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Mathematics of Machine Learning

Mathematics of Machine Learning

By : Tivadar Danka
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Mathematics of Machine Learning

Mathematics of Machine Learning

By: Tivadar Danka

Overview of this book

Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you’ll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts. PhD mathematician turned ML engineer Tivadar Danka—known for his intuitive teaching style that has attracted 100k+ followers—guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you’ll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors. By the end of this book, you’ll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements.
Table of Contents (36 chapters)
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2
Part 1: Linear Algebra
11
References
12
Part 2: Calculus
19
References
20
Part 3: Multivariable Calculus
24
References
25
Part 4: Probability Theory
29
References
30
Part 5: Appendix
31
Other Books You May Enjoy
32
Index

3.4 Problems

Problem 1. Implement the mean squared error

 ∑n MSE (x,y) = 1- (xi − yi)2, x, y ∈ ℝn n i=1

both with and without using NumPy functions and methods. (The vectors x and y should be represented by NumPy arrays in both cases.)

Problem 2. Compare the performances of the built-in maximum function max and NumPy’s np.max using timeit.timeit, like we did above. Try running a different number of experiments and changing the array sizes to figure out the breakeven point between the two performances.

Problem 3. Instead of implementing the general p-norm as we did earlier in this chapter in Section 3.1.1 , we can change things around to obtain the version below.

def p_norm(x: np.ndarray, p: float): 
    if p  1: 
        return (np.sum(np.abs(x)**p))**(1/p) 
    elif np.isinf(p): 
        return np.max(np.abs(x)) 
    else: 
        raise ValueError("/span>p must be a float larger or equal than 1.0 or inf."

However, this doesn’t work for p = . What is the problem with it?

Problem...

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