Mathematics for machine learning / Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong.

Format:

Book

Author/Creator:

Deisenroth, Marc Peter, author.

Faisal, A. Aldo, author.

Ong, Cheng Soon, author.

Language:

English

Subjects (All):

Machine learning--Mathematics.

Machine learning.

Mathematics.

Physical Description:

xvii, 371 pages : illustrations (some color) ; 26 cm

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.

Summary:

"The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability, and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models, and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts"-- Provided by publisher.

Contents:

Machine generated contents note: pt. I Mathematical Foundations

1. Introduction and Motivation

1.1. Finding Words for Intuitions

1.2. Two Ways to Read This Book

1.3. Exercises and Feedback

2. Linear Algebra

2.1. Systems of Linear Equations

2.2. Matrices

2.3. Solving Systems of Linear Equations

2.4. Vector Spaces

2.5. Linear Independence

2.6. Basis and Rank

2.7. Linear Mappings

2.8. Affine Spaces

2.9. Further Reading

Exercises

3. Analytic Geometry

3.1. Norms

3.2. Inner Products

3.3. Lengths and Distances

3.4. Angles and Orthogonality

3.5. Orthonormal Basis

3.6. Orthogonal Complement

3.7. Inner Product of Functions

3.8. Orthogonal Projections

3.9. Rotations

3.10. Further Reading

4. Matrix Decompositions

4.1. Determinant and Trace

4.2. Eigenvalues and Eigenvectors

4.3. Cholesky Decomposition

4.4. Eigendecomposition and Diagonalization

4.5. Singular Value Decomposition

4.6. Matrix Approximation

4.7. Matrix Phylogeny

4.8. Further Reading

5. Vector Calculus

5.1. Differentiation of Univariate Functions

5.2. Partial Differentiation and Gradients

5.3. Gradients of Vector-Valued Functions

5.4. Gradients of Matrices

5.5. Useful Identities for Computing Gradients

5.6. Backpropagation and Automatic Differentiation

5.7. Higher-Order Derivatives

5.8. Linearization and Multivariate Taylor Series

5.9. Further Reading

6. Probability and Distributions

6.1. Construction of a Probability Space

6.2. Discrete and Continuous Probabilities

6.3. Sum Rule, Product Rule, and Bayes' Theorem

6.4. Summary Statistics and Independence

6.5. Gaussian Distribution

6.6. Conjugacy and the Exponential Family

6.7. Change of Variables/Inverse Transform

6.8. Further Reading

7. Continuous Optimization

7.1. Optimization Using Gradient Descent

7.2. Constrained Optimization and Lagrange Multipliers

7.3. Convex Optimization

7.4. Further Reading

pt. II Central Machine Learning Problems

8. When Models Meet Data

8.1. Data, Models, and Learning

8.2. Empirical Risk Minimization

8.3. Parameter Estimation

8.4. Probabilistic Modeling and Inference

8.5. Directed Graphical Models

8.6. Model Selection

9. Linear Regression

9.1. Problem Formulation

9.2. Parameter Estimation

9.3. Bayesian Linear Regression

9.4. Maximum Likelihood as Orthogonal Projection

9.5. Further Reading

10. Dimensionality Reduction with Principal Component Analysis

10.1. Problem Setting

10.2. Maximum Variance Perspective

10.3. Projection Perspective

10.4. Eigenvector Computation and Low-Rank Approximations

10.5. PC A in High Dimensions

10.6. Key Steps of PC A in Practice

10.7. Latent Variable Perspective

10.8. Further Reading

11. Density Estimation with Gaussian Mixture Models

11.1. Gaussian Mixture Model

11.2. Parameter Learning via Maximum Likelihood

11.3. EM Algorithm

11.4. Latent-Variable Perspective

11.5. Further Reading

12. Classification with Support Vector Machines

12.1. Separating Hyperplanes

12.2. Primal Support Vector Machine

12.3. Dual Support Vector Machine

12.4. Kernels

12.5. Numerical Solution

12.6. Further Reading.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Deisenroth, Marc Peter. Mathematics for machine learning.

ISBN:

9781108470049

1108470041

9781108455145

110845514X

OCLC:

1104219401

Publisher Number:

99987423337