Chap1. Introduction & Motivation

  • We believe that the mathematical foundations of machine learning are important in order to understand fundamental principles upon which more complicated machine learning systems are built.

1.1 Finding Words for Intuitions

  • machine learning algorithm (predictor) : a system that makes predictions based on input data

  • training : a system that adapts some internal parameters of the predictor so that it performs well on future unseen input data

  • data as vectors : an array of numbers, an arrow with a direction and magnitude, an object that obeys addition and scaling

  • model : a process for generating data

→ a simplified versions of the real (unknown) data-generating process, capturing aspects that are relevant for modeling the data and extracting hidden patterns from it

→ good model can be used to predict what would happen in the real world without performing real-world experiments

  • Learning : Training the model means to use the data available to optimize some parameters of the model with respect to a utility function that evaluates how well the model predicts the training data.

1.2 Two Ways to Read the Book

  • Part 1. Mathematics : linear algebra, analytic geometry, matrix decomposition, probability theory, vector calculus, optimization

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  • Part 2. Machine Learning : linear regression, dimensionality reduction, density estimation, classification