Intro

Welcome to Why Is It Connected.

This tutorial is meant to explain the connections that are usually left implicit across statistics, machine learning, and computer science. Instead of teaching isolated techniques, it focuses on the underlying ideas that unify them.

Core writing principle:¶

• Each chapter should answer three questions:

  • 1. what is the concept?

  • 2. why does it matter?

  • 3. how does it connect to CS. statistics and data science?

• A strong recurring template for every chapters:

  • Big question

  • Core intuition

  • Formal view

  • Cs view

  • Statistics view

  • ML/data science view

  • Small example

  • Common misunderstanding

  • Key takeaway

Tutorial Structure¶

Part I. What data actually is¶

• Chapter1. What is Data?

• Chapter2. From Scalars to Vectors to Matrices.

• Chapter3. Variables, features, and Random Variables.

Part II The linear algebra layer¶

• Chapter4. Vectors as Points and Directions.

• Chapter5. Matrices as Transformations

• Chapter6. Projection and Approximation

• Chapter7. Least Squares and Linear Regression

Part III The statistics layer¶

• Chapter8. Distribution, Expectation, and Variance.

• Chapter9. Covariance and Correlation Structure

• Chapter10. Statistical Models as Simplifications

• Chapter11. Estimation and Maximum Likelihood

• Chapter12. Inference, Uncertainty and Interpretaion

Part IV The mulitivariate bridge¶

• Chapter13 Eigenvalues and Eigenvectors

• Chapter14 Principal Component Analysis

• Chapter15 Factor Analysis and Latent Structure

Part V The Machine Learning¶

• Chapter16 Loss Function and Learning Objectives

• Chapter17 Optimization and Gradient Decent

• Chapter18 Regularization and Generalization

Part VI THe computer Science¶

• Chapter19 Algorithms, Scale and Computation

• Chapter20 Similarity, search and Data System

• Chapter21 Prediction, Explanation and Decision-making

• Chapter22 A Unified map of Data Science