Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics

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Data always comes in raw and ugly. The initial exploration tells you what’s missing, how the data is distributed, and what’s the best way to clean it to meet the end goal. Chapter 4: Linear Algebra Linear algebra is a fundamental topic for data science, and this chapter covers it nicely. It starts with the basics of vectors and matrices, making it accessible to those new to the subject. In linear algebra, the information concerning a linear transformation can be represented as a matrix. Moreover, every linear transformation can be expressed as a matrix. Figure 2: Illustration of the entropy as the weighted sum of the Shannon information. (Image by author) Linear functions change at a constant rate, and that in turn, makes the rate of change of a linear function a constant. This and other related insights into linear and other mathematical functions can be quantified using calculus. Through this course, you'll examine the steps involved in applying the differentiation operation to study a moving particle. You'll then understand how the partial derivative of a function that depends on multiple independent variables is computed with respect to one of those independent variables by holding all other independent variables constant. This course will also allow you to investigate how partial derivatives play a crucial role in the training phase of building a machine learning (ML) model. Upon completion of this course, you will be able to compute the partial derivative of a function that depends on multiple independent variables and better understand the training process of a machine learning model.

Through the course of this book, you'll learn how to use mathematical notation to understand new developments in the field, communicate with your peers, and solve problems in mathematical form. You'll also understand what's under the hood of the algorithms you're using. At the start of this year, I published a mind map on the Data Science learning roadmap (shown below). Many people found the roadmap useful, my article got translated into different languages, and a large number of folks thanked me for publishing it. What I find surreal is asking questions, especially the uncomfortable ones that challenge popular assumptions, really took me for a ride. It frustrated some folks, but I got relieved gratitude from others simply by cutting through narratives and seeking grounded information. I now teach at University of Southern California advising government, military, and aerospace agencies on artificial intelligence system safety… simply by asking questions. I now wrote a book on a subject I’d never think I was qualified to write, simply by asking questions. Bottom line: a resource that covers just enough applied math or statistics or programming to get started with data science or ML is missing. Wiplane Academy — wiplane.comThe word vector can refer to multiple concepts. Let’s learn more about geometric and coordinate vectors. I get this question in some flavor a lot. It’s easy to feel like a hammer looking for nails, which is pretty common for those who study machine learning. You can always create your own self-study projects, on public datasets or toy datasets you create (which I like doing as controlled experiments). But if you have a job that has you doing less glamorous tasks with data and isn’t providing you opportunities to use machine learning, try to take a problem-first approach. What problems does your employer have? And once you’ve identified that, try not to bludgeon the problem with machine learning but rather look at what other solutions are out there: linear programming, optimization, heuristics, metaheuristics… pairing the right solution to a problem is an invaluable skill. I think half the value of knowing machine learning is just simply recognizing what it doesn’t do, and confused employers can benefit from that kind of knowledge expert.

ML is inherently data-driven. Data is at the heart of machine learning. We can think of data as vectors — an object that adheres to arithmetic rules. This leads us to understand how rules of linear algebra operate over arrays of data. You'll Use Calculus to Train ML Models Let's go through these essential skills in a bit more detail to see what you need to learn to get into Data Science and Machine Learning. Essential Programming Skills for Data Science and Machine Learning Here is what Google recommends that you do before taking an ML course: Google's recommended Python skills for Data Science and Machine Learning Google's recommended Math and Statistics skills for ML and DS ( Source) Let’s take an example to see what a bit describes. Erica sends you a message containing the result of three coin flips, encoding ‘heads’ as 0 and ‘tails’ as 1. There are 8 possible sequences, such as 001, 101, etc. When you receive a message of one bit, it divides your uncertainty by a factor of 2. For instance, if the first bit tells you that the first roll was ‘heads’, the remaining possible sequences are 000, 001, 010, and 011. There are only 4 possible sequences instead of 8. Similarly, receiving a message of two bits will divide your uncertainty by a factor of 2²; a message of three bits, by a factor of 2³, and so on.Chapter 1: Basic Mathematics and Calculus The book starts with an introduction to basic mathematics and calculus. This chapter serves as a refresher for those new to mathematical concepts. It covers topics like limits and derivatives, making it accessible for beginners while providing a valuable review for others. The use of coding exercises helps reinforce understanding. Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning So, I decided to give in and do it all myself. I have spent the last 3 months developing a curriculum that will provide a solid foundation for your career as a Each of these transformed probabilities is weighted by the corresponding raw probability. If an outcome occurs frequently, it will give more weight into the entropy of the distribution. This means that a low probability (like 0.1 in Figure 2) gives a large amount of information (3.32 bits) but has less influence on the final result. A larger probability (like 0.4 in Figure 2) is associated with less information (1.32 bits as shown in Figure 2) but has more weight.