来源：LinkedIn
原文：https://www.linkedin.com/pulse/mathematics-machine-learning-wale-akinfaderin

机器学习需要哪些数学知识的问题在QQ群内高频出现，这个问题没有标准答案，取决于每个人本身的能力和面对的问题。但无论分歧多大，大家貌似一致首推Linear Algebra，Strang老人家讲得太好可能也是原因之一。

这篇文章的作者甚至把机器学习所需数学量化为5个维度的饼图了，不妨看看。

摘录了作者部分结论：

1. Linear Algebra: A colleague, Skyler Speakman, recently said that “Linear Algebra is the mathematics of the 21st century” and I totally agree with the statement. In ML, Linear Algebra comes up everywhere. Topics such as Principal Component Analysis (PCA), Singular Value Decomposition (SVD), Eigendecomposition of a matrix, LU Decomposition, QR Decomposition/Factorization, Symmetric Matrices, Orthogonalization & Orthonormalization, Matrix Operations, Projections, Eigenvalues & Eigenvectors, Vector Spaces and Norms are needed for understanding the optimization methods used for machine learning. The amazing thing about Linear Algebra is that there are so many online resources. I have always said that the traditional classroom is dying because of the vast amount of resources available on the internet. My favorite Linear Algebra course is the one offered by MIT Courseware (Prof. Gilbert Strang).

2. Probability Theory and Statistics: Machine Learning and Statistics aren’t very different fields. Actually, someone recently defined Machine Learning as ‘doing statistics on a Mac’. Some of the fundamental Statistical and Probability Theory needed for ML are Combinatorics, Probability Rules & Axioms, Bayes’ Theorem, Random Variables, Variance and Expectation, Conditional and Joint Distributions, Standard Distributions (Bernoulli, Binomial, Multinomial, Uniform and Gaussian), Moment Generating Functions, Maximum Likelihood Estimation (MLE), Prior and Posterior, Maximum a Posteriori Estimation (MAP) and Sampling Methods.

3. Multivariate Calculus: Some of the necessary topics include Differential and Integral Calculus, Partial Derivatives, Vector-Values Functions, Directional Gradient, Hessian, Jacobian, Laplacian and Lagragian Distribution.

4. Algorithms and Complex Optimizations: This is important for understanding the computational efficiency and scalability of our Machine Learning Algorithm and for exploiting sparsity in our datasets. Knowledge of data structures (Binary Trees, Hashing, Heap, Stack etc), Dynamic Programming, Randomized & Sublinear Algorithm, Graphs, Gradient/Stochastic Descents and Primal-Dual methods are needed.

5. Others: This comprises of other Math topics not covered in the four major areas described above. They include Real and Complex Analysis (Sets and Sequences, Topology, Metric Spaces, Single-Valued and Continuous Functions, Limits), Information Theory (Entropy, Information Gain), Function Spaces and Manifolds.

Some online MOOCs and materials for studying some of the Mathematics topics needed for Machine Learning are:

• Khan Academy’s Linear Algebra, Probability & Statistics, Multivariable Calculus and Optimization.
• Coding the Matrix: Linear Algebra through Computer Science Applications by Philip Klein, Brown University.
• Linear Algebra – Foundations to Frontiers by Robert van de Geijn, University of Texas.
• Applications of Linear Algebra, Part 1 and Part 2. A newer course by Tim Chartier, Davidson College.
• Joseph Blitzstein – Harvard Stat 110 lectures
• Larry Wasserman’s book – All of statistics: A Concise Course in Statistical Inference .
• Boyd and Vandenberghe’s course on Convex optimisation from Stanford.
• Linear Algebra – Foundations to Frontiers on edX.
• Udacity’s Introduction to Statistics.