Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong.
Mathematical Foundations.
Linear Algebra.
Systems of Linear Equations.
a_ij units of resource R_i.
Classification, specifically in the context of support vector machines.
Cholesky Decomposition.
Data, models, and learning.
Christfried Webers.
As the intersection of two lines.
Chapter 6.
Practitioners may become unaware of design decisions and the limits of machine learning algorithms.
A guidebook to the vast mathematical literature that forms the foundations of modern machine learning.
Undergraduate university students, evening learners, and online machine learning course participants.
Linear algebra.
Eigenvalues and Eigenvectors.
Programming tutorials using Jupyter notebooks.
To democratize education and learning.
Singular Value Decomposition.
Data, a model, and learning.
Parameswaran Raman and anonymous reviewers organized by Cambridge University Press.
Partial derivative of f with respect to x.
It may indicate that the model has memorized the data rather than generalized.
To find functions that map inputs to corresponding observed function values.
Polynomials are instances of vectors because they can be added together and multiplied by a scalar.
Mathematics for Machine Learning.
Linear Regression.
Problem Setting for Dimensionality Reduction with Principal Component Analysis.
The concept of a gradient.
To determine how many units x_j of product N_j should be produced given resource constraints.
Re-distribution, re-sale, or use in derivative works.
GitHub.
To express some sort of uncertainty and quantify the confidence about the value of the prediction at a particular test data point.
Eigendecomposition and Diagonalization.
EM Algorithm for Density Estimation with Gaussian Mixture Models.
Differentiation of Univariate Functions.
The solution set is empty.
A process for generating data that captures relevant aspects of the real data-generating process.
The gap between high school mathematics and the mathematics level required for standard machine learning textbooks.
To express gratitude to those who contributed feedback and suggestions on early drafts.
Exercises that can be done mostly by pen and paper.
To distill human knowledge and reasoning into a form suitable for constructing machines and engineering automated systems.
Designing algorithms that automatically extract valuable information from data.
Classification, Density Estimation, Regression, Dimensionality Reduction.
a_11 x_1 + · · · + a_1n x_n = b_1, ..., a_m1 x_1 + · · · + a_mn x_n = b_m.
Suggestions for improvements, bug reports, and relevant literature.
In classification, the labels are integers, while in regression, the labels are real-valued.
Mathematics for Machine Learning.
A system that makes predictions based on input data, referred to as predictors.
Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong.
The adaptation of internal parameters of a predictor to perform well on future unseen input data.
A line on the x1-x2 plane.
They provide tools for formulating and solving many problems.
2020.
Machine learning serves as an obvious and direct motivation for people to learn mathematics.
No solutions, exactly one solution, or infinitely many solutions.
Vectors x and y are orthogonal.
At https://mml-book.com.
Chapter 5.
Chapter 3 (Analytic Geometry), Chapter 5 (Vector Calculus), Chapter 10 (Dimensionality Reduction), and Chapter 9 (Linear Regression).
Dinesh Singh Negi.
Analytic Geometry.
Bottom-up and top-down approaches.
Audio signals can be added together and scaled, making them a type of vector.
To make it easier to read other machine learning textbooks by providing the necessary mathematical background.
Determinant and Trace.
It results in a scaled vector λa in R^n.
A vector space is the set of vectors that can be formed by adding and scaling a small set of vectors.
Image of linear mapping Φ.
Readers should have seen derivatives, integrals, and geometric vectors in two or three dimensions.
The intersection of the lines defined by the equations.
1. An array of numbers (computer science view), 2. An arrow with direction and magnitude (physics view), 3. An object that obeys addition and scaling (mathematical view).
To prepare students who may not have a strong background in mathematics and statistics.
Kernels in Support Vector Machines.
They benefit from open-source software and tools without worrying about the specifics of pipelines.
A plane, a line, a point, or empty (no common intersection).
Principal component analysis.
Automatically finding patterns and structure in data by optimizing model parameters.
Gaussian Mixture Model.
It means that one equation can be omitted because it does not provide new information.
Linear algebra.
Vectors.
⟨ x , y ⟩.
As vectors, having been converted into a numerical representation suitable for computer programs.
Programming languages, data analysis tools, large-scale computation, mathematics, and statistics.
It focuses on the mathematical concepts behind the models rather than methods and models themselves.
The analogy of music, with roles such as Astute Listener, Experienced Artist, and Fledgling Composer.
As vectors and matrices.
Optimizing some parameters of the model with respect to a utility function that evaluates prediction accuracy on training data.
Its performance on a given task improves after the data is taken into account.
Principal Component Analysis.
To develop new methods and extend existing algorithms, similar to music composers.
A triplet of numbers, such as a = [1, 2, 3].
The result is another vector c in R^n, calculated component-wise.
It allows for the generation of a family of solutions based on the value of a.
Most algorithms in linear algebra are formulated in R^n, and it corresponds to arrays of real numbers on a computer.
Inverse of a matrix.
tr(A).
Yes, it is free to view and download for personal use only.
Orthogonal complement of vector space V.
To perform well on unseen data.
Construction of a Probability Space.
A plane in three-dimensional space.
It satisfies the system of equations given in the form of (2.3).
To narrow or close the skills gap in understanding basic machine learning concepts.
It connects practical questions in machine learning with fundamental choices in the mathematical model.
Matrix Decompositions.
Machine learning algorithms and methodologies, assuming competence in mathematics and statistics.
Gaussian distribution with mean μ and covariance Σ.
Similarity and distances between vectors.
Regression, dimensionality reduction, density estimation, and classification.
Existential quantifier: there exists x.
Determinant of matrix A.
Maximus McCann, Mengyan Zhang, Michael Bennett, Michael Pedersen, Minjeong Shin, Mohammad Malekzadeh, Naveen Kumar, Nico Montali, Oscar Armas, Patrick Henriksen, Patrick Wieschollek, Pattarawat Chormai, Paul Kelly, Petros Christodoulou, Piotr Januszewski, Pranav Subramani, Quyu Kong, Ragib Zaman, Rui Zhang, Ryan-Rhys Griffiths, Salomon Kabongo, Samuel Ogunmola, Sandeep Mavadia, Sarvesh Nikumbh, Sebastian Raschka, Senanayak Sesh Kumar Karri, Seung-Heon Baek, Shahbaz Chaudhary, Shakir Mohamed, Shawn Berry, Sheikh Abdul Raheem Ali, Sheng Xue, Sridhar Thiagarajan, Syed Nouman Hasany, Szymon Brych, Thomas B¨ uhler, Timur Sharapov, Tom Melamed, Vincent Adam, Vincent Dutordoir, Vu Minh, Wasim Aftab, Wen Zhi, Wojciech Stokowiec, Xiaonan Chong, Xiaowei Zhang, Yazhou Hao, Yicheng Luo, Young Lee, Yu Lu, Yun Cheng, Yuxiao Huang, Zac Cranko, Zijian Cao, Zoe Nolan.
Classification with Support Vector Machines.
Data, models, and parameter estimation.
Knowledge of matrix operations.
Lauren Cowles.
The value x* that minimizes f (note: arg min returns a set of values).
Empirical Risk Minimization.
X is conditionally independent of Y given Z.
It helps uncover relationships between different tasks and develop new methods.
Scalars.
Transpose of a vector or matrix.
Absolute value or determinant, depending on context.
Because machine learning is inherently data-driven.
https://mml-book.com.
Gradient.
To formalize the idea of similarity between vectors.
Optimization Using Gradient Descent.
A compact notation that collects coefficients into vectors and matrices.
Gaussian mixture models.
To provide feedback and practice.
Knowledge may be built on shaky foundations.
Yes, they are loosely coupled and can be read in any order.
dim.
x_1, x_2, ..., x_n.
To extract valuable patterns from data without much domain-specific expertise.
To estimate parameters.
Skilled practitioners who can integrate tools and libraries into analysis pipelines.
It allows for an intuitive interpretation of data and more efficient learning.
(1, 1, 1).
Readers can rely on previously learned concepts.
A variable that can take any value, allowing for multiple solutions.
Principal component analysis.
a is proportional to b.
Eigenvalue or Lagrange multiplier.
Individuals who should have some understanding of the underlying principles of machine learning.
Bayes’ Theorem.
It plays a crucial role in solving problems such as linear regression and dimensionality reduction.
x_1 + x_2 + x_3 = 3, x_1 - x_2 + 2x_3 = 2, 2x_1 + 3x_3 = 1.
In the computer science department.
Identifying the true underlying signal from noisy observations.
Maximum Likelihood as Orthogonal Projection.
Maximum a posteriori.
It is split into two parts: foundational concepts and applications.
Dot product of x and y.
Academic mathematical style, which aims for precision about the concepts behind machine learning.
Angles and Orthogonality.
To find a probability distribution that describes a given dataset.
A foundation for thinking about certification and risk management of machine learning systems.
Foundational concepts may not be interesting and can be quickly forgotten.
It refers to the set of all vectors that can result from starting with a small set of vectors and performing operations like addition and scaling.
Norm; typically Euclidean unless specified.
Climbing a hill to reach its peak, where the peak corresponds to a maximum of some utility function.
Covariance between x and y.
They help understand fundamental principles, create new solutions, and debug existing approaches.
Similar vectors are predicted to have similar outputs by the machine learning algorithm.
Readers understand why they need to learn a particular concept.
Matrices.
Universal quantifier: for all x.
Kernel (null space) of a linear mapping Φ.
