Mathematic For Machine Learning
What Level of Maths Do You Need?
The main question when trying to understand an interdisciplinary field such as Machine Learning is the amount of maths necessary and the level of maths needed to understand these techniques. The answer to this question is multidimensional and depends on the level and interest of the individual. Research in mathematical formulations and theoretical advancement of Machine Learning is ongoing and some researchers are working on more advance techniques. I'll state what I believe to be the minimum level of mathematics needed to be a Machine Learning Scientist/Engineer and the importance of each mathematical concept.
Why To Worry About The Maths?
There are many reasons why the mathematics of Machine Learning is important and I'll highlight some of them below:
1. Selecting the right algorithm which includes giving considerations to accuracy, training time, model complexity, number of parameters and number of features. learn machine learning online for more details.
2. Choosing parameter settings and validation strategies.
3. Identifying underfitting and overfitting by understanding the Bias-Variance tradeoff.
4. Estimating the right confidence interval and uncertainty.
1. Linear Algebra: A colleague, 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.
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. machine learning online training online training India will helps you to learn more effectively.
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.
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.
“Mathematics for Machine Learning”, will uncover itself keeping the beginners in the area of machine learning in mind.
The book, that is meant to be for beginners mainly aims at motivating people to learn mathematical concepts and therefore does not intend to cover any advanced machine learning techniques since there already are a number of books doing the same. for more details go through machine learning online course
The aim here is to provide the readers with all the necessary mathematical skills so that they can efficiently read those other books.
What all areas will the book cover?
The book is to be split into two parts:
Mathematical Foundations:
- Introduction and Motivation
- Linear Algebra
- Analytic Geometry
- Matrix Decompositions
- Vector Calculus
- Probability and Distribution
- Continuous Optimization
Example Machine Learning Algorithms That Use The Mathematical Foundations:
- When Models Meet Data
- Linear Regression
- Dimensionality Reduction with Principal Component Analysis
- Density Estimation with Gaussian Mixture Models
- Classification with Support Vector Machines