What is a T-Test? The t-test tests the significance of the difference of measured means. Differences can be measured within the same

What Math is Required for Machine Learning?

You are probably here because you are thinking about entering the exciting field of machine learning. But on your road to mastery, you see a big roadblock that scares you. It is called math. Perhaps your last math class was in high school and you are from a non-technical background. Perhaps you have worked

Chi-Square Test for Independence and Goodness of Fit

In this post, we will introduce the chi-square test. We discuss how to calculate a chi-square statistic, how to perform a chi-square test for independence, and finally how to use the chi-square test for goodness of fit. What is a Chi-Square Test? Pearson’s chi-square test in statistics measures the difference between an observed value

Type 1 and Type 2 Error

When you are testing hypotheses, you might encounter type 1 and type 2 errors. Identifying them and dealing with them is essential for setting up statistical testing scenarios. They also play a huge role in machine learning. What is a Type 1 Error in Statistics? When you reject the null hypothesis although it is

Z Score Table for Confidence Intervals

Negative Z Table These are z-values to the left of the mean. Positive Z Table These are z-values to the right of the mean. Two-Sided Z-Score Table These are z_Value to the left and the right of the mean.

Student’s T-Distribution

In this post we introduce student’s t-distribution and learn how to construct t-confidence intervals. The t distribution is usually applied when you want to estimate the mean of normally distributed data but the sample size is small and you don’t know the population standard deviation. Like the Chi-Square distribution, it relies on degrees of

Chi-Square Distribution Table

Looking for an intuitive explanation of the Chi-Square distribution? Check out the blog post I wrote on the Chi-Square distribution and degrees of freedom. For a step-by-step explanation on Chi-Square testing, check out my post on the Chi-Square test for independence and goodness of fit. This post table is part of a blog post