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markkm / math-for-ml

Licence: MIT license
Mathematical preliminaries for machine learning

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Mathematical Preliminaries for Machine Learning

This repository contains notes on the mathematical preliminaries for machine learning, originally conceived as supplementary notes to the Fall 2017 incarnation of Carnegie Mellon University's 10-715: Advanced Introduction to Machine Learning.

Contents

  1. Functions
  2. Metric Spaces
  • Basic Definitions
  • Limit and Continuity
  • Complete Metric Spaces
  • Compact Metric Spaces
  1. Normed Linear Spaces
  • Vector Spaces
  • Norm
  • Euclidean Space
  • Sequence Spaces
  • Lebesgue Spaces
  • Uniform Norm
  • Operator Norm
  • Matrix Operator Norm
  • Frobenius Norm
  • Norms on a Finite-Dimensional Normed Linear Space
  1. Inner Product Spaces
  • Definitions and Examples
  • Orthogonality
  • Unitary Classification of Hilbert Spaces
  • Hilbert Spaces with a Countable Orthonormal Basis
  • Finite-Dimensional Hilbert Spaces
  1. Interlude: Basic Numerical Analysis
  • NumPy
  • Floating-Point Arithmetic
  1. Singular Value Decomposition
  • Invertibility of Linear Operators and Matrices
  • Singular Values

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Licenses

Unless otherwise specified, the licensing details for this repository are as follows.

The notes are distributed with CC-by-4.0. The homework problems, taken from the 10-715 course page, are copyrighted by Barnabas Poczos. The written homework solutions are distributed with CC-by-4.0. Programming homework solutions are distributed with the MIT License.

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