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Mathematics of Machine Learning : Master Linear Algebra, Calculus, and Probability for Machine Learning.

O'Reilly Online Learning: Academic/Public Library Edition Available online

Format:: Book
Author/Creator:: Danka, Tivadar.
Contributor:: Valdarrama, Santiago.
Language:: English
Physical Description:: 1 online resource (0 pages)
Edition:: 1st ed.
Place of Publication:: Birmingham : Packt Publishing, Limited, 2025.
Summary:: Build a solid foundation in the core math behind machine learning algorithms with this comprehensive guide to linear algebra, calculus, and probability, explained through practical Python examplesPurchase of the print or Kindle book includes a free PDF eBook Key Features Master linear algebra, calculus, and probability theory for ML Bridge.
Contents:: Cover; Title Page; Copyright Page; Foreword; Contributors; Table of Contents; Introduction; Part 1: Linear Algebra; Chapter 1: Vectors and Vector Spaces; What is a vector space?; Examples of vector spaces; The basis; Linear combinations and independence; Spans of vector sets; Bases, the minimal generating sets; Finite dimensional vector spaces; Why are bases so important?; The existence of bases; Subspaces; Vectors in practice; Tuples; Lists; NumPy arrays; NumPy arrays as vectors; Is NumPy really faster than Python?; Summary; Problems; Chapter 2: The Geometric Structure of Vector Spaces; Norms and distances; Defining distances from norms; Inner products, angles, and lots of reasons to care about them; The generated norm; Orthogonality; The geometric interpretation of inner products; Orthogonal and orthonormal bases; The Gram-Schmidt orthogonalization process; The orthogonal complement; Chapter 3: Linear Algebra in Practice; Vectors in NumPy; Norms, distances, and dot products; Matrices, the workhorses of linear algebra; Manipulating matrices; Matrices as arrays; Matrices in NumPy; Matrix multiplication, revisited; Matrices and data; Chapter 4: Linear Transformations; What is a linear transformation?; Linear transformations and matrices; Matrix operations revisited; Inverting linear transformations; The kernel and the image; Change of basis; The transformation matrix; Linear transformations in the Euclidean plane; Stretching; Rotations; Shearing; Reflection; Orthogonal projection; Determinants, or how linear transformations affect volume; How linear transformations scale the area; The multi-linearity of determinants.; Fundamental properties of the determinants; Chapter 5: Matrices and Equations; Linear equations; Gaussian elimination; Gaussian elimination by hand; When can we perform Gaussian elimination?; The time complexity of Gaussian elimination; When can a system of linear equations be solved?; Inverting matrices; The LU decomposition; Implementing the LU decomposition; Inverting a matrix, for real; How to actually invert matrices; Determinants in practice; The lesser of two evils; The recursive way; How to actually compute determinants; Chapter 6: Eigenvalues and Eigenvectors; Eigenvalues of matrices; Finding eigenvalue-eigenvector pairs; The characteristic polynomial; Finding eigenvectors; Eigenvectors, eigenspaces, and their bases; Chapter 7: Matrix Factorizations; Special transformations; The adjoint transformation; Orthogonal transformations; Self-adjoint transformations and the spectral decomposition theorem; The singular value decomposition; Orthogonal projections; Properties of orthogonal projections; Orthogonal projections are the optimal projections; Computing eigenvalues; Power iteration for calculating the eigenvectors of real symmetric matrices; Power iteration in practice; Power iteration for the rest of the eigenvectors; The QR algorithm; The QR decomposition; Iterating the QR decomposition; Chapter 8: Matrices and Graphs; The directed graph of a nonnegative matrix; Benefits of the graph representation; The connectivity of graphs; The Frobenius normal form; Permutation matrices; Directed graphs and their strongly connected components; Putting graphs and permutation matrices together; References; Part 2: Calculus; Chapter 9: Functions.; Functions in theory; The mathematical definition of a function; Domain and image; Operations with functions; Mental models of functions; Functions in practice; Operations on functions; Functions as callable objects; Function base class; Composition in the object-oriented way; Chapter 10: Numbers, Sequences, and Series; Numbers; Natural numbers and integers; Rational numbers; Real numbers; Sequences; Convergence; Properties of convergence; Famous convergent sequences; The role of convergence in machine learning; Divergent sequences; The big and small O notation; Real numbers are sequences; Series; Convergent and divergent series; Properties of series; Conditional and absolute convergence; Revisiting rearrangements; Convergence tests for series; The Cauchy product of series; Chapter 11: Topology, Limits, and Continuity; Topology; Open and closed sets; Distance and topology; Sets and sequences; Bounded sets; Compact sets; Limits; Equivalent definitions of limits; Continuity; Properties of continuous functions; Chapter 12: Differentiation; Differentiation in theory; Equivalent forms of differentiation; Differentiation and continuity; Differentiation in practice; Rules of differentiation; Derivatives of elementary functions; Higher-order derivatives; Extending the Function base class; The derivative of compositions; Numerical differentiation; Chapter 13: Optimization; Minima, maxima, and derivatives; Local minima and maxima; Characterization of optima with higher order derivatives; Mean value theorems; The basics of gradient descent; Derivatives, revisited; The gradient descent algorithm; Implementing gradient descent; Drawbacks and caveats.; Why does gradient descent work?; Differential equations 101; The (slightly more) general form of ODEs; A geometric interpretation of differential equations; A continuous version of gradient ascent; Gradient ascent as a discretized differential equation; Gradient ascent in action; Chapter 14: Integration; Integration in theory; Partitions and their refinements; The Riemann integral; Integration as the inverse of differentiation; Integration in practice; Integrals and operations; Integration by parts; Integration by substitution; Numerical integration; Implementing the trapezoidal rule; Part 3: Multivariable Calculus; Chapter 15: Multivariable Functions; What is a multivariable function?; Linear functions in multiple variables; The curse of dimensionality; Chapter 16: Derivatives and Gradients; Partial and total derivatives; The gradient; Higher order partial derivatives; The total derivative; Directional derivatives; Properties of the gradient; Derivatives of vector-valued functions; The derivatives of curves; The Jacobian and Hessian matrices; The total derivative for vector-vector functions; Derivatives and function operations; Chapter 17: Optimization in Multiple Variables; Multivariable functions in code; Minima and maxima, revisited; Gradient descent in its full form; Part 4: Probability Theory; Chapter 18: What is Probability?; The language of thinking; Thinking in absolutes; Thinking in probabilities; The axioms of probability; Event spaces and -algebras; Describing -algebras; -algebras over real numbers; Probability measures; Fundamental properties of probability; Probability spaces on Rn.; How to interpret probability; Conditional probability; Independence; The law of total probability revisited; The Bayes' theorem; The Bayesian interpretation of probability; The probabilistic inference process; The Monty Hall paradox; Chapter 19: Random Variables and Distributions; Random variables; Discrete random variables; Real-valued random variables; Random variables in general; Behind the definition of random variables; Independence of random variables; Discrete distributions; The Bernoulli distribution; The binomial distribution; The geometric distribution; The uniform distribution; The single-point distribution; Law of total probability, revisited once more; Sums of discrete random variables; Real-valued distributions; The cumulative distribution function; Properties of the distribution function; Cumulative distribution functions for discrete random variables; The exponential distribution; The normal distribution; Density functions; Density functions in practice; Classification of real-valued random variables; Chapter 20: The Expected Value; The expected value in poker; Continuous random variables; Properties of the expected value; Variance; Covariance and correlation; The law of large numbers; Tossing coins…; …rolling dice…; …and all the rest; The weak law of large numbers; The strong law of large numbers; Information theory; Guess the number; Guess the number 2: Electric Boogaloo; Information and entropy; Differential entropy; The Maximum Likelihood Estimation; Probabilistic modeling 101; Modeling heights; The general method; The German tank problem; Part 5: Appendix; Appendix A: It's Just Logic.; Mathematical logic 101.
Notes:: Description based on publisher supplied metadata and other sources.
ISBN:: 1-83702-786-2
OCLC:: 1521455536

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Mathematics of Machine Learning : Master Linear Algebra, Calculus, and Probability for Machine Learning.

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