Reading An Introduction To Statistical Learning: Day 1

(This post is part of my 20 Minutes of Reading Every Day project. My current book of choice is An Introduction to Statistical Learning. I skipped the Preface, and went directly to Chapter 1: Introduction.)

What is Statistical Learning?

Consider a function f that maps X1, X2,…,Xp (also known as independent variables, features, or predictors) to Y (a.k.a.: output, response, or dependent variable). This relationship can be written in a very general form:

I think Chapter 1 can be skipped. The only interesting thing is the premises on which the book is based:

  1. Many statistical learning methods are relevant and useful in a wide range of academic and non-academic disciplines. So the book is presenting the methods that are most widely applicable.
  2. There is a nice balance between knowing the intricate details of every single building blocks of statistical learning, vs. knowing enough to know which ones would works best in which scenarios. While the former might make you better at stat learning, the point is that you don’t have to wait until you’ve reached that before you can create stuff and solve problems. This covers premise 2 and 3.
  3. It comes with lab problems. Which is nice to cement your understanding. I’m not sure if I’ll have the time to do them along with this 20-minute reading project though!

Conventions for Notation

Knowing this in advance will make going through the book easier, so I went through this. Without further ado:

  • n: the number of observations / distinct data points in the sample
  • p: the number of variables available for use in making predictions
  • xij is the value of the jth variable of the ith observation, where i = 1, 2,…, n, and j = 1, 2,…, p.
  • X is then an n * p matrix.
  • xi then represents the ith observation containing the p variable measurements.
  • xj is a vector that contain n values of the jth variable.
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